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Fundamentals of Trigonometry - 9th edition
Summary: Taking a unit-circle first approach, this proven book helps students learn, understand, and appreciate trigonometry without compromising mathematical integrity. The book incorporates the use of the graphing calculator (although use of the graphing calculator is not required). Numerous application problems are used throughout to help motivate students toward success in learning trigonometry.
Step-by-step ...show moreexplanations accompany the examples and help students better understand the material.
Graphics and scientific-calculator exercises are integrated within the text so students can apply the latest technology.
The book features more than 1,000 pieces of mathematically precise artwork and figures.
This edition places a greater emphasis on technology and graphing calculators, set up in a flexible format so professors can use as much or as little as desired.
The appendix contains problem-solving exercises using the TI-82/83.
Chapter one has been reworked as a stand-alone, optional review chapter.
Expanded discussion exercises. New "Discussion Exercises" have been added at the end of each chapter to promote further exploration of concepts and group work.
Increased number of modeling applications.
Color is used pedagogically to clearly distinguish parts of figures and includes matching, color-coded labels.
New discussion exercises at the end of each chapter to promote further exploration of concepts and group work.
Many engaging new exercises require students to estimate, approximate, interpret a result, create a model, explore, or find a generalization. Overall, there are an increased number of modeling applications.
The Law of Sines. The Law of Cosines. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. Vectors. The Dot Product. Chapter 4 Review Exercises. Chapter 4 Discussion Exercises.
Shows definite wear, and perhaps considerable marking on inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy!
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Hardcover 9th Edition text. Hardcover. Book is in good condition, worn corners, has little to no writing/highlighting. Used textbooks may have used book stickers and varying degrees of shelf wear.. Sh...show moreips fast. Expedited shipping 2-4 business days; Standard shipping 7-14 business days. Ships from USA! ...show less
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"Learn everything you possibly can from your professors. They are there to help and will prepare you well for whatever you choose to do upon graduation." [more]
--David DeMarchis '93
Computer & Mathematical Sciences Graduate
Under- standing the Fourier Transform
Edward Kramer
Fourier transforms are used for obtaining the frequency spectrum of a signal. For instance, in nuclear magnetic resonance spectroscopy, a molecule's spin in a magnetic field is analyzed to discover its oscillation frequencies and draw conclusions about its chemical consistency. In this work, the basic definitions and elementary mathematical properties of the Fourier integral, used as the main theoretical tool in Fourier transform analysis, were studied, together with some applications of these properties in computing the Fourier integral of some functions perceived as time signals in order to discover their frequency spectra.
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9780486638300Geometry of Complex Numbers (Dover Books on Mathematics)
Since its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of the connections between different branches of geometry. Its focus lies in the intersection of geometry, analysis, and algebra, with the exposition generally taking place on a moderately advanced level. Much emphasis, however, has been given to the careful exposition of details and to the development of an adequate algebraic technique. In three broad chapters, the author clearly and elegantly approaches his subject. The first chapter, Analytic Geometry of Circles, treats such topics as representation of circles by Hermitian matrices, inversion, stereographic projection, and the cross ratio. The second chapter considers in depth the Moebius transformation: its elementary properties, real one-dimensional projectivities, similarity and classification of various kinds, anti-homographies, iteration, and geometrical characterization. The final chapter, Two-Dimensional Non-Euclidean Geometries, discusses subgroups of Moebius transformations, the geometry of a transformation group, hyperbolic geometry, and spherical and elliptic geometry. For this Dover edition, Professor Schwerdtfeger has added four new appendices and a supplementary bibliography. Advanced undergraduates who possess a working knowledge of the algebra of complex numbers and of the elements of analytical geometry and linear algebra will greatly profit from reading this book. It will also prove a stimulating and thought-provoking book to mathematics professors and teachers
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Algebra and Trigonometry with Modeling and Visualization, Books a la Carte Edition
Synopses & Reviews
Publisher Comments:
Gary Rockswold teaches algebra in context, answering the question, Why am I learning this? By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Introduction to Functions and Graphs; Linear Functions and Equations; Quadratic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra For all readers interested in college algebra and trigonometry
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Preston, WA Prealgebra
...Elementary mathematics should prepare students to transition from the concrete thinking of arithmetic to the abstract thinking of algebra and geometry. To do this, teachers should build a solid foundation of number sense and problem solving strategies based on the students' firm grasp of operati...
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The Integral -
Summary: This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introductio...show moren to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics
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Combinatorics Topics, Techniques, Algorithms
9780521457613
ISBN:
0521457610
Pub Date: 1995 Publisher: Cambridge University Press
Summary: A textbook in combinatorics for second-year undergraduate to beginning graduate students. The author stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter. The book is divided into two parts, the second at a higher level and with a wider range than the first. More advanced topics are given as projects, and there are a number of exercise...s, some with solutions given.
Cameron, Peter J. is the author of Combinatorics Topics, Techniques, Algorithms, published 1995 under ISBN 9780521457613 and 0521457610. Four hundred eighty nine Combinatorics Topics, Techniques, Algorithms textbooks are available for sale on ValoreBooks.com, sixty one used from the cheapest price of $40.87, or buy new starting at $80
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every result and explanation, this edition containsAn exciting approach to the history and mathematics of number theory ". . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story." —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes... more... interconnections of the subject to geometry, algebra,... more...
Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten... more...
What is algebra? For some, it is an abstract language of x?s and y?s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall
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This website can be used by teachers or students in utilizing dense information with assesments. This exercise is designed...
see more
This website can be used by teachers or students in utilizing dense information with assesments. This exercise is designed for anyone who wants an introduction or review of the fundamentals of chemistry that will be used in freshman level chemistry classes. The goal of the program is to provide an introduction or a review to incoming freshman chemistry students on the basic mathematical skills that are required to be successful in freshman chemistry. In addition, the materials last year worked to introduce or review basic skills in the use of a calculator.
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Resources
Below are some of the resources that students have at their disposal.
The navigation panel on the left also lists more specific resources that students can take advantage of.
Department Office: The Mathematics Department Office, wonderfully staffed by Ms. Melanie Chamberlin, is located in SCI 361. Her extension is x3148. The office contains information about summer work and research opportunities, actuarial opportunities, and information about graduate studies.
Common room (SCI 362): The department common room is located in SCI 362. Whenever it is not being used for a department event, the common room is available to students for study or discussion. If you need to consult someone on a mathematical idea, the common room is one place to try. This room is also used in the evenings as the Math Help Room.
The Mathematics Computer Laboratory (SCI 257): Outfitted with Macintosh computers, the computer lab is open all day and evening most days, and the computers are available for students to use whenever the lab is not being used for a class. Each of the computers is equipped with Mathematica and Joy of Mathematica, as well as a variety of other software. Both Mathematica and Joy of Mathematica are also available at various sites around campus, including the Science Center Minifocus.
Science Library: The Science Library is a wonderful resource. Explore it for suggested alternative texts, for popular mathematics books, or biographies of famous mathematicians. Check out on their webpage of interesting mathematics sources
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- Bare Bones explanations of theorems - Usually the example problems are trivial - Teaches material out of a proper canonical order
- One definitely should have an adequate professor to back the material presented in this text. I didn't. Just had to grind through the material and absorb it bit by bit on my own.
- You most definitely CAN learn linear algebra from this text, just not very efficiently.
Side Note: I highly suggest watching Gilbert Strang's MIT OpenCourseWare to accompany this course as well as using his text as a supplement.
[...]
19 of 23 people found the following review helpful
1.0 out of 5 starsStudents in my class (including myself) have given up21 May 2012
By Perfectrancenow - Published on Amazon.com
Format:Hardcover
For the student who is proficient in calculus and algebra but is taking linear algebra for the first time, this book is mostly unreadable. Here is my overall summary of the book: heavy on symbol usage, theorems, and proofs, light on examples. Then after reading the section, you get thrown off into the deep end with tons of complicated word problems. You are left with the task of connecting theorems with the applications. If you ask me, this is just plain lazy on the author's part.
My advice: as a punishment to your instructor for picking this book for your class, be in his or her office every single day and ask them to explain all of the problems past number 30 to you. You will get a good laugh when you realize that THEY struggle with them.
6 of 7 people found the following review helpful
1.0 out of 5 starsTERRIBLE DISCONNECT FROM EXAMPLES TO PROBLEMS13 July 2011
By Joseph - Published on Amazon.com
Format:Loose Leaf
Ditto on most of the bad reviews: bad, if not overly simple examples compared to assignments; bad order (studying supspaces before defining vector spaces). Why didn't we choose Strang's book for this class I'll never know. Thankfully there was a great teacher to teach from this terrible text.
2 of 2 people found the following review helpful
1.0 out of 5 starsAuthor or Editor fail? Not sure.23 July 2013
By Kyle Haley - Published on Amazon.com
Format:Loose Leaf|Verified Purchase
I am currently enrolled in a summer semester course for Linear Algebra. It's not a heavy class, nor is it lightweight. We have extensive homework assignments... hence where the reason I hate it comes in.
It actually is not that the book doesn't provide examples for the types of problems it expects you to answer. A student of science and mathematics becomes accustomed to this.
What IS frustrating is that the homework sections are asking you to solve problems where the explanation of how to solve the problem is in a section further along in the chapter. For instance, section 2.1 had many problems related to inverse matrices. There was a very brief (more or less an example story) about inverse matrices earlier in the section, but it provided no theorems. It supplied a more or less example of application. So if you skip ahead to section 2.4, you may be surprised to find it titled "The Inverse of Linear Transformation", which provides detailed examples of matrix inversion and the associated theorems.
The reason I am writing this is review is for those that get stuck with this book. Look in the sections ahead if something seems unfamiliar or if you cannot find enough detailed examples in the current chapter. You will likely find your answers to assist you in answering the questions in a manner that is conducive to Linear Algebra.
12 of 17 people found the following review helpful
5.0 out of 5 starsI really loved this book5 Aug 2011
By dwu - Published on Amazon.com
Format:Hardcover|Verified Purchase
In sincere disagreement with the negative reviews here, I absolutely loved this book. I took a class on linear algebra my freshman year of college that used Otto Bretscher's book, and I read it pretty much from cover to cover. Now, I wasn't a very studious student at the time, so this says a lot about just how well Bretscher presented the subject -- it was so interesting that I just wanted to keep reading. Unlike more advanced textbooks in math, Bretscher's book is rigorous while remaining friendly. I was always assured that I could understand anything in the text after a few tries and a bit of thinking, because enough detail is included to make sure the engaged reader does not get lost. The result is a highly streamlined presentation that makes you really appreciate the beauty of linear algebra, and takes you through some cool theorems, like the Spectral Theorem.
Other reviewers have remarked that the writing is "terse" or complained that examples are "done in symbols". In response to the former complaint, I don't think the explanations are terse at all. Sure, the text might make you think more and work out more things on your own than any math book you've encountered before reading this one, but it's certainly very doable for those who aren't lazy. In fact, in comparison to an often-used math book (though not linear algebra) like Rudin's Principles of Mathematical Analysis, Bretscher's book helps the reader out way more. So much more. The text is just really clear and unintimidating. I can't emphasize this enough.
In response to the complaint about examples, I found the examples to be very accessible, straightforward and illustrative of the concept at hand. They're well-integrated and, yes, they're done in math symbols, but, well, what else could you expect from a math book? Sure, you could try to explain concepts verbally instead, but usually it's just better to be walked through a "symbolic" example and see how the math is really done. After all, as a learner of the subject, you'll have to do it yourself as well.
And the problems are great. They can definitely be solved using knowledge gained from the relevant section in the text, though not all are completely straightforward, as previous unsatisfied reviewers seem to be expecting. I say this with such confidence because I did many of the problems myself without knowing anything about linear algebra that Bretscher's book did not teach me.
Since taking linear algebra, I've had to recall concepts I'd learned and use them in other science and math courses, and to my surprise I still have a good grasp of the important ideas, no doubt due in large part to the fine teaching of the book being reviewed.
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Mathematical Biology is a first year course in the Natural Sciences Tripos. The course is taught by biologists from the Departments of Plant Sciences and Zoology who use mathematics in their research. It is one of two courses in mathematics specially designed for first year biologists.
Mathematical Biology is designed for students who have continued with mathematics during their sixth form (or equivalent) studies, and a certain level of prior knowledge is assumed. For students from England, Wales or Northern Ireland this would most likely have been gained by the study of GCE Mathematics at A Level. Students who have only taken mathematics as far as AS Level would be well advised to carefully consider taking Elementary Mathematics for Biologists.
Experience proves that students with other qualifications can perform very well on this course. In particular students who have studied the International Baccalaureate, Scottish Highers, the German Abitur and other similar qualifications have all performed outstandingly in the past. However students who do not have a thorough grounding in calculus (including differentiation of polynomials and other simple forms such as trigonometric functions; the product and quotient rules; the chain rule; and integration at least as far as integration by substitution and parts) and algebra (including exponentials and logarithms) are unlikely to succeed.
Any student who is concerned about their background should discuss this with their Director of Studies soon after arriving in Cambridge. In borderline cases it is possible that their College will be able to make extra support available (e.g. extra supervisions). Students can also discuss their background with the lecturer and/or practical demonstrators during the first week or two of term. Please note that prior study of statistics is definitely NOT necessary for this course; statistics is less than a quarter of the material you will be learning, and we teach all necessary concepts from scratch.
All biology students must either do one or other of these courses or the mathematics course designed for physical scientists.
Online resources are provided through the CamTools Site. You will automatically be subscribed to this site as part of the NST subject choice procedures but if you join the course after the start of term, send an email to teachco@plantsci.cam.ac.uk requesting that you are added to the course. You will need to use your Raven ID and password to log onto CamTools, which you will also be able to access during the vacation.
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College Math 116 and College Math 117 Study Guide - Algebra 1A - College Math Help and Algebra Help
Algebra 1A Overview
College Math 116 at College is one of the most challenging courses in the Associates degree curriculum. This is a fast paced Algebra class and is the #1 most failed and withdrawn course at College. The guide below will help you find the answers needed to be successful in this class and get you to graduation. Each week is broken down to help you with quiz and appendix problems. MyMathLab problems are not includeded.
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model-fitting problems. Please do at least two of the problems; you pick. In each case, the idea is to argue for the form of the best fit from among a specified set of models (linear, quadratic, cubic, quartic, exponential, and power law). The underlying theory, if you can find one, can help in model...
as
the International System of Units (abbreviated SI ), and the abbreviations sec (instead of s),
gm (instead of g), and nt (instead of N) are also used.
System of units
Length
Mass
Time
Force
cgs system
centimeter (cm)
gram (g)
second (s)
dyne
mks system
meter (m)
kilogram (kg)
second...
known as the International System of Units (abbreviated SI), and the abbreviations sec (instead of s), gm (instead of g), and nt (instead of N) are also used.
System of units cgs system mks system Engineering system
Length centimeter (cm) meter (m) foot (ft)
Mass gram (g) kilogram (kg) slug
Time...
and the key skills you will need We signpost how each chapter links to the syllabus and the study guide We provide lots of exam focus points demonstrating what the examiner will want you to do We emphasise key points in regular fast forward summaries We test your knowledge of what you've studied in quick...
need to do something but we do not know what. Therefore, decision making is a reasoning process which can be rational or irrational, and can be based on explicit assumptions or tacit assumptions.
Common examples include shopping, deciding what to eat, when to sleep, and deciding whom or what to vote...
3
Ways That Algebra Affects Business or Science ………………………………….. 5
How Algebraic Concepts Can Solve Everyday Problems in Life …………………. 6
Ways Algebra Can Solve Everyday Problems in Business or Science ……………. 9
A Surprising Finding About How Algebra Affects...
his and dependent variables?
The independent...
UNDERTAKEN AS A 10-CREDIT OR A 20-CREDIT SUBJECT AT STAGE 2. STUDENTS WHO COMPLETE 10 CREDITS OF STAGE 2 MATHEMATICAL APPLICATIONS WITH A C GRADE OR BETTER WILL MEET THE NUMERACY REQUIREMENT OF THE SACE.
Mathematics is a diverse and growing field of human endeavour. Mathematics makes a unique contribution...
learning as he often refuses to attempt tasks that he perceives as being difficult.
How Joshua's difficulty was identified
To Identify the area in which Joshua has difficulty, a collaboration of documents and aspects were considered including;
1- Joshua's report cards were observed to see how his...
3
Introduction to Linear
Programming
The development of linear programming has been ranked among the most important scientific advances of the mid-20th century, and we must agree with this assessment. Its impact since just 1950 has been extraordinary. Today it is a standard tool that has saved many
...
TLFeBOOK
WHAT READERS ARE SAYIN6
"I wish I had had this book when I needed it most, which was
during my pre-med classes. I t could have also been a great tool for me in a few medical school courses."
Or. Kellie Aosley8 Recent Hedical school &a&ate
"CALCULUS FOR THE UTTERLY CONFUSED has proven...
dual problem from the primal problem.
Linear Programming: The Simplex Method
LEARNING OBJECTIVES
After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3...
QUANTITATIVE DECISION MAKING - AN OVERVIEW
Objectives After studying this unit, you should be able to: • • • • • • • understand the complexity of today's managerial decisions know the meaning of quantitative techniques know the need of using quantitative approach to managerial decisions appreciate the...
MB0048 –Operation Research
Q1. a. Explain how and why Operation Research methods have been valuable in aiding executive decisions.
b. Discuss the usefulness of Operation Research in decision making process and the role of computers in this field.
Ans.
Churchman, Aackoff and Aruoff defined Operations...
If youfeel after two weeks of semester that MATH1131 is too demanding for you, then you should seek advice from the Student Services Office, RC-3090. Students with a Mathematics Extension 2 combined mark above 176 or an Extension 1 combined mark above 145 are encouraged to enrol in MATH1141, which is...
a large number of books meant for the business professionals. It has pioneered the publication of low-cost high-quality affordable texts in India, which are adopted in premier institutions. PHI Learning has publishing partnerships with University Presses of MIT, Harvard, American Management Association...
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Course Activities and Design
This course will be delivered through a combination of lecture and student activities including group and individual problem solving during class. Emphasis is to be given to applications from outside the mathematics classroom. At least 2 hours per week must be set aside for students to work problems in class.
Course Content (Themes, Concepts, Issues and Skills)
Exponents and Polynomials
Arithmetic with Polynomials
Special Products
Polynomials in Several Variables
Negative Exponents and Scientific Notation
Factoring Polynomials
Greatest Common Factor and Grouping
Factoring Trinomials
Factoring Special Forms
General Factoring Strategy
Solving Quadratic Equations by Factoring.
Rational Expressions
Rational Expressions and Simplification
Arithmetic of Rational Expressions
Complex Rational Expressions
Solving Rational Equations
Variation and Other Applications Using Rational Equations
Root and Radicals
Finding Roots
Operations with Radicals
Rationalizing
Radical Equations
Rational Exponents
Quadratic Equations
Solving Quadratic Equations
Quadratic Formula
Imaginary Numbers (In the Context of Solutions)
Graphing Quadratic Equations
Introduction to Functions
Department Notes
Word problems are to be answered using complete sentences and include appropriate units.
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Math Course Takes 'Real Life' Approach to Algebra
Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life."
Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts.
The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback
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Galena Park StatisticsThis can be approached as a discovery project, a computer based visual learning program, a tactile course taught with manipulatives a traditional textbook based approach or a combination of any of these. Algebra 2 expands on the topics covered in algebra 1 by focusing on symbolic reasoning. We study functions, equations, and their relationships.
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Mathematics Course Descriptions
MAT 050 Basic Math Skills
This course is designed to strengthen basic math skills. Topics include properties, rounding, estimating, comparing, converting, and computing whole numbers, fractions, and decimals. Upon completion, students should be able to perform basic computations and solve relevant mathematical problems. A discussion of ratios, rates, proportions, and applications of these topics will be included.
MAT 110
Math Measurement and Literacy
This course provides an activity-based approach that develops measurement skills and mathematical literacy using technology to solve problems for non-math intensive programs. Topics include unit conversions and estimation within a variety of measurement systems; ratio and proportion; basic geometric concepts; financial literacy; and statistics including measures of central tendency, dispersion, and charting of data. Upon completion, students should be able to demonstrate the use of mathematics and technology to solve practical problems, and to analyze and communicate results.
MAT 121 Algebra/Trigonometry
I
This course provides an integrated approach to technology and the skills required to manipulate, display, and interpret mathematical functions and formulas used in problem solving. Topics include the properties of plane and solid geometry, area and volume, and basic proportion applications; simplification, evaluation, and solving of algebraic equations and inequalities and radical functions; complex numbers; right triangle trigonometry; and systems of equations. Upon completion, students will be able to demonstrate the ability to use mathematics and technology for problem-solving, analyzing and communicating results.
MAT 122 Algebra/Trigonometry
II
This course is designed to cover concepts in algebra, function analysis, and trigonometry. Topics include exponential and logarithmic functions, transformations of functions, Law of Sines, Law of Cosines, vectors, and statistics. Upon completion, students should be able to demonstrate the ability to use mathematics and technology for problem-solving, analyzing and communicating results.
MAT 140 Survey of Mathematics
This course provides an introduction in a non-technical setting to selected topics in mathematics. Topics include, but are not limited to, sets, logic, probability, statistics, matrices, mathematical systems, geometry, topology, mathematics of finance, and modeling. Upon completion, students should be able to understand a variety of mathematical applications, think logically, and be able to work collaboratively and independently. This course has been approved to satisfy the Comprehensive Articulation Agreement for the general education core requirement in natural sciences/mathematics.
MAT 140A Survey of Mathematics
This course is a laboratory
for MAT 140. Emphasis is on experiences that enhance
the materials presented in the class. Upon completion, students should
be able to solve problems, apply critical thinking, work in teams, and
communicate effectively. This course has been approved to satisfy the
Comprehensive Articulation Agreement for transferability as a pre-major
and/or elective course requirement.
MAT 143 Quantitative Literacy
This course is designed to engage students in complex and realistic situations involving the mathematical phenomena of quantity, change and relationship, and uncertainty through project- and activity-based assessment. Emphasis is placed on authentic contexts which will introduce the concepts of numeracy, proportional reasoning, dimensional analysis, rates of growth, personal finance, consumer statistics, practical probabilities, and mathematics for citizenship. Upon completion, students should be able to utilize quantitative information as consumers and to make personal, professional, and civic decisions by decoding, interpreting, using, and communicating quantitative information found in modern media and encountered in everyday life.
This is a Universal General Education Transfer Component (UGETC) course
MAT 152 Statistical Methods I
This course provides a project-based approach to introductory statistics with an emphasis on using real-world data and statistical literacy. Topics include descriptive statistics, correlation and regression, basic probability, discrete and continuous probability distributions, confidence intervals and hypothesis testing. Upon completion, students should be able to use appropriate technology to describe important characteristics of a data set, draw inferences about a population from sample data, and interpret and communicate results.
This is a Universal General Education Transfer Component (UGETC) course
MAT
171 Precalculus Algebra
This course is designed to develop topics which are fundamental to the study of Calculus. Emphasis is placed on solving equations and inequalities, solving systems of equations and inequalities, and analysis of functions (absolute value, radical, polynomial, rational, exponential, and logarithmic) in multiple representations. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to algebra-related problems with and without technology.
This is a Universal General Education Transfer Component (UGETC) course
MAT
172 Precalculus Trigonometry
This course is designed to develop an understanding of topics which are fundamental to the study of Calculus. Emphasis is placed on the analysis of trigonometric functions in multiple representations, right and oblique triangles, vectors, polar coordinates, conic sections, and parametric equations. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to trigonometry-related problems with and without technology.
This is a Universal General Education Transfer Component (UGETC) course
MAT
263 Brief Calculus
This course is designed to introduce concepts of differentiation and integration and their applications to solving problems. Topics include graphing, differentiation, and integration with emphasis on applications drawn from business, economics, and biological and behavioral sciences. Upon completion, students should be able to demonstrate an understanding of the use of basic calculus and technology to solve problems and to analyze and communicate results.
This is a Universal General Education Transfer Component (UGETC) course
MAT
271 Calculus I
This course is designed to develop the topics of differential and integral calculus. Emphasis is placed on limits, continuity, derivatives and integrals of algebraic and transcendental functions of one variable. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to derivative-related problems with and without technology.
This is a Universal General Education Transfer Component (UGETC) course
MAT
272 Calculus II
This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals, infinite series, conic sections, parametric equations, polar coordinates, and differential equations. Upon completion, students should be able to select and use appropriate models and techniques for finding solutions to integral-related problems with and without technology.
MAT
273 Calculus III
This course is designed to develop the topics of multivariate calculus. Emphasis is placed on multivariate functions, partial derivatives, multiple integration, solid analytical geometry, vector valued functions, and line and surface integrals. Upon completion, students should be able to select and use appropriate models and techniques for finding the solution to multivariate-related problems with and without technology.
MAT
285 Differential
Equations
This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear higher-order differential equations, systems of differential equations, numerical methods, series solutions, eigenvalues and eigenvectors, and LaPlace transforms. Upon completion, students should be able to demonstrate understanding of the theoretical concepts and select and use appropriate models and techniques for finding solutions to differential equations-related problems with and without technology.
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Applied Combinatorics, 6th Edition
The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.
Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems. Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.
This new sixth edition has new examples, expanded discussions, and additional exercises throughout the text.
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MATH 203: MATH FOR ELEMENTARY TCHRS I
(F) The purpose is to develop understanding by emphasizing mathematical concepts and connections. The course is based on NCTM standards. Students use manipulatives in the study of concepts and procedures for whole numbers, fractions, ratios, integers and real numbers. Problem solving, math journals, alternative assessment, structure, calculators. This course no longer fulfills the Liberal Education Math requirement in the Liberal Education Core. Prerequisite: fulfillment of the Liberal Education Core Math requirement
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Precalculus
Precalculus : A Problems-Oriented Approach
Precalculus, 7th Edition
Student Solutions Manual for Cohen/Lee/Sklar's Precalculus, 7th
Summary
Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student!
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Precalculus: Graphing and Data Analysis
This book motivates students by highlighting real people facing real challenges finding real solutions. This series features real workers at Motorola ...Show synopsisThis book motivates students by highlighting real people facing real challenges finding real solutions. This series features real workers at Motorola, along with hundreds of applications and real data sets highlighting the relevance and scope of activities a reader may encounter in life. Covers such topics as graphs, functions, polynomial and rational functions, the zeros of a polynomial function, exponential and logarithmic functions, trigonometric functions, analytic trigonometry, applications of trigonometric functions, polar coordinates, vectors, analytic geometry, systems of equations and inequalities, sequence, induction, the binomial theorem, counting and probability, and more. For anyone interested in Precalculus.Hide synopsis
Description:Fair. 0130289558 Well used book with very heavy cover wear and...Fair. 0130289558 0130269271 Some wear on cover, inside has no writing or...Fair. 0130269271 Some wear on cover, inside has no writing or highlighting in the text. Choose Expedited Shipping if you need it quick Precalculus Graphing Data Analysis. This book is in Good...Good. Precalculus Graphing Data Analysis
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Brighton, CO SAT MathAt the simplest level there are two types of calculus - differential calculus (analysis of derivatives) and integral calculus (analysis of integrals). For functions of the form y = f(x), differential calculus is often associated with rates of change, while integral calculus is typically associat...
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Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
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Foundations of Algorithms, Fourth Edition offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity. The volume is accessible to mainstream computer science students who have a background in college algebra and discrete structures. To support their approach, the authors present mathematical concepts using standard English and a simpler notation than is found in most texts. A review of essential mathematical concepts is presented in three appendices. The authors also reinforce the explanations with numerous concrete examples to help students grasp theoretical
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Overview
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and
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and Technics / Science / Mathematics / Geometry2014-08-22T23:45:24Z Essentials For Dummies Ryan Dummies2011-05-11Just the critical concepts you need to score high in geometryThis practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills a...192 pages9.8 MB6.99Geometry DeMYSTiFieD, 2nd Edition Gibilisco Professional2011-01-26A new ANGLE to learning GEOMETRY Trying to understand geometry but feel like you're stuck in another dimension? Here's your solution. Geometry Demystified, Second Edition helps you grasp the essential concepts with ease. Written in a step-by-ste...410 pages7.5 MB15.79Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM- University Press2011-05-30Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic...440 pages16.1 MB74.29A First Course in Geometry T Walsh Publications2014-08-03This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The ...400 pages22.1 MB18.29Scientific Essays in Honor of H Pierre Noyes on the Occasion of His 90th Birthday book is a Festschrift for the 90th birthday of the physicist Pierre Noyes. The book is a representative selection of papers on the topics that have been central to the meetings over the last three decades of ANPA, the Alternative Natural Phil...400 pages22.9 MB66.49Solutions Manual to Accompany Classical Geometry: Euclidean, Transformational, Inversive, and Projective E. Leonard E. Lewis C. F. Liu Manual to accompany Classical Geometry: Euclidean, Transformational, Inversive, and ProjectiveWritten by well-known mathematical problem solvers, Classical Geometry: Euclidean, Transformational, Inversive, and Projective features up-to-d...176 pages6.8 MB23.99Theta Functions and Knots Gelca book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical...468 pages24.5 MB66.49Discrete and Computational Geometry L. 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The compendium is organized in four parts — Algebra, Geometry, Topology, and Ap...524 pages16 MB30.79Classical Geometry: Euclidean, Transformational, Inversive, and Projective E. Leonard E. Lewis C. F. Liu the classical themes of geometry with plentiful applications in mathematics, education, engineering, and scienceAccessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers ...496 pages15.6 MB79.99The King of Infinite Space: Euclid and His Elements Berlinski Books2014-04-07Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book...176 pages669 KB10.99Schaum's Outline of Geometry, 4ed Rich Thomas Test Questions? Missed Lectures? Not Enough Time? Lucky for you there is Schaum's. For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates...336 pages14.3 MB15.79Algebraic Geometry Modeling in Information Theory & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-B...336 pages9.4 MB56.29Euclid's Window Mlodinow Press2010-09-27Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is...320 pages3.3 MB11.99Structural Aspects of Quantum Field Theory and Noncommutative Geometry: (In 2 Volumes) GRENSING book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particu...1,596 pages162.3 MB102.99Knots and Physics H Kauffman invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully in...864 pages35.8 MB47.79Number Theory: Arithmetic in Shangri-La volume is based on the successful 6th China–Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in th...272 pages9.6 MB75.49Oblique Derivative Problems for Elliptic Equations M LIEBERMAN book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such prob...528 pages10.1 MB75.49Emerging Topics on Differential Equations and Their Applications aim of the Sino–Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges an...320 pages4.3 MB66.49
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Information and Departmental Plan of Study
Most freshmen and sophomores interested in science, engineering, or finance take courses from the standard calculus and linear algebra sequence 103-104-201-202, which emphasizes concrete computations over more theoretical considerations. Note that 201 and 202 can be taken in either order.
Students who are not prepared to begin with 103 may take 100, a rigorous precalculus/prestatistics refresher offered only in the fall semester and intended for students whose highest math SAT score is below 650.
More mathematically inclined students, especially prospective physics majors, may opt to replace 201-202 with 203-204, for greater emphasis on theory and more challenging computational problems.
Prospective mathematics majors must take at least one course introducing formal mathematical argument and rigorous proofs. The recommended freshman sequence for prospective majors is 215-217. Prospective majors who already have substantial experience with university-level proof-based analysis courses may consider the accelerated sequence 216-218 instead. Other possible sequences for prospective majors include 214-204-203 and 203-204-215, although the latter two are relatively rare. Note that 203 and 204 can be taken in either order.
Placement. Students with little or no background in calculus are placed in 103, or in 100 if their SAT mathematics scores indicate insufficient background in precalculus topics. To qualify for placement in 104 or 175, a student should score 5 on the AB Advanced Placement Examination or a 4 on the BC Advanced Placement Examination. To qualify for placement into 201 or 202, a student should have a score of 5 on the BC Examination. Students who possess in addition a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 214 or 215 or 216 instead. For more detailed placement information, consult the Department of Mathematics home page or placement officer.
Advanced Placement
One unit of advanced placement credit is granted when a student is placed in MAT 104 or 175. Two units of advanced placement credit are granted when a student is placed in MAT 201, 203, or 217.
Prerequisites
Generally, either 215-217 or 216-218 or 203-204-215 are strongly recommended for admission to the department. Prospective mathematics majors should consult the department early and plan a program that includes as much of the 215-217 or 216-218 sequence as possible. Most majors begin taking courses at the 300-level by the second semester of the sophomore year, in preparation for their junior independent work.
Further information for prospective majors is available on the department home page.
It is recommended that students complete some of these core requirements by the end of the sophomore year. Completing these core courses early gives more options for junior and senior independent work.
Note: One course in discrete mathematics (e.g. 375, 377 or 378) can replace the geometry/topology core requirement, if desired.
In addition to the four core requirements, students must complete an additional four courses at the 300 level or higher, up to three of which may be cognate courses outside the mathematics department, with permission from the junior or senior advisers or departmental representative.
The departmental grade (the average grade of the eight departmental courses) together with grades and reports on independent work is the basis on which honors and prizes are awarded on graduation.
Students should refer to Course Offerings to check which courses are offered in a given term. Programs of study in various fields of pure mathematics and applied mathematics are available. Appropriate plans of study may be arranged for students interested in numerical analysis, discrete mathematics, optimization, physics, the biological sciences, probability and statistics, finance, economics, or computer science. For students interested in these areas, a coherent program containing up to three courses in a cognate field may be approved.
Independent Work
All departmental students engage in independent work, supervised by a member of the department chosen in consultation with a departmental adviser. The independent work of the junior year generally consists of participating actively in a junior seminar in both the fall and the spring semesters. Alternatively, a student may opt to replace one junior seminar with supervised reading in a special subject and then writing a paper based on that reading. The independent work in the senior year centers on writing a senior thesis. A substantial percentage of our majors work with faculty in other departments on their senior project.
Senior Departmental Examination
Courses
MAT 100
Precalculus/Prestatistics
Fall
QR
An intensive and rigorous treatment of algebra and trigonometry as preparation for further courses in calculus or statistics. Topics include functions and their graphs, equations involving polynomial and rational functions, exponentials, logarithms and trigonometry.
J. Johnson
MAT 102
Survey of Calculus
Not offered this year
QR
One semester survey of the major concepts and computational techniques of calculus including limits, derivatives and integrals. Emphasis on basic examples and applications of calculus including approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Prerequisites: MAT100 or equivalent. Restrictions: Cannot receive course credit for both MAT103 and MAT102. Provides adequate preparation for MAT175. Three classes.
Staff
MAT 103
Calculus I
Fall, Spring
QR
First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus. The fall offering will emphasize applications to physics and engineering in preparation for MAT104; the spring offering will emphasize applications to economics and life sciences, in preparation for MAT175. Prerequisite: MAT100 or equivalent. Three classes.
Staff
MAT 104
Calculus II
Fall, Spring
QR
Continuation of MAT103. Topics include techniques of integration, arclength, area, volume, convergence of series and improper integrals, L'Hopital's rule, power series and Taylor's theorem, introduction to differential equations and complex numbers. Prerequisite: MAT103 or equivalent. Three classes.
Staff
MAT 151
Problem Solving in Mathematics (see APC 151)
MAT 175
Mathematics for Economics/Life Sciences
Fall, Spring
QR
Survey of topics from multivariable calculus as preparation for future course work in economics or life sciences. Topics include basic techniques of integration, average value, vectors, partial derivatives, gradient, optimization of multivariable functions, and constrained optimization with Lagrange multipliers.
Students preparing for math track econometrics and finance courses need MAT201/202 instead. Students who complete 175 can continue in 202 if they wish.
Staff
Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields, and Stokes's theorem. Prerequisite: 104 or equivalent. Three classes.
Staff
Vector spaces, limits, derivatives of vector-valued functions, Taylor's formula, Lagrange multipliers, double and triple integrals, change of coordinates, surface and line integrals, generalizations of the fundamental theorem of calculus to higher dimensions. More abstract than 201 but more concrete than 218. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or MAT215 or equivalent. Three classes.
Staff
MAT 204
Advanced Linear Algebra with Applications
Spring
QR
Companion course to MAT203. Linear systems of equations, linear independence and dimension, linear transforms, determinants, (real and complex) eigenvectors and eigenvalues, orthogonality, spectral theorem, singular value decomposition, Jordan forms, other topics as time permits. More abstract than MAT202 but more concrete than MAT217. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or MAT215 or equivalent. Three classes.
Staff
MAT 214
Numbers, Equations, and Proofs
Fall
QR
An introduction to classical number theory to prepare for higher-level courses in the department. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions, and quadratic reciprocity. There will be a topic from more advanced or more applied number theory such as p-adic numbers, cryptography, and Fermat's Last Theorem. This course is suitable both for students preparing to enter the mathematics department and for non-majors interested in exposure to higher mathematics.
Staff
MAT 215
Honors Analysis (Single Variable)
Fall, Spring
QR
An introduction to the mathematical discipline of analysis, to prepare for higher-level course work in the department. Topics include the rigorous epsilon-delta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The Heine-Borel theorem, the Riemann integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor's theorem.
S. Chang,
M. McConnell
A development of logic from the mathematical viewpoint, including propositional and predicate calculus, consequence and deduction, truth and satisfaction, the Goedel completeness and incompleteness theorems. Applications to model theory, recursion theory, and set theory as time permits. Some underclass background in logic or in mathematics is recommended.
Staff
MAT 306
Advanced Logic (see PHI 323)
MAT 320
Introduction to Real Analysis
Fall
QR
Introduction to real analysis, including the theory of Lebesgue measure and integration on the line and n-dimensional space and the theory of Fourier series. Prerequisite: MAT201 and MAT202 or equivalent.
N. Mřller
Draws problems from the sciences & engineering for which mathematical models have been developed and analyzed to describe, understand and predict natural and man-made phenomena. Emphasizes model building strategies, analytical and computational methods, and how scientific problems motivate new mathematics. This interdisciplinary course in collaboration with Molecular Biology, Psychology and the Program in Neuroscience is directed toward upper class undergraduate students and first-year graduate students with knowledge of linear algebra and differential equations.
Staff
The theory of functions of one complex variable, covering power series expansions, residues, contour integration, and conformal mapping. Although the theory will be given adequate treatment, the emphasis of this course is the use of complex analysis as a tool for solving problems. Prerequisite: MAT201 and MAT202 or equivalent.
Staff
MAT 335
Analysis II: Complex Analysis
Fall
QR
Study of functions of a complex variable, with emphasis on interrelations with other parts of mathematics. Cauchy's theorems, singularities, contour integration, power series, infinite products. The gamma and zeta functions and the prime number theorem. Elliptic functions, theta functions, Jacobi's triple product and combinatorics. An overall view of Special Functions via the hypergeometric series. This course is the second semester of a four-semester sequence, but may be taken independently of the other semesters.
I. Rodnianski
MAT 345
Algebra I
Fall
QR
This course will cover the basics of symmetry and group theory, with applications. Topics include the fundamental theorem of finitely generated abelian groups, Sylow theorems, group actions, and the representation theory of finite groups. Prerequisites: MAT202 or 204 or 217.
S. Sivek
MAT 346
Algebra II
Spring
QR
Algebra and Applications: To develop curiosity about algebraic structures by exploring examples that connect to higher mathematics and to applications in computer science, the natural sciences and electrical engineering. This is an undergraduate course for sophomores and juniors. The only prerequisite is a solid understanding of linear algebra. There will be opportunities for a student to explore an advanced topic in great depth, possibly for a junior project.
Staff
Combinatorics is the study of enumeration and structure of discrete objects. These structures are widespread throughout mathematics, including geometry, topology and algebra, as well as computer science, physics and optimization. This course will give an introduction to modern techniques in the field, and how they relate to objects such as polytopes, permutations and hyperplane arrangements.
R. Ehrenborg,
M. Readdy
Topics introducing various aspects of number theory, including analytic and algebraic number theory, L-functions, and modular forms.. Prerequisites: MAT 215, 345, 346 or equivalent.
Staff
MAT 425
Analysis III: Integration Theory and Hilbert Spaces
Spring
QR
The theory of Lebesgue integration in n-dimensional space. Differentiation theory. Hilbert space theory and applications to Fourier Transforms, and partial differential equations. Introduction to fractals. This course is the third semester of a four-semester sequence, but may be taken independently of the other semesters. Prerequisites: MAT215 or 218 or equivalent.
Staff
MAT 427
Ordinary Differential Equations
Fall
QR
Introduction to the study of ordinary differential equations; explicit solutions, general properties of solutions, and applications. Topics include explicit solutions of some non-linear equations in two variables by separation of variables and integrating factors, explicit solution of simultaneous linear equations with constant coefficients, explicit solution of some linear equations with variable forcing term by Laplace transform methods, geometric methods (description of the phase portrait), and the fundamental existence and uniqueness theorem.
J. Mather
MAT 429
Topics in Analysis
Fall
QR
Introduction to incompressible fluid dynamics. The course will give an introduction to the mathematical theory of the Euler equations, the fundamental partial differential equation arising in the study of incompressible fluids. We will discuss several topics in analysis that emerge in the study of these equations: Lebesgue and Sobolev spaces, distribution theory, elliptic PDEs, singular integrals, and Fourier analysis. Content varies from year to year.
V. Vicol
MAT 449
Topics in Algebra
Fall
QR
Topics in algebra selected from areas such as representation theory of finite groups and the theory of Lie algebras. Three classes. Prerequisite: MAT 345 or MAT 346.
S. Morel
MAT 459
Topics in Geometry
Not offered this year
QR
Topics in geometry selected from areas such as differentiable and Riemannian manifolds, point set and algebraic topology, integral geometry. Prerequisite: departmental permission.
Staff
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Algebra 2 Problem Solver
Algebra problems are often avoided by most students who find the problems too tough to solve by themselves. The result is that come exam time, these students struggle to cram a year's Algebra classes over a few weeks or days. This scenario can be avoided quite easily if students work on their Algebra 2 problem solving skills from day one.
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Algebra word problems have always bee a thorn for many students who cannot seem to figure out what the question is asking for and what information they have been provided. A good Algebra 2 word problem solver can fix that by explaining algebraic terms and their meaning to students. Students are taught to look out for certain terms which are repeated often and give clues into what kind of operation the students need to do.
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#1 Linear Algebra and Geometry
This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from most existing textbooks in approach, the work illustrates the various applications and connections of linear algebra with functional analysis, quantum mechanics, and algebraic and differential geometry.
#2 Linear Algebra Examples
The book is a collection of solved problems in linear algebra, this first volume covers linear equations, matrices and determinants. All examples are solved, and the solutions usually consist of step-by-step instructions, and are designed to assist students in methodically solving problems.
#3 Linear Algebra Done Right (2nd Edition)
This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs.
#4 Linear Algebra Demystified
With Linear Algebra Demystified, you master the subject one step at a time -- at your own speed. This unique self-teaching guide offers problems at the end of each chapter and section to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book.
#5 Basic Topology
3-08-2010, 04:54
Basic Topology 2007 | 452 pages | ISBN:0387908390 | PDF | 8 Mb
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject.
#7 Auslogics Registry Defrag 6.0.6.55 Portable
13-12-2010, 19:48
Auslogics Registry Defrag 6.0.6.55 Portable | 5.04#8 Maxon Cinema 4D 11.008 (Portable)
#9 Auslogics Registry Defrag 6.0.4.45
6-09-2010, 11:31
Auslogics Registry Defrag 6.0.4.45 | 5.3Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23 27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.
#15 Engineering Mathematics, Second Edition
This book is the sequel to Stroud's excellent "Engineering Mathematics", which focused on the undergraduate engineer and the math that he/she should know by graduation. This book continues on with crystal-clear discussions of numerical methods, linear algebra including the singular value decomposition and its uses, linear programming methods, multiple integration, and partial differential equations, to name a few of the topics covered. Just because the mathematics is more advanced in this book does not mean that it is any less clear than its less advanced predecessor
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Intermediate Algebra: Connecting Concepts through Applications
9780534496364
ISBN:
0534496369
Edition: 1 Pub Date: 2011 Publisher: Brooks Cole
Summary: INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate so...lutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skills.
Clark, Mark is the author of Intermediate Algebra: Connecting Concepts through Applications, published 2011 under ISBN 9780534496364 and 0534496369. Four hundred forty seven Intermediate Algebra: Connecting Concepts through Applications textbooks are available for sale on ValoreBooks.com, one hundred twenty eight used from the cheapest price of $30.68, or buy new starting at $15896369 Used text may NOT contain supplemental materials-Book may contain some stickers on co... [more] 0534405344
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Elementary Linear Algebra
A...more Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice.(less)
Community Reviews
8 Complex Vector Spaces
8.1 Complex Numbers 8.2 Conjugates and Divisors of Complex Numbers 8.3 Polar Form and DeMoivre's Theorem 8.4 Complex Ve...moreI could perhaps be talked into believing that chapter 10 could be made an online supplement, as numerical methods are a huge subject with their own course, and to which any student of college mathematics will get some limited exposure through via calculus and differential equations courses.
But relegating complex-valued matrices, complex spaces, and linear programming to PDFs on the web where few students will see them is a crime against education.
I dock this textbook a star for its price and another for shunting three chapters into the online ghetto. However, compared to many other linear algebra textbooks I looked at, Larson/Falvo appears to be nearly the broadest survey of the subject around while remaining accessible to beginners (where "beginners" have at least a semester of single-variable calculus under their belt and ideally at least a brief exposure to ordinary differential equations). This text is heavy on applications, which I consider a major virtue.(less)
Basic LA, some nice geo demo of low dimensional example to illustrate some theories. I expect more about eigenvector and eigenvalue however, so that I can better understand PCA, which is completely untouched here. Perhaps that is what "elementary" means.
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A group in which the binary operation is commutative, that is, ab=ba for all elements a abd b in the group.
abscissa
The x-coordinate of a point in a 2-dimensional coordinate system.
absolute value
The positive value for a real number, disregarding the sign. Written |x|. For example, |3|=3, |-4|=4, and |0|=0.
abundant number
A positive integer that is smaller than the sum of its proper divisors.
acceleration
The rate of change of velocity with respect to time.
acute angle
An angle that is less than 90 degrees
addition
The process of adding two numbers to obraint heir sum.
algebraic equation
An equation of the form f(x)=0 where f is a polynomial.
algebraic number
A number that is the root of an algebraic polynomial. For example, sqrt(2) is an algebraic number because it is a solution of the equation x2=2.
alphametic
A cryptarithm in which the letters, which represent distinct digits, form related words or meaningful phrases.
altitude
The altitude of a triangle is the line segment from one vertex that is perpendicular to the opposite side.
amicable numbers
Two numbers are said to be amicable if each is equal to the sum of the proper divisors of the other.
angle
The figure formed by two line segments or rays that extend from a given point.
annulus
The region enclosed by two concentric circles.
arc
A portion of a circle.
area
The amount of surface contained by a figure.
arithmetic
The type of mathematics that studies how to solve problems involving numbers (but no variables).
arithmetic mean
The arithmetic mean of n numbers is the sum of the numbers divided by n.
automorphism
An isomorphism from a set onto itslef.
average
Typically this refers to the arithmetic mean.
ball
A sphere together with its interior.
bar graph
A type of chart used to compare data in which the length of a bar represents the size of the data.
base
In the expression xy, x is called the base and y is the exponent.
Bayes's Rule
A rule for finding conditional probability.
binary number
A number written to base 2.
binary operation
A binary operation is an operation that involves two operands. For example, addition and subtraction are binary operations.
bijection
A one-to-one onto function.
binomial
An expression that is the sum of two terms.
binomial coefficient
The coefficients of x in the expansion of (x+1)n.
biquadratic equation
A polynomial equation of the 4th degree.
bisect
to cut in half.
bit
A binary digit.
braces
The symbols { and } used for grouping or to represent a set.
byte
The amount of memory needed to represent one character on a computer, typically 8 bits.
Calculator
A machine for performing arithemtical calculations.
Caliban puzzle
A logic puzzle in which one is asked to infer one or more facts from a set of given facts.
cardinal number
A number that indicates the quantity but not the order of things.
catenary
A curve whose equation is y = (a/2)(ex/a+e-x/a). A chain suspended from two points forms this curve.
ceiling function
The ceiling function of x is the smallest integer greater than or equal to x.
central angle
An angle between two radii of a circle.
centroid
The center of mass of a figure. The centroid of a triangle is the intersection of the medians.
cevian
A line segment extending from a vertex of a triangle to the opposite side.
Chebyshev polynomials
chord
The line joining two points on a curve is called a chord.
circle
The set of points equidistant from a given point (the center).
circular cone
A cone whose base is a circle.
circumcenter
The circumcenter of a triangle is the center of the circumscribed circle.
circumcircle
The circle circumscribed about a figure.
circumference
The boundary of a circle.
cissoid
A curve with equation y2(a-x)=x3.
coefficient
The constant multipliers of the indeterminate variable in a polynomial. For example, in the polynomial x2+3x+7, the coefficients are 1, 3, and 7.
common denominator
A multiple shared by the denominators of two or more fractions.
complementary angles
Two angles whose sum is 90o.
complex number
The sum of a real number and an imaginary number, for example 3+4i where i=sqrt(-1).
compute
To solve problems that use numbers.
concave
curved from the inside.
cone
A three-dimensional solid that rises froma circular base to a single point at the top.
congruent figures
two geometric figures that are identical in size and shape.
conic section
The cross section of a right circular cone cut by a plane. An ellipse, parabola, and hyperbola are conic sections.
coordinates
Numbers that determine the position of a point.
coprime
Integers m and n are coprime if gcd(m,n)=1.
cryptarithm
A number puzzle in which an indicated arithmetical operation has some or all of its digits replaced by letters or symbols and where the restoration of the original digits is required. Each letter represents a unique digit.
cube
A solid figure bounded by 6 congruent squares.
cubic equation
A polynomial equation of degree 3.
cyclic polygon
A polygon whose vertices lie on a circle.
cylinder
A rounded three-dimensional solid that has a flat circular face at each end.
data
Facts that have been collected but not yet interpreted.
decagon
A polygon with 10 sides.
decimal number
A number written to the base 10.
decimal point
The period in a deimal number separating the integer part from the fractional part.
deficient number
A positive integer that is larger than the sum of its proper divisors.
degree
The degree of a term in one variable is the exponent of that variable. For example, the degree of 7x5 is 5.
denominator
In the fraction x/y, x is called the numerator and y is called the denominator.
diagonal
In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal.
diameter
The longest chord of a figure. In a circle, a diameter is a chord that passes through the center of the circle.
difference
The difference between two numbers is what you get when you subtract one from the other.
differential calculus
That part of calculus that deals with the opeation of differentiation of functions.
In the expression "a divided by b", a is the divident and b is the divisor.
division
A basic arithmetical operation determining how many times one quantity is contained within another.
divisor
In the expression "a divided by b", a is the divident and b is the divisor.
divisor
The nonzero integer d is a divisor of the integer n if n/d is an integer.
Diophantine equation
An equation that is to be solved in integers.
dodecagon
A polygon with 12 sides.
dodecahedron
A solid figure with 12 faces A regular dodecahedron is a regular polyhedron with 12 faces. Each face is a rgular pentagon.
domain
The domain of a function f(x) is the set of x values for which the function is defined.
domino
Two congruent squares joined along an edge.
duodecimal number system
The system of numeration with base 12.
Egyptian fraction
A number of the form 1/x where x is an integer is called an Egyptian fraction.
eigenvalue
characteristic value
elementary function
one of the functions: rational functions, trigonometric functions, exponential functions, and logarithmic functions.
ellipse
A plane figure whose equation isx2/a2+y2/b2=1.
ellipsoid
A solid figure whose equation is x2/a2+y2/b2+z2/c2=1.
empty set
The set with no elements in it.
enumerable set
A countable set.
equation
A statement that two expressions are equal to each other.
equiangular polygon
A polygon all of whose interior angles are equal.
equichordal point
A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length.
equilateral polygon
A polygon all of whose sides are equal.
equilateral triangle
A triangle with three equal sides.
escribed circle
An escribed circle of a triangle is a circle tangent to one side of the triangle and to the extensions of the other sides.
estimate
A rough guess at the value of a number.
Euler line
The Euler line of a triangle is the line connecting the centroid and the circumcenter.
Euler's constant
The limit of the series 1/1+1/2+1/3+...+1/n-ln n as n goes to infinity. Its value is approximately 0.577216.
even function
A function f(x) is called an even function if f(x)=f(-x) for all x.
even number
An integer that is divisible by 2.
excenter
The center of an excircle.
excircle
An escribed circle of a triangle.
exponent
In the expression xy, x is called the base and y is called the exponent.
exponential function
The function f(x)=ex.
expoential function to base a
The function f(x)=ax.
exradius
An exradius of a triangle is the radius of an escribed circle.
face angle
The plane angle formed by adjacent edges of a polygonal angle in space.
factor (noun)
An exact divisor of a number. This 7 is a factor of 28.
factor (verb)
To find the factors of a number.
factorial
n! (read n factorial) is equal to the product of the integers from 1 to n.
Farey sequence
The sequence obtained by arranging in numerical order all the proper fractions having denominators not greater than a given integer.
Fermat number
A number of the form 2^{2^n}+1.
Fermat's spiral
A parabolic spiral.
Fibonacci number
A member of the sequence 0, 1, 1, 2, 3, 5,... where each number is the sum of the previous two numbers.
figurate numbers
polygonal numbers
finite group
A group containing a finite number of elements.
floor function
The floor function of x is the greatest integer in x, i.e. the largest integer less than or equal to x.
focal chord
A chord of a conic that passes through a focus.
focal radius
A line segment from the focus of an ellipse to a point on the perimeter of the ellipse.
foot of altitude
The intersection of an altitude of a triangle with the base to which it is drawn.
foot of line
The point of intersection of a line with a line or plane.
formula
A concise statement expressing the symbolic relationship between two or more quantities.
Fourier series
A periodic function with period 2 pi.
fraction
An expression of the form a/b.
frequency
The number of times a value occurs in some time interval.
frustum
For a given solid figure, a related figure formed by two parallel planes meeting the given solid. In particular, for a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base. NOTE: this word is frequently incorrectly misspelled as frustrum.
Gaussian curve
A normal curve.
geoboard
A flat board into which nails have been driven in a regular rectangular pattern. These nails represent the lattice points in the plane.
geodesic
The arc on a surface of shortest length joining two given points.
geodesy
A branch of mathematics dealing with the shape, size, and curvature of the Earth.
geometric mean
The geometric mean of n numbers is the nth root of the product of the numbers.
geometric progression
A sequence in which the ratio of each term to the preceding term is a given constant.
geometric series
A series in which the ratio of each term to the preceding term is a given constant.
geometric solid
The bounding surface of a 3-dimensional portion of space.
geometry
The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.
Gergonne point
In a triangle, the lines from the vertices to the points of contact of the opposite sides with the inscribed circle meet in a point called the Gergonne point.
gnomon magic square
A 3 X 3 array in which the elements in each 2 X 2 corner have the same sum.
golden ratio
(1+Sqrt[5])/2.
golden rectangle
A rectangle whose sides are in the golden ratio.
graceful graph
A graph is said to be graceful if you can number the n vertices with the integers from 1 to n and then label each edge with the difference between the numbers at the vertices, in such a way that each edge receives a different label.
grad (or grade)
1/100th of a right angle
graph
A graph is a set of points (called vertices) and a set of lines (called edges) joinging these vertices.
great circle
A circle on the surface of a sphere whose center is the center of the sphere.
greatest common divisor
The greatest common divisor of a sequence of integers, is the largest integer that divides each of them exactly.
greatest common factor
Same as greatest common divisor.
greatest lower bound
The greatest lower bound of a set of real numbers, is the largest real number that is smaller than each of the numbers in the set.
group
A mathematical system consisting of elements from a set G and a binary operation * such that
x*y is a member of G whenever x and y are
(x*y)*z=x*(y*z) for all x, y, and z
there is an identity element e such that e*x=x*e=e for all x
each member x in G has an inverse element y such that x*y=y*x=e
half-line
A ray.
half-plane
The part of a plane that lies on one side of a given line.
Hankel matrix
A matrix in which all the elements are the same along any diagonal that slopes from northeast to southwest.
harmonic analysis
The study of the representation of functions by means of linear operations on characteristic sets of functions.
harmonic division
A line segment is divided harmonically by two points when it is divided externally and internally int he same ratio.
harmonic mean
The harmonic mean of two numbers a and b is 2ab/(a + b).
hectare
A unit of measurement in the metric system equal to 10,000 square meters (approximately 2.47 acres).
helix
The path followed by a point moving on the surface of a right circular cylinder that moves along the cylinder at a constant ratio as it moves around the cylinder. The parameteric equation for a helix is
x=a cos t
y=a sin t
z=bt
heptagon
A polygon with 7 sides.
hexagon
A polygoin with 6 sides.
hexagonal number
A number of the form n(2n-1).
hexagonal prism
A prism with a hexagonal base.
hexahedron
A polyhedron having 6 faces. The cube is a regular hexahedron.
hexomino
A six-square polyomino.
Heronian triangle
A triangle with integer sides and integer area.
homeomorphism
A one-to-one continuous transformation that preserves open and closed sets.
homomorphism
A function that preserve the operators associated with the specified structure.
The element x in some algebraic structure is called idempotent if x*x=x.
imaginary axis
The y-axis of an Argand diagram.
imaginary number
A complex number of the form xi where x is real and i=sqrt(-1).
imaginary part
The imaginary part of a complex number x+iy where x and y are real is y.
incenter
The incenter of a triangle is the center of its inscribed circle.
incircle
The circle inscribed in a given figure.
inequality
The statement that one quantity is less than (or greater than) another.
infinite
becoming large beyond bound.
infinitesimal
A variable that approaches 0 as a limit.
infinity
A reference to a quantity larger than any specific integer.
inflection
A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction.
injection
A one-to-one mapping.
inscribed angle
The angle formed by two chords of a curve that meet at the same point on the curve.
integer
One of the numbers ..., -3, -2, -1, 0, 1, 2, 3, ...
intersect
Two figures are said to intersect if they meet or cross each other.
irrational number
A number that is not rational.
isogonal conjugate
Isogonal lines of a triangle are cevians that are symmetric with respect to the angle bisector. Two points are isogonal conjugates if the corresponding lines to the vertices are isogonal.
isometry
A length preserving map.
isosceles tetrahedron
A tetrahedron in which each pair of opposite sides have the same length.
isosceles triangle
A triangle with two equal sides.
isosceles trapezoid
Ain which the two non-parallel sides have the same length.
isotomic conjugate
Two points on the side of a triangle are isotomic if they are equidistant from the midpoint of that side. Two points inside a triangle are isotomic conjugates if the corresponding cevians through these points meet the opposite sides in isotomic points.
joint probability function
A function that gives the probability that each of two or more random variables takes at a particular value.
joint variation
A variation in which the values of one variable depend upon those of 2 or more variables.
Jordan curve
A simple closed curve.
Jordan matrix
A matrix whose diagonal elements are all equal (and nonzero) and whose elements above the principal diagonal are equal to 1, but all other elements are 0.
joule
A unit of energy or work.
jump discontinuity
A discontinuity in a function where the left and righ-hand limits exist but are not equal to each other.
kilometer
A unit of length equal to 1,000 meters.
kinematics
A branch of mechanics dealing with the motion of rigid bodies without reference to their masses or the forces acting on the bodies.
kite
A quadrilateral which has two pairs of adjacent sides equal.
knight's tour
A knight's tour of a chessboard is a sequence of moves by a knight such that each square of the board is visited exactly once.
knot
A curve in space formed by interlacing a piece of string and then joining the ends together.
knot
a unit of speed in navigation equal to one nautical mile per hour.
L-tetromino
A tetromino in the shape of the letter L.
latera recta
plural of lattice rectum.
latin square
An n X n array of numbers in which only n numbers appear. No number appears more than once in any row or column.
latitude
The angular distance of a point on the Earth from the equator, measured along the meridian through that point.
lattice point
A point with integer coordinates.
latus rectum
A chord of an ellipse passing through a focus and perpendicular to the major axis of the ellipse.Plural: latera recta.
least common multiple
The least common multiple of a set of integers is the smallest integer that is an exact multiple of every number in the set.
least upper bound
The least upper bound of a set of numbers is the smallest number that is larger than every member of the set.
lemata
plural of lemma.
lemma
A proposition that is useful mainly for the proof of some other theorem.
length
The straight line distance between two points.
Legendre polynomials
line
A geometrical figure that has length but no width.
linear function
A function of the form y=ax+b.
line graph
A chart that shows data by means of points connected by lines.
line segment
The part of a line between two given distinct points on that line (including the two points).
locus
The set of all points meeting some specified condition.
logic
The study of the formal laws of reasoning.
lowest common denominator
The smallest number that is exactly divisible by each denominator of a set of fractions.
loxodrome
On a sphere, a curve that cuts all parallels under the same angle.
lowest common denominator
The smallest multiple shared by the denominators of a set of fractions.
lowest terms
A fraction is said to be in lowest terms if its numerator and denominator have no common factor.
Lucas number
A member of the sequence 2, 1, 3, 4, 7,... where each number is the sum of the previous two numbers. L0=2, L1=1, Ln=Ln-1+Ln-2.
lune
The portion of a sphere between two great semicircles having common endpoints (including the semicircles).
magic square
A square array of n numbers such that sum of the n numbers in any row, column, or main diagonal is a constant (known as the magic sum).
magic tour
If a chess piece visits each square of a chessboard in succession, this is called a tour of the chessboard. If the successive squares of a tour on an n X n chessboard are numbered from 1 to n^2, in order, the tour is called a magic tour if the resulting square is a magic square.
main diagonal
In the matrix [aij], the elements a11, a22, ..., ann.
major axis
The major axis of an ellipse is it's longest chord.
Malfatti circles
Three equal circles that are mutually tangent and each tangent to two sides of a given triangle.
maximum
The largest of a set of values.
matrix
A rectangular array of elements.
mean
Same as average.
medial triangle
The triangle whose vertices are the midpoints of the sides of a given triangle.
median
The median of a triangle is the line from a vertex to the midpoint of the opposite side.
median
When a set of numbers is ordered from smallest to largest, the median number is the one in the middle of the list.
Mersenne number
A number of the form 2p-1 where p is a prime.
Mersenne prime
A Mersenne number that is prime.
midpoint
The point M is the medpoint of line segment AB if AM=MB. That is, M is halfway between A and B.
minor axis
The minor axis of an ellipse is its smallest chord.
minimum
The smallest of a set of values.
mode
The most frequently occurring value in a sequence of numbers.
modulo
The integers a and b are said to be congruent modulo m if a-b is divisible by m.
monomial
An algebraic expression consisting of just one term.
monotone
A sequence is monotone if its terms are increasing or decreasing.
monic polynomial
A polynomial in which the coefficient of the term of highest degree is 1.
monochromatic triangle
A triangle whose vertices are all colored the same.
multinomial
An algebraic expression consisting of 2 or more terms.
multiple
The integer b is a multiple of the integer a if there is an integer d such that b=da.
multiplication
The basic arithemtical operation of repeated addition.
nadir
The point on the celestial spehere in the direction downwards of the plumb-line.
Nagel point
In a triangle, the lines from the vertices to the points of contact of the opposite sides with the excircles to those sides meet in a point called the Nagel point.
natural number
Any one of the numbers 1, 2, 3, 4, 5, ... .
negative number
A number smaller than 0.
nine point center
In a triangle, the circumcenter of the medial triangle is called the nine point center.
nine point circle
In a triangle, the circle that passes through the midpoints of the sides is called the nine point circle.
nomograph
A graphical device used for computation which uses a straight edge and several scales of numbers.
nonagonal number
A number of the form n(7n-5)/2.
nonary
associated with 9
normal
perpendicular
null hypothesis
The null hypothesis is the hypothesis that is being tested in a hypothesis-testing situation.
null set
the empty set
number line
A line on which each point represents a real number.
number theory
The study of integers.
numeral
A symbol that stands for a number.
numerator
In the fraction x/y, x is called the numerator and y is called the denominator.
numerical analysis
The study of methods for approximation of solutions of various classes of mathematical problems including error analysis.
oblate spheroid
An ellipsoid produced by rotating an ellipse through 360o about its minor axis.
oblique angle
an angle that is not 90o
oblique coordinates
A coordinate system in which the axes are not perpendicular.
oblique triangle
A triangle that is not a right triangle.
obtuse angle
an angle larger than 90o but smaller than 180o
obtuse triangle
A triangle that contains an obtuse angle.
octagon
A polygon with 8 sides.
octahedron
A polyhedron with 8 faces.
octant
any one of the 8 portions of space dtermined by the 3 coordinate planes.
odd function
A function f(x) is called an odd function if f(x)=-f(-x) for all x.
odd number
An integer that is not divisible by 2.
one to one
A function f is said to be one to one if f(x)=f(y) implies that x=y.
onto
A function f is said to map A onto B if for every b in B, there is some a in A such f(a)=b.
open interval
An interval that does not include its two endpoints.
ordered pair
A pair of numbers in which one number is distinguished as the first number and the other as the second number of the pair
ordinal number
A number indicating the order of a thing in a series
ordinate
The y-coordinate of a point in the plane.
origin
The point in a coordinate plane with coordinates (0,0).
orthic triangle
The triangle whose vertices are the feet of the altitudes of a given triangle.
orthocenter
The point of intersection of the altitudes of a triangle.
palindrome
A positive integer whose digits read the same forward and backwards.
palindromic
A positive integer is said to be palindromic with respect to a base b if its representation in base b reads the same from left to right as from right to left.
pandiagonal magic square
A magic square in which all the broken diagonals as well as the main diagonals add up to the magic constant.
pandigital
A decimal integer is called pandigital if it contains each of the digits from 0 to 9.
paraboloid
A paraboloid of revolution is a surface of revolution produced by rotating a parabola about its axis.
parallel
Two lines in the plane are said to be parallel if they do not meet.
parallelogram
A quadrilateral whose opposite sides are parallel.
parallelepiped
A prism whose bases are parallelograms.
parentheses
The symbols ( and ) used for grouping expressions.
Pascal's triangle
A triangular array of binomial coefficients.
pedal triangle
The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC.
Pell number
The nth term in the sequence 0, 1, 2, 5, 12,... defined by the recurrence
P0=0, P1=1, and Pn=2Pn-1+Pn-2.
pentagon
A polygon with 5 sides.
pentagonal number
A number of the form n(3n-1)/2.
pentomino
A five-square polyomino.
percent
A way of expressing a number as a fraction of 100.
perfect cube
An integer is a perfect cube if it is of the form m3 where m is an integer.
perfect number
A positive integer that is equal to the sum of its proper divisors. For example, 28 is perfect because 28=1+2+4+7+14.
perfect power
An integer is a perfect power if it is of the form mn where m and n are integers and n>1.
perfect square
An integer is a perfect square if it is of the form m2 where m is an integer.
perimeter
The distance around the edge of a multisided figure.
perpendicular
Two straight lines are said to be perpendicular if they meet at right angles.
pi
The ratio of the circumference of a circle to its diameter.
pie chart
A type of chart in which a circle is divided up into portions in which the area of each portion represents the size of the data.
place value
Within a number, each digit is given a place value depending on it's location within the number.
plane
A two-dimensional area in geometry.
point
In geometry, a point represents a position, but has no size.
polygon
A plane figure with many sides.
polyomino
A planar figure consisting of congruent squares joined edge-to-edge.
positive number
A number larger than 0.
power
A number multiplied by itself a specified number of times.
practical number
A practical number is a positive integer m such that every natural number n not exceeding m is a sum of distinct divisors of m.
prime
A prime number is an integer larger than 1 whose only positive divisors are 1 and itself.
primitive Pythagorean triangle
A right triangle whose sides are relatively prime integers.
primitive root of unity
The complex number z is a primitive nth root of unity if zn=1 but zk is not equal to 1 for any positive integer k less than n.
probability
The chance that a particular event will happen.
product
The result of multiplying two numbers.
pronic number
A number of the form n(n+1).
proper divisor
The integer d is a proper divisor of the integer n if 0<d<n and d is a divisor of n.
proportion
A comparison of ratios.
pyramid
A three-dimensional solid whose base is a polygon and whose sides are triangles that come to a point at the top.
Pythagorean triangle
A right triangle whose sides are integers.
Pythagorean triple
An ordered set of three positive integers (a,b,c) such that a2+b2=c2.
QED
Abbreviation for quod erat demonstrandum, used to denote the end of a proof.
quadrangle
A closed broken line in the plane consisting of 4 line segments.
quadrangular prism
A prism whose base is a quadrilateral.
quadrangular pyramid
A pyramid whose base is a quadrilateral.
quadrant
Any one of the four portions of the plane into which the plane is divided by the coordinate axes.
quadratfrie
square free
quadratic equation
An equation of the form f(x)=0 where f(x) is a second degree polynomial. That is, ax2+bx+c=0.
quadrature
The quadrature of a geometric figure is the determination of its area.
quadric curve
The graph of a second degree equation in two variables.
quadric surface
The graph of a second degree equation in three variables.
quadrilateral
A geometric figure with four sides.
quadrinomial
An algebraic expression consisting of 4 terms.
quartic polynomial
A polynomial of degree 4.
quartile
The first quartile of a sequence of numbers is the number such that one quuarter of the numbers in the sequence are less than this number.
quintic polynomial
A polynomial of degree 5.
quotient
The result of a division.
radian
A unit of angular measurement such that there are 2 pi radians in a complete circle. One radian = 180/pi degrees. One radian is approximately 57.3o.
radical axis
the locus of points of equal power with respect to two circle.
radical center
The radical center of three circles is the common point of interesection of the radical axes of each pair of circles.
radii
Plural of radius.
radius
The length of a stright line drown from the center of a circle to a point on its circumference.
radix point
The generalization of decimal point to bases of numeration other than base 10.
range
The set of values taken on by a function.
rate
A way of comparing two quantities.
ratio
quotient of two numbers.
rational number
A rational number is a number that is the ratio of two integers. All other real numbers are said to be irrational.
real axis
The x-axis of an Argand diagram.
real part
The real number x is called ther eal part of the complex number x+iy where x and y are real and i=sqrt(-1).
real variable
A variable whose value ranges over the real numbers.
reciprocal
The reciprocal of the number x is the number 1/x.
rectangle
A quadrilateral with 4 right angles.
reflex angle
An angle between 180o and 360o.
remainder
The number left over when one number is divided by another.
repdigit
An integer all of whose digits are the same.
repeating decimal
A decimal whose digits eventually repeat.
repunit
An integer consisting only of 1's.
rhombus
A parallelogram with four equal sides.
right angle
an angle formed by two perpendicular lines; a 90o angle.
right triangle
A triangle that contains a right angle.
roman numerals
A system of numeration used by the ancient Romans.
root of unity
A solution of the equation xn=1, where n is a positive integer.
round-off error
The error accumulated during a calculation due to rounding intermediate results.
rounding
The process of approximating a number to a nearby one.
ruled surface
A surface formed by moving a straight line (called the generator).
rusty compass
A pair of compasses that are fixed open in a given position.
scalene triangle
A triangle with unequal sides.
secant
A straight lien that meets a curve in two or more points.
semi-magic square
A square array of n numbers such that sum of the n numbers in any row or column is a constant (known as the magic sum).
sequence
A collection of numbers in a prescribed order: a1, a2, a3, a4, ...
series
The sum of a finite or infinite sequence
set
A collection of objects.
similar figures
Two geometric figures are similar if their sides are in proportion and all their angles are the same.
skeleton division
A long division in which most or all of the digits have been replaced by asterisks to form a cryptarithm.
slide rule
A calculating device consisting of two sliding logarithmic scales.
solid
A three-dimensional figure.
solid of revolution
A solid formed by rotation a plane figure about an axis in three-space.
solidus
The slanted line in a fraction such as a/b dividing the numerator from the denominator.
sphere
The locus of pointsin three-space that are a fixed distance froma given point (called the center).
spherical trigonometry
The branch of mathematics dealing with measurements on the sphere.
square
A quadrilateral with 4 equal sides and 4 right angles.
square free
An integer is said to be square free if it is not divisible by a perfect square, n2, for n>1.
square number
A number of the form n2.
square root
The number x is said to be a square root of y if x2 = y.
Stirling numbers
subtraction
A basic operation of arithemtic in which you take away one number from another.
sum
The result of adding two or more numbers.
supplementary
Two angels are supplementary of they add up to 180o.
surface area
The measure of a surface of a three-dimensional solid indicating how large it is.
symmedian
Reflection of a median of a triangle about the corresponding angle bisector.
tangent
A line that meets a smooth curve at a single point and does not cut across the curve.
tautology
A sentence that is true because of its logical structure.
tetrahedron
A polyhedron with four faces.
tetromino
A four-square polyomino.
Toeplitz matrix
A matrix in which all the elements are the same along any diagonal that slopes from northwest to southeast.
torus
A geometric solid in the shape of a donut.
trace
The trace of a matrix is the sum of the terms along the principal diagonal.
transcendental number
A number that is not algebraic.
trapezium
A quadrilateral in which no sides are parallel.
trapezoid
A quadrilateral in which two sides are parallel.
tree
A tree is a graph with the property that there is a unique path from any vertex to any other vertex traveling along the edges.
triangle
A geometric figure with three sides.
triangular number
A number of the form n(n+1)/2.
trinomial
An algebraic expression consisting of 3 terms.
tromino
A three-square polyomino.
truncated pyramid
A section of a pyramid between its base and a plane parallel to the base.
twin primes
Two prime numbers that differ by 2. For example, 11 and 13 are twin primes.
unilateral surface
A surface with only one side, such as a Moebius strip.
unimodal
A finite sequence is unimodal if it first increases and then decreases.
unimodular
A square matrix is unimodular if its determinant is 1.
unit circle
A unit circle is a circle with radius 1.
unit cube
A cube with edge length 1.
unit fraction
A fraction whose numerator is 1.
unit square
A unit square is a square of side length 1.
unitary divisor
A divisor d of c is called unitary if gcd(d,c/d) = 1.
unity
one
variable
A symbol whose value can change.
velocity
The rate of change of position.
vertical line
A line that runs up and down and is perpendicular to a horizontal line.
vigesimal
related to intervals of 20.
vinculum
The horizontal bar in a fraction separating the numerator from the denominator.
volume
The measure of spce occupied by a solid body.
vulgar fraction
A common fraction.
weak inequality
An inequality that permits the equality case. For example, a is less than or equal to b.
wff
A well-formed formula.
whole number
A natural number.
winding number
The number of times a closed curve in the plane passes around a given point in the counterclockwise direction.
witch of Agnesi
A curve whose equation is x2y=4a2(2a-y).
X
Roman numeral for 10.
x-axis
The horizontal axis in the plane.
x-intercept
The point at which a line crosses the x-axis.
X-pentomino
A pentomino in the shape of the letter X.
y-axis
The vertical axis in the plane.
y-intercept
The point at which a line crosses the y-axis.
yard
A measure of length equal to 3 feet.
year
A measure of time equal to the period of one revolution of the earth about the sun. Approximately equal to 365 days.
z-intercept
The point at which a line crosses the z-axis.
zero
0
zero divisors
Nonzero elements of a ring whose product is 0.
zero element
The element 0 is a zero element of a group if a+0=a and 0+a=a for all elements a.
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History of Mathematics An Introduction
9780072885231
ISBN:
0072885238
Publisher: McGraw-Hill Higher Education
Summary: This text is designed for the junior/senior mathematics major who intends to teach mathematics in high school or college. It concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary schools or high schools. At least one year of calculus is a prerequisite for this course. This book contains enough material for a 2 semester course but it is flexible enough to be used... in the more common 1 semester course.
Burton, David M. is the author of History of Mathematics An Introduction, published under ISBN 9780072885231 and 0072885238. Twenty one History of Mathematics An Introduction textbooks are available for sale on ValoreBooks.com, sixteen used from the cheapest price of $0.32, or buy new starting at $120edited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
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Math Study Skills Workbook - 3rd edition
Summary: This best-selling workbook helps traditionally unsuccessful students learn to effectively study mathematics. Typically used for a Math Study Skills course Freshman Seminar or as a supplement to class lectures the Nolting workbook helps students identify their strengths weaknesses and personal learning styles in math. Nolting offers proven study tips test-taking strategies a homework system and recommendations for reducing anxiety and improving grades. New features to the Third Editio...show moren include the Learning Modality Inventory and Dan's Take. Since students become more motivated when they understand how math directly relates to their lives a new appendix chart shows how mathematical success can impact their career opportunities and earning potential. Material has also been streamlined and updated to make it more relevant to today's students. New!Learning Modality Inventoryhelps students determine their own learning style. With this knowledge students can identify and implement study habits that are best suited to them. New!Dan's Takeappears in every chapter and presents a student's perspective of different challenges that are encountered in the classroom. These segments are designed to inspire students and decrease their anxiety about math. New!Coverage of cooperative learning has been added to assist instructors who favor group work. New!Another exciting new student support resourceBecoming an Online Learneroffers essential guidance for using technology to study and learn. LikewiseOvercoming Technophobiaa boxed feature from the best-selling Houghton Mifflin series Becoming a Master Student offers helpful suggestions to students intimidated by technology. Updated!The chapter opening sections have been redesigned to include captivating photographs and more clearly defined objectives which help students navigate each chapter more smoothly. ...show less
3. How to Reduce Math Test Anxiety Understanding Math Anxiety How to Recognize Test Anxiety The Causes of Test Anxiety The Different Types of Test Anxiety How to Reduce Test Anxiety
4. How to Improve Your Listening and Note Taking Skills How to Become an Effective Listener How to Become a Good Note Taker The Seven Steps to Math Note Taking How to Rework Your Notes
5. How to Improve Your Reading Homework and Study Techniques How to Read a Math Textbook How to Do Your Homework How to Solve Word Problems How to Work With a Study Buddy The Benefits of Study Breaks Using Online/Computer Resources to Support Learning
6. How to Remember What You Have Learned How You Learn How to Use Learning Styles to Improve Memory How to Use Memory Techniques How to Develop Practice Tests How to Use Number Sense
7. How to Improve Your Math Test-Taking Skills Why Attending Class and Doing Your Homework May Not Be Enough to Pass Pre-Test Check-Off List The Ten Steps to Better Test Taking The Six Types of Test-Taking Errors How to Prepare for the Final Exam Appendix. Math Autobiography Best Jobs Requiring a Bachelor's Degree Bibliography Author Biographies Index0618837469Better World Books Mishawaka, IN
100% Money Back Guarantee. Former Library book. Shows definite wear, and perhaps considerable marking on inside. Shipped to over one million happy customers. Your purchase benefits world literacy!
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KEY MESSAGE: Tom Carson's Prealgebra, Third Edition responds to individual learning styles with a complete study system. The system begins with a Learning Styles Inventory and then presents targeted learning strategies to guide students to success. Tom speaks to readers in everyday language and walks them through the concepts, explaining not only how to do the math, but also where the concepts come from and why they work. KEY TOPICS: Whole Numbers; Integers; Expressions and Polynomials; Equations; Fractions and Rational Expressions; Decimals; Ratios, Proportions, and Measurement; Percents; More with Geometry and Graphs MARKET: For all readers interested in prealgebra.
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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In this lesson you will learn how Algebra is used in everyday life and how to solve basic problems using multiplication and division along with addition and subtraction from Algebra 101. This application includes a detailed description of basic algebra functions, an unlimited number of practice problems and a step by step solution to each
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In this matter and motion worksheet, pupils solve 4 different problems that relate to determining the matter and motion of a function problem. First, they find the limit of a as n to infinity and then, determine whether each series converges or diverges. Then, students determine the first three non zero terms of the Maclaurin Series for a function.
In this graphing functions worksheet, students solve and complete 16 various types of problems. First, they evaluate each of the limits provided. Then, students graph each of the functions and their asymptotes as given.
In this Calculus worksheet, 12th graders are provided with practice problems for their exam. Topics covered include limits, derivatives, area bounded by a curve, minimization of cost, and the volume of a solid of revolution. The four page document contains seventeen multiple choice questions. Answers are not included.
In this calculus worksheet, students find the derivative of a given function, evaluate limits, and integrals, and find the area of a region. The one page interactive worksheet contains eight multiple choice questions and is self checking.
The typical introductory environmental questions are asked in this two-page worksheet. Emerging ecologists define populations, limiting factors, carrying capacity, and trophic levels. They analyze a population graph and consider the impact of humans on the biogeochemical cycles. Give your middle school or high school life science class these 20 questions to answer for homework.
Pupils explore and practice the concepts of the limit of a function, approaches of an arbitrary constant and functions of infinity. They investigate the vertical and horizontal asymptotes of a rational function, graphically, numerically and symbolically.
Students are introduced to stoichiometric relationships in chemical equations with a Trail Mix activity before performing a lab to reinforce stoichiometry. Students complete the unit with a lab about limiting reactants in chemical reactions.
In this college level calculus worksheet, students evaluate the given limits or show that the limit does not exist. Students determine the derivative of the given functions. The two page worksheet contains twenty-six problems. Answers are not included.
Students explore the success of members of racial and ethnic minorities in the business world through discussing a related New York Times article. They interview successful people in various professions who would be considered minority.
Students examine the issue of tribal sovereignty for Native Americans. Following a mock trial simulation based on the case of Johnson v. McIntosh, they write opinion papers based on the results of the Supreme Court decision in 1823.
Students hypothesize as to the spread of dandelion seeds and its effectiveness. Throughout the remaining lesson plan, students experiment and discuss their results. This usually leads to a discussion of natural selection, populations, exponential growth, etc.
In this college level calculus learning exercise, students determine if a limit exists and if so, find it, and solve differential equations. The one page learning exercise contains seven problems. Answers are not provided.
Work on stoichiometry with this instructional activity, which focuses on the concept of limiting reactants. It provides the concentrations and amounts of reactants in particular situations. Your students then give amounts of products, reactants used, and molarity of the solutions involvedStudents develop arguments for and against campaign finance reform, examine federal and state laws that attempt to limit contributions to political candidates, evaluate various plans for campaign finance reform and formulate their own programs.
Sal continues where he left off with the last video, �Derivatives 1,� by looking at the equation y = x2 and examining the slope of the secant line at a specific point, and again defining the limit as _x approaches zero to get the slope of the tangent line (derivative to the curve) at a specific point. He then generalizes this technique to find the general formula for the slope at any point. Note: This video has similar content to the Khan Academy videos �Derivatives 2� and �Derivatives 2.5� with the �(new HD version)� label, however, the graphs on the HD versions are clearer
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Students can take this course after successfully completing MAT105 Technical Mathematics I at Clinton Community College (CCC) or an equivalent course at another recognized institution. Students may also place directly into this course by scoring sufficiently high on the CCC math placement exam or by recommendation of a math faculty member.
This course is generally taken by students enrolled in technology programs (e.g. Computer Technology, Electrical Technology, Industrial Technology, and Wind Energy & Turbine Technology); however, other students who have met the prerequisites may take this course as a math elective. Successful completion of MAT205 will satisfy the SUNY General Education Requirement for the knowledge area of mathematics.
This is the second course in a two-semester sequence of intermediate algebra and trigonometry with technical applications. Course topics include operations on exponents and radicals, exponential and logarithmic functions and equations, radians, trigonometric functions of any angle, sinusoidal functions and graphing, oblique triangles, vectors, complex numbers and their applications, inequalities, ratio and proportion, variation, and (optional) an introduction to statistics. If time permits, a brief intuitive approach to calculus will be covered. The use of a graphing calculator is required for this course to further the exploration of these topics and their applications. Near the end of the course, students will complete a comprehensive, departmental final exam.
(If you have the textbook listed above, you should review chapters 1- 7.)
You can do this from home by selecting any of the aforementioned topics on the math-tutorial websites listed below; there you will find mini-lectures, worked problems, practice problems and helpful tips.
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algebra-based Introductory Statistics Courses. This very popular text is written to promote student success while maintaining the statistical integrity of the course. The author draws on his teaching experience and background in statistics and mathematics to achieve this balance. Three fundamental objectives motivate this text: (1) to generate and maintain student interest, thereby promoting student success and confidence; (2) to provide extensive and effective opportunity for student practice; (3) Allowing for flexibility of teaching styles. Datasets and other resources (where applicable) for this book are available here.
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Learn more with other tutorials...
In all electronic computation environments the equality symbol requires special treatment because of the different roles this symbol plays in mathematical communication (definition, evaluation, equality). In a Mathcad worksheet definition (or assignment), numeric evaluation, and symbolic evaluation (CAS) provide users with a great deal of power in a computational document. This brief video compares and introduces Mathcad's numeric evaluation (=) and symbolic evaluation (->) symbols by comparing results from the evaluation or two simple algebraic expressions.... (Show more)(Show less)
Want more? Boost your PTC Mathcad skills!
Whether you're looking for specific training courses, or a personalized corporate learning program that meets your training schedule and budget requirements, PTC University can help you boost your productivity.
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It would be so if we were told that books in each branch are identical. But that's not our case, for example, out of 2 math books one could be on algebra and another on arithmetic thus they can be arranged within math branch as {algebra}{arithmetic} or {arithmetic }{algebra}.
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Short-cut math
Clear, concise compendium of about 150 time-saving math short-cuts features faster, easier ways to add, subtract, multiply, and divide. Each problem ...Show synopsisClear, concise compendium of about 150 time-saving math short-cuts features faster, easier ways to add, subtract, multiply, and divide. Each problem includes an explanation of the method. No special math ability needed 0486246116 Acceptable condition books may have...Fair. 0486246116
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Concentration in Elementary Mathematics Education
Learn more about mathematics! Gain a deeper understanding of mathematics and how it can be conceptualized in elementary school. These courses are designed specifically for Elementary Education majors. The program consists of 15 hours in mathematics. After you take MATH 151 and 152 (Elements of Mathematics I and II), you select nine hours (three courses) from the courses below. Completing this concentration will be indicated on your diploma and will be an excellent addition to your resume!
MATH 471: Basic Concepts in Algebra
Learn how algebra can be thought of in interesting ways, with hands-on activities.
MATH 481: Special Topics in Mathematics
Special topics in mathematics, relevant to elementary and middle school education.
Notes:
Testing out of MATH 151 or MATH 152 by the exemption exam does not count toward the concentration. An additional course from the above courses would be taken in this case.
The prerequisite for the courses listed is successful completion of MATH 152 or exemption.
A maximum of one course passed with a grade of C or better (above MATH 101) may be used as a three-credit substitution with the approval of the Chair of the Elementary Mathematics Education Committee. A substitution should be cleared before enrolling in any concentrate courses beyond MATH 152.
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books.google.com - With an emphasis on problem solving, this book introduces the basic principles and fundamental concepts of computational modeling. It emphasizes reasoning and conceptualizing problems, the elementary mathematical modeling, and the implementation using computing concepts and principles. Examples are included... to Elementary Computational Modeling
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Math "Head Start" Workshops
Tunxis Community College Academic Support Center offers Tunxis students who are planning to enroll in Pre-Algebra, Elementary or Intermediate Algebra the opportunity to get a free head start in math before the stress of the semester begins.
You will refresh your memory on the foundations of the course, and learn key math study skills. This is your chance to ask the questions that have always plagued you about math.
Basic Math
The session is designed to prepare you for MAT*085 Pre-Algebra and Elementary Algebra by refreshing your memory on key concepts like:
Adding and Subtracting
Multiplying and Dividing
Decimals and Fractions
Positive and Negative Numbers
And more
When?
Sign Up for a Basic Math Refresher Workshop
If you have registered for MAT*085Elementary Algebra
The session is designed to prepare you for MAT*094 Introductory Algebra, MAT*095 Elementary Algebra Foundations, or MAT*139 Elementary & Intermediate Algebra Combined by refreshing your memory on key concepts like:
Integers/ Fractions
Combining Like Terms
Word problems
And more
When?
Sign Up for an Elementary Algebra Workshop
If you have registered for MAT*094, MAT*095, or MAT*139Intermediate Algebra
The session is designed to prepare you for MAT*137 Intermediate Algebra by refreshing your memory on key concepts like:
Fun with polynomials
Laws of exponents
Linear Equations
Word problems
And more
When?
Sign Up for an Intermediate Algebra Workshop
If you have registered for MAT*137 Intermediate Algebra then you can sign up for this workshop by emailing Adam Woolford at AWoolford@tunxis.edu or by calling 860-255-3583. Please indicate which workshop and on which day you would like to attend.
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Algebra and Trigonometry : Graphs and Models -Text Only - 4th edition
Summary: The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class
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Numerical Analysis, 9e
Written for students, Numerical Analysis provides a comprehensive introduction to the theory and application of modern numerical approximation techniques. The book contains examples and exercises that help develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. Topics include numerical linear algebra, initial-value and boundary-value ordinary differential equations, numerical differentiation and integration, approximation theory, and numerical solutions to partial differential equations.
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kdawson posted more than 4 years ago | from the we-can-forget-it-for-you-wholesale dept.
nwm writes "I am trying to refresh my math skills back to the point that I can take college-level statistics and calculus courses. I took everything through AP calculus in high school, had my butt kicked by college calculus, and dropped out shortly thereafter. Twenty+ years later, I need to take a few math courses to wrap up a degree. I've dug around some and found a few sites with useful information, but I'm hoping the Slashdot crowd can offer some good resources — sites, books, programs, online tutors, etc. I really don't want to have to take a series of algebra-geometry-trig 'pre-college' level courses (each at full cost and each a semester long) just to warm my brain up; I'd much rather find some resources, review, cram, and take the placement test with some confidence. Any suggestions?"
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If you can't handle calculus, science isnt for you (4, Funny)
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Re:If you can't handle calculus, science isnt for (5, Interesting)
Oh bullshit. Those are both overt and ridiculous generalizations. First off, many scientists use statistics every day (at the least, much more than "never"). Second, not all scientists use calculus "every day", and many use it almost never.
As a calculus teacher, I can tell you this: you need skills in symbolic manipulation. Your algebra needs to be rock solid before you attempt college level calculus. In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right. My experience = flunked high school math and went back to college 10 years later, and am now working towards a PhD in math.
Re:If you can't handle calculus, science isnt for (3, Informative)
I was in the same situation as submitter. In fact, it was the reason why I switched majors from CompSci - being in a hurry to get a degree in a science and too much bullshit math I'd never use. I'll go back for Compsci when I can learn on my own terms, for fun.
However, you were spot-on about this: Calc 1 is 90% algebra(with 20-30% of the problems involving trig)and you're gonna be fucked if you don't have a good grasp of algebraic manipulation. My recommendation to submitter is to take online calculus(where available) at an accredited junior college and use a computer algebra system to help them through the homework visually, especially with regards to roots and asymptotes.
Constructing Maple worksheets gives one a good step-by-step process for visualizing the steps necessary to solve the problems. Iterative methods like Newton's, Simpson's, Trapezoid rule etc. would come naturally to a programmer.
Submitter - stats is just arithmetic and basic algebra, it's the concepts and knowing what to do with the data that are the hard part. Again get a T.I. and learn all of the functions, there is a LOT of tedium. Don't be afraid of the weird greek variables and big formulae...it's just arithmetic and algebra 1, you will hate it when you take it, but you will love it when you pass it.
Ethanol-fueled
Re:If you can't handle calculus, science isnt for (-1, Flamebait) Insightful)
Really... No business getting a degree in ANYTHING? That's a rather closed and inappropriate (IMO) view. If he's worked in a field for years that doesn't require he use any algebra how's he supposed to keep up with his skills other than doing algebra problems in his spare time? He never indicated the degree he's completing was heavily math-biased or math-dependent. Stats and Calc may be akin to gen-eds.
When you paint such ridiculously broad statements you risk your own image before anyone else's. Informative)
Another thing that you might want to brush up, in addition to those things the parent post mentions, would be trigonometry. A healthy portion of the various calc courses I've taken have used trig identities fairly heavily. It also helps to remember the values of trig functions for common angles. Depending on the college, you may have to be decent at mental arithmetic. My school frowned upon using calculators in class.
Re:If you can't handle calculus, science isnt for (4, Interesting)
I would mod you up if I had any points. Sad as it may seem calculus was where I *learned* trig. For me, trig is one of those subjects that you beat your head against for months and years and one day *POOF* it makes sense. My first semester of college level calculus was were I learned trig. The second time I took that first semester of calculus - man I got it.
Don't forget to brush up on the basics - algebra, trig, analytical geometry as well as your calculus.
goes looking for an old text book just to tinker around with it.......
Re:If you can't handle calculus, science isnt for (2, Insightful)
Practice, practice, practice (3, Insightful)
The parent is absolutely right. You need practice. Actually, you need what Anders Ericcson calls 'deliberate practice'. Solve every example in the book as follows:
Write down the problem. Close the book and try to solve the problem. If you got it right, go on to the next problem. If you didn't get it, look at how the example is solved. Close the book and try again until you get it right. Repeat until you have solved every example in the text.
BTW, Jamie Escalante, [wikipedia.org] , just died. He was the real life teacher who proved that you can teach calculus to just about anybody. They made the movie 'Stand and Deliver' about his life. Ability is highly over-rated. Most people can, as Escalante proved, learn math to quite a high level of accomplishment.
Most people think math is some magic thing that some people just can't get. They are wrong. Almost everyone is wired to learn math. If you are missing some important skills, go back to the level where you were good and start from there. John Mighton points out that most people discover that they have no math ability the same year they have a bad math teacher.;-)
If you want, you can learn math as long as you practice, practice, practice.
Re:If you can't handle calculus, science isnt for (1)
you can't say such a thing without knowing what specialization a person would have. Statistics is the bread and butter of some work, for others just plugging numbers into formulas that have been known for a century or two (my job at national lab was like that for 10 years!), for others the heavy duty tensor calculus or partial diffy-Qs. Same situation in engineering.
Re:If you can't handle calculus, science isnt for (2)
Were did they say they were getting a science degree?
Needing to take a few math courses to wrap up a degree
implies that most of the course work is done. I can't think
of a science or engineering major that would allow you
take the required courses without having completed
calculus first.
Re:If you can't handle calculus, science isnt for (1)
My dad got a degree in a technical field--CS or something related, IIRC--and he never even had to take a calculus class at all. He took classes overseas while in the military through UMUC [umuc.edu] . It does happen.
Re:If you can't handle calculus, science isnt for (4, Insightful)
As a scientist I learned a long time ago not to make general and unsubstantiated claims like "No matter what kind of scientist you plan to be, your knowledge of calculus will be essential." As a practicing molecular geneticist and cell biologist I use statistics quite often. I cannot remember ever having to (directly) use calculus in the last 20 years for any of my research. I really enjoyed all of the calculus (and linear and set theory and...) that I took a long time a ago. When I look back at it what I really got out of all my math classes (and O-Chem too for that matter) was the the knowledge that I could learn anything I really set my mind to - if I have to.
Re:If you can't handle calculus, science isnt for (1)
If you had to do any linear regression or error analysis, knowledge of statistics is important (e.g. being able to answer questions like "Is this a good datapoint or an outlier"). And Calculus is used to derive the formula for linear regression. I didn't touch it since I was an undergrad, but I still know and can use it. My sister-in-law who got the same B.S. in chemistry asked me why I remember this stuff when she was studying for a nursing degree. It trained my mind. Being able to do algebraic manipulation should be send nature to you. Do whatever you need to do to learn that cold. You'll need it for calculus and statistics.
Re:If you can't handle calculus, science isnt for (-1, Flamebait)
Why do I never have mod points when I need them . . . good points all around. I mean, calculus is the core of our understanding of change. Without calculus, you might as well just things "improved" or "declined" and call it at that. And stats is pretty useless, especially in light of the fact it exists mostly to provide the cover of math to people who wish numbers weren't being used against them.
Re:If you can't handle calculus, science isnt for (4, Insightful)
No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics
This has to be about the worst piece of advice about a science education I've ever seen. Like anything, it depends. Calculus is extraordinarily useful to someone in physics, but less so in biology. Statistics is insanely important in an experimental science (actually it's insanely important in just about any science I can think of). Hell, statistics should be a mandatory class taught in High School. It's far more applicable to everyday life than trig is.
Re:If you can't handle calculus, science isnt for (0)
Another working scientist PhD here. Unless you are going to be involved in hardcore theoretical physics or math work then calculus won't crop up very often. However, you DO need to know what it means and how it works - software solutions generally can do the hard yards after that. Statistics crops up a LOT more often and that really pays off.
Just my experience guys.
Re:If you can't handle calculus, science isnt for (1)
That's rather amusing. What I've noticed is that in the life sciences, it's very rare to see someone who didn't struggle with physics and calculus. Conversely, statistics are used all the time. There are two main reasons for this. First, biology is more memorization and less mathematical, and requires a different skill set than math or physics. Second, biology is messy, most numbers are inexact, and everything follows a normal distribution.
That said, not being proficient in math means that you'll also likely struggle with statistics. I've heard estimates that more than half of research articles in the life sciences have at least one statistical error. When I say "everything follows a normal distribution", that's because everything is assumed to do so. I have yet to see a research article actually verify or check to see if that assumption is true. Last year I read a paper concerning some high profile discovery in medicine that actually reported a negative p value (reminder: probabilities range from zero to one).
Re:If you can't handle calculus, science isnt for (5, Insightful)
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Are you wooshing me here?
Having an understanding of what a derivative or integral of a function is a good insight to have, no doubt.
But I would argue that statistics is much more broadly applicable, and extremely important for a clear understanding of scientific discourse and all the 'facts' that the poster will encounter.
In reply to the original query, what you're going to need to do is a lot of problems. You need to look at this like getting in shape--you can't do it overnight.
I returned to college after about 5 years off and needed to take placement exams myself. Turned out the test allowed using a Ti-89. I cheated myself out of really 'placing' myself by being able to approximate/calculate all the multiple choice answers and placed highly.
After a few attempts in the classes I was placed in, in the end, I re-took precal and calculus.
I could have avoided that if I had actually done a large volume of problems rather than skimming some books and looking at the answers and deciding that it was 'easy enough'.
Never look at the answers of problems until you try them. Once you know the right answer, you convince yourself the problem was easy and that you didn't need to do it. This will fuck you over in the end.
Find an approach to doing math that makes it enjoyable for you. One thing that helped me a lot was getting a large whiteboard. I find I enjoy doing math more pacing back in front of a board and whatever else comes along with doing work on a board rather than a piece of lined paper. Chalk would have been better.
Lastly, ignore the assholes here who are going to berate you for not knowing what they think is simple, obvious knowledge. Math is rife with 'tricks' and non-intuitive methods to solving problems that come through experience. Someone who had a good experience with math through school and went straight into college is not going to understand your position.
Good luck to you, and if you really want this, do problems and problems and more problems. Put on some music you love and shred through a book or two. Get help at local colleges. Bribe a friend to help you study, or just hire a tutor.
Otherwise, you're going to end up doing it by taking the classes (as I did). One way or another, you have to do the work.
Re:If you can't handle calculus, science isnt for (0)
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Always without a calculator. (4, Funny)
It's essential that he pass calculus I, III, III and Diff EQ without the use of a calculator. Just in case we are bombed back into the stoneage, he wont have to worry about losing his job as a scientist.
Re:Always without a calculator. (5, Insightful)
"Bombed back to the stone age" is best regarded as just an expression. The iron age is here to stay, no matter how much civilization declines. Even if we forget how to smelt iron ore, there would be billions of tons of refined iron lying around in abandoned machinery, buildings, and such.
Re:Define: "a few math courses to wrap up a degree (4, Informative)
I have gone through those at MIT, just for fun. I also found that Khan Academy [khanacademy.org] was really interesting and perhaps is easier for some. Strang at MIT is awesome and also the courses at Yale are good.
UCLA has some great courses too. science and magic [academicearth.org] was very informative. It doesn't hurt that some of the profs are also quite entertaining.OR science and magic on youtube [youtube.com]
Engineering Math by Stroud (5, Informative)
This book uses programmed learning that goes step by step through everything you will need and more. It is designed for self study. There is also a sequel book that goes into some much higher stuff. I used just this book as preparation for classes requiring calc 3 as a prerequisite.
Why? (4, Insightful)
If you haven't needed a degree or calculus in 20 years, why bother now?
If you're job hunting, your time would be better spent making yourself relevant to current employers or starting a consulting business than trying to match your calc and trig skills with a recent grad and get a degree.
A degree is a nice "filter" when hiring new applicants, since it proves that they were able to deal with BS for at least 4 years, however with 20 years of actual job experience, you'll do much better off trying to differentiate yourself from the recent grads than you will if you try to "look better on paper."
That said, if you want to do this just because it's "unfinished business" lots of community colleges have entire departments dedicated to getting us old folks "up to speed". Just stop by and talk to someone.
Re:Why? (2, Interesting)
If you haven't needed a degree or calculus in 20 years, why bother now?
In case you haven't realised it, there is a recession going on, a -lot- of people are either unemployed, their spouse is unemployed or they need a way to secure their job. Rather than doing the rational thing of looking at productivity, most businesses hire and pay based on education. If his wife lost her job and he was expecting the income, the only way he can get a raise to keep up his standard of living might be through a degree.
Most degrees are completely useless when done for a raise, but, money is money.
Re:Why? (1)
Ever spend some time in a company? Generally the people who are paid the most do the least amount of work. It is generally the people with a bit of college doing the bulk of the work while the people with the highest forms of education are sitting at their desks doing nothing.
Re:Why? (1)
Sometimes a degree is useful when you want to leave one area of his career and enter another. For instance, perhaps the guy has been doing field engineering all this time, but now wants to do design? Maybe he's sick of working/running a lab, and instead wants to create and run the projects?
Re:Why? (2, Interesting)After 20 years, an MBA would be really useful. After 20 years of not needing them, calculus and trig are a waste unless the OP is trying to switch careers or just wants the satisfaction.
FWIW, it's much more profitable to go into consulting and do/manage whatever it is that you're good at and happy doing, than try to maintain a dead-end job as one of the "cogs." Businesses are much happier to pay someone a good rate for services that they need, when they need them, as long as the consultant will happily vanish when the need vanishes.
Some sites I've come across (5, Informative)
Helpful handouts [germanna.edu] from Germanna Community College's tutoring Center. (I used to work there a few years ago; these resources are not only helpful, but free.) Drexel's Math Forum [mathforum.org] (full disclosure: I'm a current Drexel employee and student -- but the Math Forum strikes me as pretty cool.) Project Euler [projecteuler.net] (more oriented toward programming and numerical methods, but interesting site for developing your math skills. The problems range from not-too-hard to mind-boggling.) Purple Math [purplemath.com]
Re:Some sites I've come across (1)
Interestingly enough, I used to take a handful of classes at Germanna. To add to the list, I would say that Wolfram Alpha can be helpful, because it can be used to break down more complicated integrals and derivatives into steps when you don't understand them. Just don't become dependent upon them. Also, one thing that can be helpful is to go to Yahoo Answers and answer math related problems. Break everything down into steps, explain the theorems needed, and bask in the knowledge that teaching is a good way to learn. By breaking things down for people who may not have a good understanding of math, you will help build up your own understanding too. I actually used this while taking various Calc classes to help practice what I knew, and help break down how exactly I knew it and thought about it.
Hard work should do the trick (3, Insightful)
Most text books have practice questions for each chapter, and some answers in the back. Why not just work through some of those on your own? Math is the kind of subject that you can only learn by doing problems, so I don't think there's any shortcuts. But I suppose if you work on problems, it's nice to have a teacher to help if you get stuck, but perhaps a reasonable substitute would be forums.
CC (1)
Just do Community college summer sessions or something similar, should be enough and they only cost like 60 bucks a class. Taking the college level calc classes would be good too at CC unless they are upper division differential equations or something as those are not offered.
Re:CC (1)
I second the community college courses, but you might need to sift through till you get a good instructor. I lucked out in the ones I have had so far have been able to explain things quite well and have good homework polices. $60 a class is unreal though, mine cost about $350 per class.
Re:CC (1)
I was going back to school to become a teacher. In so doing I had to take a Trig course. I did so online from my local community college. It really refreshed my math skills (that were ~20 years old).
Keep in mind I had taken through Series and Diff Eq. in college, so I had mastered the material previously. (Don't ask why I needed trig. in spite of having had the upper level courses. Just a magic hoop to jump through).
-Chris
Re:CC (1)
Don't ask why I needed trig. in spite of having had the upper level courses. Just a magic hoop to jump through.
In high school, I had that same sort of problem. I moved from one school system where you took World History in two parts, one in 8th grade (middle school) and one in 9th grade (high school), to one where the two parts were pushed up a year. Despite having completed both classes successfully, they made me retake history part I, because they just didn't trust that I learned anything. They also made me take the standardized test for the second history class, which I passed with a perfect score on, making their theory that being taught something a year earlier isn't good look a little silly.
Krzysztof Wilczynski (4, Informative)
Keith,
I would start with YouTube. Crazy as it sounds, but there are many free training videos there. Especially, look up channels maintained by the universities like i.e. MIT or Yale, etc etc. They have recordings of lecture sessions available for free to watch, of course. And some of them are of finest quality. Anyway, that is just a start...
Good luck,
KW
A Bit of Advice and a Few Suggestions (5, Insightful)
I don't know how bad you want this but I can tell you that nothing feels better than finishing something you started even if it comes two decades later.
What you're mostly going to find in these replies are codices. Not teaching. Not knowledge. You're going to get information sources. What you do with those sources, that will be the teaching, the learning and the progress. No one's going to help you get your math back but you. You're going to get static nonliving information and it's going to be up to you to bring that alive. Frankly, on your part it's going to require the will of a volcano otherwise I suggest a tutor or precalculus class.
This material could conceivably be studied by a student on his or her own, but this seldom works out. Students tend to get stuck on something, and, having no goad to keep them going, they try to get past it with decreasing energy, and ultimately develop mental blocks against going on. Having an organized course prevents this by forcing them to face obstacles like exams and assignments.
If you attempt this and get stuck, as is almost inevitable, you could try emailing us and we can try to unstick you.
Did you catch that last part? You're going to need help. Whether it's bribing your nerdy friends with cases of beer or Star Wars Galaxy Series Five collectible card packs (*cough* *cough*) you are going to need guidance at certain points in time. Don't be afraid to ask those around you or -- and I recommend this only in dire cases -- dressing up like a student and rolling into your local university asking to see the precalc professor for help.
Your codex might be Wikipedia [wikipedia.org] . Your codex might be Wolfram's MathWorld [wolfram.com] . My codex sits three feet in front of my face as I type this. My codex (and this is purely personal) Bronshtein et al's Handbook of Mathematics [amazon.com] . The binding is acceptable. The paper is not the greatest. The content is priceless. This is not a teaching device. This is my starting point. If I were you my ending point would be at my college's library pouring over all calculus textbooks. The great thing about this starting point is that I like how it lays out all the starting points leading up to that starting point in case I need to start backwards. Another great thing about this particular resource is that it has nearly everything imaginable and is well organized. The bad thing is that it costs $71.97. I think I paid $60 for mine but either way it's not free like Wikipedia.
I don't know where you are comfortable starting from but if I were you I would simply research what your learning institutions pre requisites are and spend your free time now acquiring their books and notes in order to make sure you have them covered. All of my old University of Minnesota syllabuses are online [umn.edu] although I cannot find the Math department equivalent (aside from the registration listings).
If you could name your courses, I'd suggest books like The Annotated Turing [theannotatedturing.com] which has been a page turner for me and actually starts with basic set theory to work up to automata. I'm guessing you're aiming for more Multivariable and Diff Eq type stuff. Let us know what the courses are and perhaps more human readable works can be suggested that aren't as laboriously mind numbing as reading a codex would be.
Let me google that for you... (0)
I've been studying for the FE exam (Fundamentals in Engineering) and bought the Lindeburg FE Review Manual. It has a lot of explanation and practice problems, but includes a lot more than just math (thermodynamics, physics, etc.). I bet there are similar review manuals for just math though. You could also pay for a tutor, I've seen adds on craigslist before.
Go to your public library (1)
and check out all of the relevant math textbooks. Make sure there are exercises for each chapter for which answers are provided somewhere in the book.
Then, read the chapters, and do the problems. Keep doing the problems until you get every . single . one . of . them . right and you understand what you've previously done wrong in each case.
Pour over it until you really understand the relationships between the quantities.
It is very hard work, but there is no shortcut to understanding math and science, and if you don't understand them, you'll never be good at them, even if you manage to solve a few problems using memorized patterns.
Cheap, easy classes (1)
My advice is go for cheap and easy classes that count for your degree, especially if the classes are useless for your job (as most will be) try taking them at a community college, or see if a "degree mill" offers the course for cheap that will transfer. Many universities will take community college or other sub-par classes if they are for general education or basic requirements. Now, if you are, say, a biology major, taking all your biology classes through a community college might not transfer, but taking math classes should.
Motivation (4, Insightful)
In my experience in school, if you are motivated to pass, you will find a way to pass (most of the time). But if you are motivated to learn, passing the class will come as a pleasant side effect. Not knocking your stated intentions, but approach this as a learning experience, a thoroughfare in self-enlightenment, and you will reap the test-score rewards.
Re:Get a real life tutor (1)
I concur. Through high school I missed out on Geometry. When I got to college and started Calculus the prof asked if anyone had not had Geometry and Trigonometry, so I raised my hand. He tutored me for a few hours and I was good to go. Much of geometry and trig is taking the time to prove the various relationships. I just had to accept that they were correct, never went through the pain of the proof process. One could argue that I missed something valuable, but it has never come up in 30 yrs of working as a scientist.
I attended a small liberal arts college and the professors were all about teaching. My prof was a very good teacher, so that may account for his skill in getting me up to speed. So try to seek out the best teachers (small colleges, maybe community colleges) and pay for a tutor, these profs can always use the cash.
I agree with an earlier post that I have used calculus rarely (and just went to the book to look up the integration/ differentiation rules). On the other hand in the last 10 years the use of statistics has really jumped in industry (I am a chemist/mauf engineer not a programmer) with Six Sigma and the like. So again you don't need to learn all the proofs behind the statistics, but you need to know how to run software for analyzing the data and what the results mean. How to run a DOE, how to plot an M&IR, how to use ANOVA to prove that a statistically significant exists/doesn't exist with data sets.
Your mileage may vary, since you might be in a vastly different arena. And of course there is the internet and various web sites where you could get help if you get in too deeply.
MIT Opencourseware? (3, Informative)
Dunno about college placement tests, but to start thinking about maths in general there's nothing like just buying a couple of books and going at it (but make sure you have the answer booklet/solutions are in the back of the book). If you're feeling a little panicky you might even want to start with something really un-threatening ('Statistics for dummies' exists for that). You might want to see what the standard textbooks would be for the courses that are prerequisites for the ones you're looking to study, and perhaps ask which areas you would be expected to be comfortable with.
As regards an online tutor, depending on whether you currently live near a college/university/miscellaneous site of higher learning, you might want to see if there are any postgrads in applicable subjects who are willing to tutor. In my experience online tutors are seldom worth half as much as talking to a real live actual human being, and they are usually more expensive. YMMV - especially if you are extremely busy an online tutor may actually suit you better than scheduling another real live person into your week.
Sigh... (3, Insightful)
It's not your fault; it's the structure of the educational system. You
are clearly not interested in mathematics, since you just want to cram
and pass some test. You don't specify exactly for what you need
mathematics, but I'm guessing it's for some other thing, possibly
something computer related.
It's a big lie that you'll ever use calculus for anything except for
specialised degrees (and if you were to use it for anything you
personally would want to do in your future, you would already be
interested in it). It's also profoundly strange that calculus seems to
be pinnacle of mathematical education if you're not going to go on to
study something like mathematics itself or physics.
To put my frustration another way, why doesn't anybody ever ask
similar questions for sculpture, or Schaum's Outlines on Basket
Weaving or all the other myriad useless things we humans do for our
edification? Why is western society obsessed with mathematics, deluded
into thinking it's useful in general, and why are people so stressed
over learning this useless and dryly-presented subject? Why aren't you
required to achieve a certain level of chess expertise before you can
complete a computer science degree? A lot of early computer science
was concerned with chess playing, let us not forget!
It's pointless. It's pointless to cram for exams about subjects you
don't care about in order to satisfy requirements you don't genuinely
need.
My recommendation is, are you really interested in learning this
stuff? If so, just spend hours and hours in your local university
library in the math section browsing books you're interested in. If
you're not really interested, go grab some Schaum's Outlines or the
Complete Idiot's guide or whatever, and use that to pass whatever
bureaucratic and pointless requirement your educational institute
imposes before you're allowed to study what you really want to study.
Re:Sigh... (4, Informative)
Why is western society obsessed with mathematics, deluded into thinking it's useful in general, and why are people so stressed over learning this useless and dryly-presented subject?
Math is useful in general. And western society doesn't just stress about learning math. An even greater number are probably stressed about passing english tests [ets.org] . Society thinks language and math are important to education; your basket-weaving and sculpture not so much. I personally don't see the problem with this.
Re:Sigh... (0)
Many mathematicians have thought about the prestige of mathematics. IIRC some big name (Kolmogorov? Arnold?) was writing about how maths-fanaticism in France allowed under-10-year-olds to engage in conversations like "Q: What is 2 + 5? A: It is 5 + 2 of course."
The problem is that if you don't do this, then no maths will be learned by anyone, which is a worse outcome.
Re:Sigh... (4, Informative)
I *HATE* math, but I use it every single day, and in the areas I'm known for, I can do the math needed...mostly in my head. I've also found that as I've tried to branch out of my areas of expertise, that I can't rely on the few areas of math that I know fluently, because I'm starting to bang my head against the ceiling.
For instance, I took a few basic undergrad courses recently (I have a masters in psychology), and I couldn't remember the damn quadratic equation...I could get the answer just fine -- if I wanted to spend 15 minutes solving it (or as I did, write a quick plot app on my laptop to show the answers figuring it out computationally as opposed to mathematically)...and it was only after one of my twenty-something classmates looked at me and said Dude, Why Don't You Just Use The Quadratic Equation that I realized how much I had forgotten (I had no use for math 20 years ago and slept through this).
It is funny how knowing the simple concepts can make your life simple. Anyone can brute force just about anything.
If you don't want to do anything science based...and this includes almost any social science even if people think these are not real...or any advanced art (I have a friend that does weavings, and to get what she wants, and for the patterns to work out in real life, not just paper, she needs to know math to get these to work)...math is the basis for all of this. Oh and the chess algs? it is all math...pretty advanced math...it isn't chess these guys were after...it was computational mathmatics to attack a human problem.
This summer, I am signing up for a 100 level math course and getting the basics back again...I wish I would have done it before...it sucks that I can get results from Mathematica or SPSS, but I can't do simple algebraic equations. You might not think it interesting or necessary, but then again, I can't tell if you are being serious or if your humor is just VERY dry...if you are serious...wow...
Always been a pet peeve of mine (1)
I was told how much math I'd need since I wanted to get in to technology. Math teachers always kept on about how important it was. Well, they are dad wrong. I need a good understanding of arithmetic, and some basic algebra is also useful. Past that, I use nothing. Had I stuck with CS, linear algebra would be good (since a lot of programming relates to it) but certainly not calc. Knowing calc is kinda neat, it allows me to understand how some things are done, but they aren't things I need to do, a program does them for me.
We really need to refactor how much of what subjects we teach people. Math is one in particular we need to get real about. I think it is a leftover of the red scare, the "Oh my god the Soviets will crush us technologically all our kids have to be math whiz kids!" That was dumb then and even dumber now. Trying to cram more math down the throats of every person does nothing. It doesn't turn someone in to a brilliant engineer. The kids that love math, well they'll discover that by having math taught to them. That love should then be nurtured and they should be taught all they can hold. The rest? Teach them what they need to know and leave it at that. What that is will vary, an engineer will need more and different kinds than a sociologist, but teach what is needed, don't just teach math for math's sake.
We should be focusing more on presenting a well rounded education, particularly at lower levels. Expose kids to a LOT of different things. Why? Because you want them to find the thing that clicks with them, the thing that they are interested in. Maybe it's math, maybe it's computers, maybe it's drama, maybe it's biology, whatever. Expose them to a lot, let them learn about all kinds of things, and then they are in a much better position to choose what they want to learn more about during secondary education.
Of course you need to include things that everyone needs to know. English is very important as all jobs demand communication, some math is for sure important, etc. But teach the amount needed and useful, don't just teach more for the sake of teaching more.
In university, this should be even more the case. Universities need to evaluate their degree programs and say "How much of what non-degree material does this really need?" Math is NOT degree material for CE or CS. It is necessary to understand some of the degree material, but it isn't actual material relevant to the degree. As such you should be teaching the level needed. You shouldn't say "Well this is a math heavy field so make them take 6 math classes." No, it should be "These are the kinds of mathematics necessary to properly understand the things they are being taught, as a result they will need to take math course A before class X and math course B before course Y and so on." Maybe that ends up being a lot of math, sure will be for some degrees, but make sure it is because it is needed and useful. Don't insist CS people take calc because computers are about math.
Schaum's outlines (1)
It depends on your overall plan whether you need new dead-tree books. But the Schaum's outline books are good, with plenty of worked problems. Look in a college bookstore or do a web search on Schaum's outline .
A Very Good Survey (3, Informative)
If what you are looking for is a way to get your mind back into "math mode", I'd suggest one book that I have used, both to refresh my memory and to read for pleasure since I was an undergrad ~40 years ago.
It's called What is Mathematics?, by Richard Courant and Herbert Robbins, in the 2nd edition (which I have).
I like the book because it is geared to an intelligent adult reader; it doesn't assume much technical math knowledge, but it gives (IMHO) an excellent overview of the concepts through calculus. It has exercises, too.
Just do it! (0)
I'm on my second college level calculus course for a computer science degree, ten years after graduating with a liberal arts degree. I took calculus in high school with no problems. My advice is not to be too worried about it; just take the class. It'll take you a few weeks in class to catch up on the algebra, but it will come back to you. You'll have 20 years more experience than your classmates learning things.
Also, chances are you had your butt kicked the first time 'round because you weren't spending enough time asking the professor to clarify things you don't understand, doing homework, or studying. I will stare at my textbook and reread a section until it makes sense. Sometimes things are easy and sometimes I spend a few hours more than I planned.
I'm at a top tier university and am having no problems so far getting A's in Calculus... while working full time.
ThatQuiz.org (1)
But I like to go back there from time to time and run through various tests just for "the fun of it." I'm not only surprised by the simple things I've forgotten over the years, but I'm also surprised at some of the things I never use but still remember.
The Teaching Company (1)
I would go to and try out their 'joy of math' class, or try some Math Tutor. The joy of math is a 24 lecture series, each is 30 minutes long, and it goes all the way from basic math to basic integral calculus. That will teach you all the theory you need. Then the Math Tutor calculus classes will easily fill in the exacting skills you need.
Or, if your not into lectures, I would highly recommend the textbook 'Calculus 6th Edition' by James Stuart. It is in easy to understand language and goes from the beginning of calculus 1 to the beginning of differential equations in the last chapter.
Also, if you want to understand 3d space in a calculitic way, just buy matlab and play with surfaces for a few weeks.
Really, I think calculus is easy if you understand the concepts, the rest is just bookkeeping. But spend enough time playing with that bookkeeping, and beautiful patterns about the very nature of the world in which we live arise, and you will be flabbergasted. The importance of numbers like pi and e become obvious, and all the frustration seen in math is gone.
The practical use is also great, besides the enhanced understanding of the world. You might not use Statistics and Calculus every day, but the concepts will change the way you see the world, and how you think. When you run into any kind of issue or problem, your tools to deal with it will be far better than before. And what once kicked your ass will be kick ass to practice.
Try not to cram to much, reading a calc textbook or watching some of those classes will let you understand what you are doing, so you won't have to worry about trying to cram.
Hope I helped, just remember to give yourself the chance to learn. Without learning, what do we have after all?
Bad textbooks, bad teachers. (1)
I don't know about other people, but it seems like the biggest inherent flaw is not a lack of resources for math, but rather that people generally don't know where to go.
Up until right now, I just used [purplemath.com] , and had no idea that other resources existed so extensively.
I enjoy math, but I'm also an unmedicated ADHD child - lectures frequently just bounce off of me; and attempting to learn from a course assigned textbook is a joke... these are designed around a lecture format that doesn't work perfectly for everybody. Nothing is more frustrating than hitting a wall due to not fully processing a lecture, and having the textbook be worthless ($180 worth of worthless, too.)
I think the best suggestion is just to wander your way through some of the recommended books and sites and not force it; as others have mentioned, if you're actively enjoying the learning experience, it'll just flow naturally.
Or, it'll fail miserably... either way, progress (not necessarily forward) will be made!
Calculus (1)
Really for me the main trick was understanding exactly what a derivative was. It sounds obvious I know but you really have to get your head wrapped around exactly what it's doing and the basic idea of summing an infinite series of slices. Do some mental exercises like the speed of a car and how a speedometer works, imagining the rate a pool of different shapes would be filling up as the water rises, etc...
Once you get the concept clear and what it means the rest is just memorizing the various transforms with the Sin, Cos, etc... and getting in good practice doing it. Then years later when you've forgotten all of those (as I have) and you run into a calculus problem you'll at least recognize it and know what the basic formula is, then use a TI calculator or whatever.
The Princeton Review (2, Informative)
When I had to do well on the GRE before entering graduate school, I used the prep book from The Princeton Review and kicked the hell out of the math section.
They have prep books for SAT Math 1 & 2 which covers (ironically) more complicated stuff, and I think that's what you really want. For getting your mind back in mathematics mode, I'd pick up both of those (twenty bucks each or less) and work through all the exercises you need to in order to jog the memory banks. Start with the GRE math and good luck!!!
For geometry (1)
If you're looking for geometry learning, try to make an asteroids-like game.
It's not too challenging as to turn someone down, but lots of fun and you'll learn how to apply geometry. Specially sine and cossine, which my teachers did a terrible job in teaching what that was all about (only teached transformation formulae, never applying them). I only learnt what it was meant to do when I tried to do a subspace-like game.
Not enough information. (3, Informative)
You haven't specified what kind of degree, and therefore, what kind of coursework is required. Moreover, even the same level of coursework taught at different institutions can vary widely in difficulty. "Undergraduate calculus" at, say, Caltech is nothing like "undergraduate calculus" two blocks away at Pasadena City College. The same goes for statistics.
If your intention is to obtain a degree, the best starting point is to figure out which text(s) are being used in those courses that are required for that degree. This will give you some idea of the scope and level of difficulty to expect. Otherwise, you could end up studying a great deal of ancillary information. Such things may be good to know, but will not contribute to your stated goal.
Regarding your plan to dive right in, I appreciate and understand your enthusiasm but I also think it is misguided and potentially counterproductive. You could very easily make it much more difficult for you to obtain your credits by not reviewing basics beforehand. Mathematics is not a subject that is easily cherry-picked, nor is it amenable to rote learning. It is more like a vast edifice, a tower whose foundations support increasingly complex and abstract concepts. Furthermore, it is a topic which is best learned through actual understanding. For instance, if you understand what integration actually means, rather than viewing it as a mechanical operation on a function, you will find it easier to interpret other concepts that employ integration, such as the calculation of moment-generating functions of continuous probability distributions.
On some level, it's possible to "get by" with simply learning the mechanics of computation and symbolic manipulation. That is pretty much what calculus is (as opposed to analysis). But if you want to make it as easy as possible on yourself, at the very least I advise you quickly review nearly everything at the high-school level, from algebra to trigonometry. Then take a more detailed look at the AP Calculus curriculum; any gaps in knowledge should be readily apparent and immediately addressed before continuing further. From there, you should compare against the aforementioned college coursework and texts.
Success in learning mathematics is not so much about the details of what you know as it is about how to think analytically and abstractly.
Book Suggestion (0)
While the initial parts of the book may be too easy for you, many people have found "Arithmetic and Algebra Again" by Immergut and Smith to be wonderfully helpful. It will help you get back into the habit of doing math (especially algrebaic functions) in an easy, tidy way, and is designed for adults. That should give you a good baseline jumping-off point.
What is Mathematics? by Courant and Robbins (1)
The book "What is Mathematics?" by Courant and Robbins, despite its cushy-sounding name, would be my recommendation. First of all, it's written by two world-class mathematicians. Second, it's not a textbook; rather, it's what you might call a celebration of how awesome math is. If you want to succeed in college math without being miserable, why not try to see the subject as thing of beauty, rather than a burden? This book will definitely help you do that. If you read through the first half of the book (it shouldn't take long) you will have a chance to warm the math parts of your brain back up, and you'll learn some extremely cool shit along the way. (A bit of geometry, a bit of topology, a bit of algebra, etc.)
When you get to the authors' lucid explanation of the main ideas behind calculus, you'll realize that (1) calculus isn't scary, (2) the computations you need to learn how to do are fun, not hard, and (3) everything comes down to a few very intuitive ideas -- it may have taken geniuses like Newton and Leibnitz to come up with them in the first place, but they are part of our common intellectual heritage, not erudite ideas reserved for mathematicians and physicists.
And, although it's not a textbook, there are some exercises which will give you the chance to test your understanding. Again, though, they are fun, not grueling.
iTunes U (3, Informative)
I know it sounds a little weird, but check out iTunes U. There are a lot of courses (many by some very well known academic establishments) including a full library of math and science. Best part is, it's free.
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Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more
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Learn or re-learn the algebra you need to know to solve math problems found on your certification exam or during your daily work. This 8 lecture course will show you how to solve problems and give you plenty of guided practice to master the techniques
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College Geometry A Problem-Solving Approach With Applications
9780131879690
ISBN:
0131879693
Edition: 2 Pub Date: 2007 Publisher: Prentice Hall
Summary: For courses in Geometry or Geometry for Future Teachers. This popular book has four main goals: 1. to help students become better problem solvers, especially in solving common application problems involving geometry; 2. to help students learn many properties of geometric figures, to verify them using proofs, and to use them to solve applied problems; 3. to expose students to the axiomatic method of synthetic Euclidea...n geometry at an appropriate level of sophistication; and 4. to provide students with other methods for solving problems in geometry, namely using coordinate geometry and transformation geometry. Beginning with informal experiences, the book gradually moves toward more formal proofs, and includes special topics sections.
Musser, Gary is the author of College Geometry A Problem-Solving Approach With Applications, published 2007 under ISBN 9780131879690 and 0131879693. Five hundred twenty six College Geometry A Problem-Solving Approach With Applications textbooks are available for sale on ValoreBooks.com, eighty four used from the cheapest price of $78.31, or buy new starting at $112.64
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Overview: Albert B. Bennett, Jr. and L. Ted Nelson have presented hundreds of workshops on how to give future teachers the conceptual understanding ...Show synopsisOverview: Albert B. Bennett, Jr. and L. Ted Nelson have presented hundreds of workshops on how to give future teachers the conceptual understanding and procedural fluency they will need in order to successfully teach elementary-school mathematics. The Eighth Edition of Mathematics for Elementary Teachers: A Conceptual Approach continues their innovative, time-tested approach: an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation. Special features in the text ensure that prospective teachers will gain not only a deeper understanding of the mathematical concepts, but also a better sense of the connections between their college math courses and their future teaching experiences, along with helpful ideas for presenting math to their students in a way that will generate interest and enthusiasm. The text draws heavily on NCTM Standards and contains many pedagogical elements designed to foster reasoning, problem-solving and communication skills. The text also incorporates references to the virtual manipulative kit and other online resources that enhance the authors' explanations and
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A few years ago I gave a review of the first edition of this book, which at the time of writing this review is still available. The new edition is smaller than the original, with a plain no-frills style cover. I have to say I preferred the original, which fitted in with the other Chambers Skills for Life books.
A smaller book means the font size is also smaller, which isn't so good if you have any degree of visual impairment. If you are giving this to someone who is nervous about Maths and is looking for an excuse not to do it, 'the print is too small' may give them the excuse they need.
Here's my original review, slightly edited to reflect my thoughts on the new book and the fact that other books have appeared on the market since it was written.
I bought this as I am an adult literacy and numeracy tutor and wanted a book I could recommend for extra home study to my students - this is an excellent choice. Starting from scratch, the book gives clear, practical examples of numeracy problems and takes the student through them step by step.
The generally clear and helpful although the small print size means that you may sometimes strain to read the labelling on diagrams, for example.
There - or perhaps there are no dedicated numeracy classes in your area - this book is very much written for you.
As a mature student positives of this book are that it was easy reading down to the basics, facts and clear explanations. on the negative the wording was small and handling the book you definitely need a bookmark. Overall a good edition to assist adult learners in numeracy
Excellent, detailed and easy to understand. I am happy i bought this book. I strongly recommend this book for anyone. Whatever your age and level, you can understand this book. Get it for yourself as an adult and for your children that are struggling with maths.
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More About
This Textbook
Overview
Choose the algebra textbook that's written so you can understand it. ALGEBRA AND TRIGONOMETRY reads simply and clearly so you can grasp the math you need to ace the test. And with Video Skillbuilder CD-ROM, you'll follow video presentations that show you step-by-step how it all works. Plus, this edition comes with iLrn, the online tool that lets you sign on, save time, and get the grade you want. With iLrn, you'll get customized explanations of the material you need to know through explanations you can understand, as well as tons of practice and step-by-step problem-solving help. Make ALGEBRA AND TRIGONOMETRY your choice today. This Enhanced Edition includes instant access to Enhanced WebAssign, the most widely-used and reliable homework system. Enhanced WebAssign presents thousands of
Editorial Reviews
Booknews
The authors of this college-level text work from the premise that conceptual understanding and technical skills are inextricable. They emphasize a view of mathematics as a problem-solving art (rather than a collection of facts) that will help students succeed not only in subsequent math and science courses, but in the increasingly technology-oriented career world as well. Based on their own experiences in teaching algebra, trigonometry, and pre-calculus, they include elements such as progressive exercise sets, projects that students can work on alone or in groups, vignettes about interesting mathematicians and uses of math, and examples of real-world applications. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology.
Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is
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When students truly understand the mathematical concepts, it's magic. Students who use this text are motivated to learn mathematics. They become more confident and are better able to appreciate the beauty and excitement of the mathematical world.
That's why the new Ninth Edition of Musser, Burger, and Peterson's best-selling textbook focuses on one primary goal: helping students develop a true understanding of central concepts using solid mathematical content in an accessible and appealing format. The components in this complete learning program—from the textbook, to the eManipulative activities, to the online problem-solving tools and the resource-rich website—work in harmony to help achieve this goal. This edition can also be accompanied with WileyPlus, an online teaching and learning environment that integrates the entire digital textbook with the most effective resources to fit every learning style.
Revised and Enriched Exercise Sets: This where necessary, to assure that they are closely aligned with and provide complete coverage to the section material. Exercises in Exercise/Problem Sets A and B are arranged in matched pairs, but problems are not. Answers are provided for all Set A exercises/problems. Answers are provided for all Set B exercises/problems in the Instructor Resource Manual.
Section Rearranged: Section 2.4 from the 8th edition has been moved to Sec 9.3 in this edition to enrich the coverage of algebra.
Chapter Revisions: Chapter 12 has been substantially revised. Sections 12.1 and 12.2 have been organized to more faithfully represent the first three van Hiele levels. In this way, students will be able to pass through the levels in a more meaningful fashion so that they will get a strong feeling about how their students will view geometry at various grade levels.
Algebraic Reasoning: To further enrich the coverage of algebra, Algebraic Reasoning margins notes have been strategically placed throughout the book to help students see how what they are studying is connected to algebra.
Check for Understanding: To help students be more active when learning the material, Check for Understanding callouts lead students to Part A exercises that are relevant to the subsection they just finished studying.
Analyzing Student Thinking: Problems have been added to the end of the Part B problems. These problems pose questions that students may face when they teach. Many of the problems that were marked with fountain pen icons at the end of the Exercise/Problems sets have been incorporated into the Analyzing Student Thinking problems in this edition.
Author Walk-Throughs: These are audio vignettes that precede each chapter and each section. These brief vignettes help students hear about points of major emphasis in each chapter/section so that their study can be more focused.
Revised Children's Literature & Reflections from Research: These margins have been revised and refreshed.
Revised Website: Nearly all of the Problems for Writing/Discussion that preceded the Chapter Tests in the 8th edition now appear on our Website.
Problem-Solving Emphasis: Features the largest collection of problems (over 3,000!), worked examples, and problem-solving strategies in any text of its kind.
Integrated Technology: Technology and content are integrated throughout the text in a meaningful way. The technology includes WileyPLUS, activities from the expanded eManipulative activities, spreadsheet activities, Geometer's Sketchpad activities, and calculator activities using a graphics calculator and Math Explorer.
Extensive Geometry Coverage: Comprehensive, five-chapter treatment of geometry based on the van Hiele model provides students with the necessary, and often neglected, background in geometry.
Appropriate Topical Sequence: Moves from the concrete to the pictorial to the abstract, reflecting the way math is generally taught in elementary schools.
NCTM Standards: These are referenced throughout in the margin and reviewed at the beginning of each chapter, giving future teachers a good idea of the standards they will be responsible for and the skills that their students will be tested on.
This manual contains chapter-by-chapter discussions of the text material, student "expectations" (objectives) for each chapter, answers for all Part B exercises and problems, and answers for all of the even-numbered problems in the Problem-Solving Guide. --Prepared by Blake E. Peterson, Brigham Young University.
Computerized Test Bank
The Computerized Test Bank includes a collection of 1,100 + open response, multiple-choice, true/false, and free-response questions, nearly 80% of which are algorithmic.
Printed Test Bank to accompany Musser 9th Edition
The Printed Test Bank includes a collection of 1,100 + open response, multiple-choice, true/false, and free-response questions, nearly 80% of which are algorithmic. supplementsENHANCE YOUR COURSE
A research-based online environment for learning and assessment. Learn moreThis manual contains hints and solutions to all of the Part A problems. It can be used to help students develop problem-solving proficiency in a self-study mode. The features include: Hints: Give students a start on all Part A problems in the text. Additional Hints: A second hint is provided for more challenging problems. Complete Solutions to Part A Problems: Carefully written-out solutions are provided to model one correct solution. --Developed by Lynn Trimpe, Vikki Maurer, and Roger Maurer of Linn-Benton Community College.
The activity manual is designed to enhance student learning as well as to begin to model effective classroom practices. Since many instructors are working with students to create a personalized journal, this edition of the manual is shrink-wrapped and three-hole punched for easy customization. This supplement is an extensive revision of the Student Resource Handbook that was authored by Karen Swenson and Marcia Swanson for the first six editions of this book. The Student Activity Manual has been developed so that it can optionally be used with the ETA Cuisenaire Physical Manipulatives Package.ADDITIONAL RESOURCES
A research-based online environment for learning and assessment. Learn more
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This book provides a comprehensive and up-to-date introduction to Hodge theory?one of the central and most vibrant areas of contemporary mathematics?from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular... more...
This Handbook presents the latest thinking and current examples of design research in education. Design-based research involves introducing innovations into real-world practices (as opposed to constrained laboratory contexts) and examining the impact of those designs on the learning process. Designed prototype applications (e.g., instructional methods,... more...
This book is an easy-to-follow, stepwise guide to handle real life Bioinformatics problems. Each recipe comes with a detailed explanation to the solution steps. A systematic approach, coupled with lots of illustrations, tips, and tricks will help you as a reader grasp even the trickiest of concepts without difficulty. This book is ideal for computational... more...
"This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation" Dr. Ian Evett, Principal Forensic Services Ltd, London, UK Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is... more...
Featuring in-depth coverage of categorical and nonparametric statistics, this book provides a conceptual framework for choosing the most appropriate type of test in various research scenarios. Class tested at the University of Nevada, the book's clear explanations of the underlying assumptions, computer simulations, and Exploring the Concept boxes... more...
Bringing together both new and old results, Theory of Factorial Design: Single- and Multi-Stratum Experiments provides a rigorous, systematic, and up-to-date treatment of the theoretical aspects of factorial design. To prepare readers for a general theory, the author first presents a unified treatment of several simple designs, including completely... more...
Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-stepAn authoritative and quantitative approach to modern game theory with applications from diverse areas including economics, political science, military science, and finance. Explores areas which are not covered in current game theory texts, including a thorough examination of zero-sum game. Provides introductory material to game theory, including
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use of general-purpose mathematical software "GPMS" as a major advancement in simplifying simulation procedures for junior level engineering studies. GPMS handles general and specific mathematical formulas and is packed with a vast array of codes to perform many scientific and engineering functions in an interactive mode. In order for the student to interact positively, the numerical examples in the textbook must be converted into an interactive media to support the theory and provide a deeper understanding of the physical phenomena. By this method, the students enhance their problem-solving abilities with minimal programming skills. By using examples, the paper presents an approach to computer-aided problem solving methods for junior level courses. The methods described in the paper have proven to be of value to students studying electric machines and power engineering at Arizona State University.
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More About
This Textbook
Overview
The need for improved mathematics education at the high school and college levels has never been more apparent than in the 1990's. As early as the 1960's, I.M. Gelfand and his colleagues in the USSR thought hard about this same question and developed a style for presenting basic mathematics in a clear and simple form that engaged the curiosity and intellectual interest of thousands of high school and college students. These same ideas, this development, are available in the following books to any student who is willing to read, to be stimulated, and to learn.
"Algebra" is an elementary algebra text from one of the leading mathematicians of the world -- a major contribution to the teaching of the very first high school level course in a centuries old topic -- refreshed by the author's inimitable pedagogical style and deep understanding of mathematics and how it is taught and learned.
Editorial Reviews
From the Publisher
"The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific 'practical' problems but there is much more development of the ideas … [The authors] have shown how to write a serious yet lively look at algebra." —The American Mathematics Monthly
"Were 'Algebra' to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics." —The Mathematical Intelligencer 22, 2004
Excellent and fascinating algebra text.
This text, which is intended as a supplement to a course on high school algebra, delves into topics not ordinarily covered in the high school curriculum. The exposition is remarkably clear and the exercises are well-chosen and often quite challenging. The text covers the laws of arithmetic and algebra, polynomials, arithmetic and geometric progressions and their sums, polynomial equations and inequalities, rational expressions, roots and rational exponents, and inequalities relating the arithmetic, geometric, harmonic, and quadratic (root-mean-square) means. Topics and exercises are chosen with higher mathematics in mind. The reader gains facility in algebraic manipulation while gaining insights into more advanced mathematics. The authors provide solutions to some of the exercises. These are instructive to read for the additional insights they offer into the problem.
2 out of 2 people found this review helpful.
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Paperback
Click on the Google Preview image above to read some pages of this book!
Essential Mathematics for the Australian Curriculum builds on established learning sequences and teaching methods to provide an authoritative and practical interpretation of all content strands, substrands and content descriptions. It also covers essential prior knowledge and includes some extension topics.
The essential foundations of the series:
The three interconnected content strands are incorporated into 11 units of work that can be completed in the school year Let's Start activities provide context and foundation for topics
Every question is grouped according to the four proficiency strands of the new Australian Curriculum: Understanding, Fluency, Problem-solving and Reasoning
Problem-solving and Reasoning questions are included in every exercise
Enrichment questions in each exercise, and investigations, challenges and puzzles in every chapter reflect curriculum aims by extending students in depth
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Advanced Engineering Mathematics - 4th edition
Summary: The computer plays a prominent role throughout the text in generating computer graphics used to display such concepts as direction fields, phase portraits, surfaces and vector fields, convergence of Fourier series, the Gibbs phenomenon, and filtering noise from signals. The author took care to make his presentation of material interesting and the text's format useful and easily read. This edition was reorganized in part to provide a more logical structure and to more...show more fully develop the connections among topics. All of the problem sets and solutions were extensively class tested and checked for accuracy, level of difficulty and suitability. Among the case studies included are an FFT analysis of tidal data and a problem in radioactive waste disposal.
Case studies explore how mathematical models are used to analyze some interesting phenomena.
Fast Fourier transform has been expanded to two sections, and includes applications.
Direction Fields are introduced in Chapter 1, allowing a visual representation of the solution to differential equations and making the subsequent analytic solution more meaningful.
Computer Graphics are used to display such concepts as direction fields, phase portraits, and Gibb's phenomenon, to name a few.
"A Guide to Major Results" is provided as an aid to locating important results.
This edition was reorganized and condensed for easier use with technology; it presents a wider range of applications; and includes a redrawn art program with computer graphics60 +$3.99 s/h
Good
Wonder Book Frederick, MD
Good condition. Highlighting inside.
$7.75 +$3.99 s/h
VeryGood
bnctucsonbooks Tucson, AZ
1997 Hardcover Very good An EXCELLENT TEXTBOOK. Clean, crisp, tight, unmarked pages. Value for the price. Only flaw is that previous owner wrote his name in edges all around the book. Interior imm...show moreaculate. We ship within 24 hours, carefully wrapped. You found it! BNCTucsonbooks ships daily. Proceeds from the sales of books support an endowed scholarship to Brandeis University, Waltham Mass
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Grades
Subjects
Targeted Math Instruction for the 2002 GED® Test
Targeted Math Instruction for the 2002 GED® Test is a focused, 12-lesson curriculum intended for use with test-takers who need to increase their score on the 2002 GED® Math Test in order to earn a GED® diploma. The lessons are aligned to specific targets in geometry, number sense, algebra, and data analysis and probability. Each lesson plan includes content background, video segment(s), practice worksheets, and online practice activities. The creation of these lesson plans was funded by Kentucky Adult Education and created for teacher use in the adult education classroom.
FormulasCoordinate GridLines and AnglesTrianglesRatio/ProportionPercent PlusCentral TendencyExponents and RadicalsGraphs, Charts, and TablesProbability
This lesson plan is one of 12 that was created for teachers to use with their students that need to brush up on their math skills in order to pass the 2002 GED® Math Test.
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than others? Each of these questions could generate many hypotheses, and students can then go on to use Matlab to analyze the data sets they collect in order to evaluate the hypotheses. Some hypotheses do not relate to a biological area and are based on mathematics alone. For example, after linear regression is introduced, students are asked whether this regression can be reasonably used to determine the y-value for an x-value for which there are no data. This leads naturally to a discussion of interpolation and extrapolation.
As each topic is introduced, the instructor includes a brief description of how it relates to biology. This is often done by having a background biological example used for each main mathematical topic being covered, which can be referred to regularly as the math is developed. For example, in covering matrices, the material can be introduced with this example: "Suppose you are a land manager in the U.S. West, and you have satellite images of the land you manage taken every year for several years. The images clearly show whether a point on the image (actually a 500 m x 500 m plot of land) is bare soil, grassland, or shrubland. How can you use these to help you manage the system?" From this, the students develop the key notion of a transition matrix; the professor can then go on to matrix multiplication, and eigenvalues and eigenvectors for describing dynamics of the landscape and the long-term fraction in bare soil, grass, and shrubs.
Attempts are made to include real, rather than fabricated, data in class demonstrations, project assignments, and exams. For example, data of monthly CO2 concentrations in the Northern Hemisphere can be used to introduce semi-log regression, and allometry data can be used for studying log-log regressions. Students are encouraged to collect their own data for appropriate portions of the course, particularly the descriptive statistics section. Scientific journal articles that use the math under study are also provided.
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Mathematics and Technology for
Talented Youth
Welcome!
Mathematics is one of the few
disciplines that teaches us about the power of thought as distinct from
the power of authority. It is not necessarily dependent on our physical
observations of the world, and yet it constantly provides models for
our observations. Such models—usually studied in applied
mathematics—may have relevance in traditional sciences such
as physics, biology, or chemistry. Topics studied by mathematicians,
such as chaos theory or dynamical systems, often serve as models for
economics, neuroscience, or predictors of fluctuations in the stock
market.
Students majoring in
mathematics take courses in the logical foundations of mathematics, the
calculus sequence, matrix algebra, and discrete mathematics. Majors
choose from a concentration of applied, traditional, or actuarial
mathematics. Both the B.A. and the B.S. in mathematics will allow entry
to advanced studies or career opportunities as diverse as the fields to
which mathematics is applied. The metro region of Washington, DC is a
particularly fertile area for related job opportunities, including
consulting, teaching, and government.
About
George Mason
Since it was founded in 1972,
George Mason University has grown into a major educational force and
earned a reputation as an innovative, entrepreneurial institution. Just
minutes from Washington, D.C., George Mason has a growing and diverse
student body and an exceptional faculty of enterprising scholars. At
the center of the world's political, information, and communications
networks, George Mason is the university needed by a region and a world
driven by new social, economic, and technological realities.
Department
of Mathematical Sciences
4400
University Drive, MS: 3F2
Exploratory Hall, room 4400
Fairfax,
Virginia 22030
Main
Phone Number: 703-993-1460
Fax
Number: 703-993-1491
News and Events
Mathematics Colloquium on August 29
The Mathematics Colloquium will meet on Friday, August 29 at 3:30 pm in Room 4106, Exploratory Hall. Matt Beck of San Francisco State University will talk on Combinatorial reciprocity theorems.
Combinatorics, Algebra and Geometry Seminar on August 29
The next meeting of
the CAGS Seminar
will be Friday, August 29 at 12:30 pm in Room 4106, Exploratory Hall.
Matt Beck will speak on
Parking functions and friends.
Applied and Computational Mathematics Seminar on August 29
The next meeting of
the Applied and
Computational Math Seminar will be Friday, August 29 at 1:30 pm in Room 4106, Exploratory Hall. Francisco Javier Sayas of the University of Delaware will speak on Transient tranmission problems with integral methods.
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You are here
Combinatorics: A Problem Oriented Approach
Publisher:
Mathematical Association of America
Number of Pages:
156
Price:
39.95
ISBN:
978-0-88385-710-6
Combinatorics: a problem oriented approach is a book on Combinatorics that mainly focuses on counting problems and generating functions. By restricting himself to an accomplishable goal, without attempting to be encyclopedic, the author has created a well-focused, digestible treatise on the subject.
According to the author's preface, the book is based on lecture notes on a course on Combinatorics taught by the author at California Polytechnic, Pomona, for more than twelve years. The intended audience is Computer Science and Mathematics majors in their junior or senior year or interested scientists, mathematicians, and amateur mathematicians who might want to use this book for self-study. Strictly speaking, there are no prerequisites for reading this book. However, mathematically less sophisticated readers might struggle with some of the terminology and notation. For example, factorials, binomial coefficients, summation notation are all used without definition. The students at Cal Poly Pomona might not experience such problems, but a more general audience might.
Minor complaints
On the reviewer's wish-list would have been a table of necessary definitions and binomial identities. A more formal definition of probability might also be appropriate. In the first problem the reader is asked what is the probability that a five letter word with letters selected from the set {A,B,C} does not contain the letter A, but no definition of probability is given. Such omissions can easily be patched up in class, when there are questions, but they are flaws in a book which intends to be accessible to students and suitable for self-study.
This book is very strong on heuristics (see below), but does not offer any of the proofs or formal definitions that a more rigid course on combinatorics usually includes. At the reviewer's institution the equivalent course is used to introduce proof techniques (especially induction). Thus the book under review would not be appropriate as a textbook for our course.
Strong points
The book is unique in that it moves from questions to the theory. It begins by asking a motivating question that leads one to introduce a basic concept, such as counting with repetition and with order, in the process of finding an answer. Thus, the book is strong on motivation and has a wealth of problems of varying degrees of difficulty. This means that even instructors who would not want to choose this book as a textbook, because of its lack of proofs, might want to choose this book as a problem source. In fact, with adequate coaching to help with some of the notation this book could also be used as a Putnam preparation or for Math summer camp instruction.
Motivated students (especially those on a self-study course) will appreciate the solutions to some problems and the guide as to their interdependence. The choice of topics is excellent. This book is one of the few that treats the Pólya-Redfield counting method and recurrence relations, although the treatment of recurrence relations is somewhat incomplete.
Conclusion
This book is certainly worth the $20 price tag
Ruth Michler is assistant professor of mathematics at the University of North Texas.
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Getting from Arithmetic to Algebra
Balanced Assessments for the Transition
Getting from Arithmetic to Algebra by Judah L. Schwartz
Book Description
The title of this book is Getting from Arithmetic to Algebra and is written by author Judah L. Schwartz. The book Getting from Arithmetic to Algebra is published by Teachers' College Press. The ISBN of this book is 9780807753200 and the format is Paperback. The publisher has not provided a book description for Getting from Arithmetic to Algebra by Judah L. Schwartz.
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Reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This title includes algebraic ideas that are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism.
The new edition of BEGINNING ALGEBRA is an exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The authors have developed a learning plan to help students succeed in Beginning Algebra and transition to the next level in their coursework.
Books By Author Judah L. Schwartz
Brings together leading experts to offer an in-depth examination of how computer technology can play an invaluable part in educational efforts through its unique capacities to support the development of students; understanding of difficult concepts
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This course is designed to introduce the student to the study of Calculus, which, in its simplest terms, is the study of...
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This course is designed to introduce the student to the study of Calculus, which, in its simplest terms, is the study of functions, rates of change, and continuity. The student will learn concrete applications of how calculus is used and, more importantly, why it works. The course addresses three major topics: limits, derivatives, and integrals, as well as study their respective foundations and applications. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Biology 103, Mathematics 101, Mechanical Engineering 001, Economics 103)
This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of...
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This course is the second installment of Single-Variable Calculus. The student will explore the mathematical applications of integration before delving into the second major topic of this course: series. The course will conclude with an introduction to differential equations. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 102, Mechanical Engineering 002, Computer Science 104)
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Series
Lessons: 258
Total Time: 33h 40m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 05/18/2010
Last Updated At: 11/30/2011
This complete series of video algebra lessons should take you through the basics of algebra all the way up to the advanced topics in college algebra. You'll start out with prerequisites and basics of algebra. Then, you'll move on to lessons on equations and inequalities. Next will come a set of lessons on relations and functions. After that, you'll learn about polynomials and rational functions. That will get you ready to stucy exponential and logarithmic functions. Thereafter, you'll be able to turn your attention to systems of equations and then conic sections. We'll wrap up with a look at some advanced study algebra topics.
About this Author
Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at
I purchased all the tutorials on logarithms and loved them. I am a calc. student in college. Having taken only algebra I am able to keep up with other students who have had Trig and Pre-calc. Worth every penny!! I'm sure I'll being buying more!!!!
Below are the descriptions for each of the lessons included in the
series:
College Algebra: An Introduction to Algebra Top Ten List of Mistakes Concepts of Inequalityequalities & Interval Not polynomial Absoluteuate Exponential the Applying the Rules of Exponents
Professor Burger introduces you to the rules of exponents, including a classic mistake made when multiplying two numbers of the same base with different exponents. You will learn that A^n * A^m = A^(n+m). Then Professor Burger will teach you the next rule, what to do when you multiply two numbers of different bases, raised to the same power (A^n * B^n = (AB)^n). The final rule of exponents teaches you what to do when you have a base raised to an exponent, with the entire expression raised to another power (or (A^n)^m Expression with Negative Exponent Decimal & Scientific Notn Rational Expon & Radicalsstems Simplifying Radical Expressions wizing Denominators
In this lesson, you will learn how to get square roots (or cube or other roots for that matter) out of the denominator of a fraction without changing the mathematical value of the fraction. This process is called 'Rationalizing' the denominator. Mathematicians agree that proper fractions should not have radical signs in the denominator, so when you end up with an answer that has a radical in the denominator, it is best to rationalize (as your answer will be marked wrong or will not appear as a choice if you do not Components & Degree
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course,Subtract,Multiply Big Special: Greatest Common Factor Group Factoring Trinomials Completely
In this lesson, you will learn how to factor trinomials using a reverse-FOIL trial-and-error method. You will start by simplifying the trinomial as much as possible, by removing any common factors or grouping any possible combinations. Then, try the reverse-FOIL by first breaking up the squared term. He also gives you a hint that when the last factor of the trinomial is negative, you know that the last terms of the binomials have to be opposites. You will walk through this process with a one-variable trinomial, a two-variable trinomial, and a trinomial with a positive last term Perfect Square Trinom Difference of Two Squares
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course Factor Sums and Differences of Cubes
In this lesson, you will learn how to factor the difference of two cubes and how to factor the sum of two cubes. Neither of these are simple factorizations, so Professor Burger will show you what the factorization is and then explain where it comes from. Additionally, he'll show you some ways to remember what these factorizations are. (x^3 - y^3) = (x - y)(x^2+xy+y^2) and (x^3+y^3) = (x+y)(x^2-xy+y^2) Any Method Expressions and Domain make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
College Algebra: Working with Fractions Lowest Term Rational Multiply-Divide Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to multiply and divide rational functions. Rational expressions can be multiplied or divided just like fractions. In walking you through examples of this type of multiplication and division, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way. He will also show you why dividing is the same thing as multiplying by the reciprocal Add-Subtract Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to add and subtract rational functions. As with any fractions, to do this, you'll need to find a common denominator. In walking you through examples of this type of addition and subtraction, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way Waterloo Rewriting Complex Fractions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. Dealing with complex rational expressions is the same basic thing as dealing with other rational functions. In a complex rational expression, you generally end up with a variable within a fraction that's with another fraction that also includes another variable. The approaches to addition, subtraction, multiplication and division that are used with simple rational expressions all work the same here. You will need to invert and multiply in order to divide and you will need to find common denominators and least common multiples, etc. In this lesson, you will see a series of examples to see how these complex rational expressions are handled (things like (1/(1/x))/(1/(1/x)^2)). Writing Rewriting Powers of i and Subtract Complex Numbers
A complex number is a number of the form a+bi where a and b are real numbers and i is equal to the square root of 1. This video lesson will walk you through the basics of addition and subtraction when dealing with complex numberslyividing Solving Linear Equation
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkations with Rationalation with Word Problems
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Beginning Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers linear equations, inequalities, polynomials, rational expressions, relations and functions, roots and radicals, quadratic equations and systems of equations. Perimeter Linear for Consecutive Numbers
Professor Burger walks you through a word problem to find consecutive numbers. First, you will read the problem and then define a variable for the numbers you need to find. Using this variable, you will write an equation to solve for the variable. Then, you can replace this variable in the equation and determine the consecutive numbers an Average
In this lesson, you will learn how to approach word problems that involve averages or means averages or means (many of which include grades or scores Constant Velocity Problem about Work Mixture Problem
In this lesson, you will learn how to approach word problems that involve equalities and ratios or fractions percentages, ratios, recipes, mixes, etc an Investment numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
College Algebra: Solving Business Quadratics by Factoring
In this lesson, you will learn to solve quadratic equations by factoring. Quadratic equations involve factors that are now squared, which could give us more than one possible answer. To discover if an equation has more than one answer, you need to set the equation equal to zero and factor. You will discover that if your quadratic equation factors into a perfect square, it will have only one solution by Completing the Square This lesson will teach you how to find solutions by completing the square. In this technique, you'll start by isolating all constants on one side of the equation and all variable terms on the other side. Then, you'll add or subtract something to both sides to complete the square. In this case, you'll end up with x^2+6+9 = 9-1. This equation will be easier to evaluate given that you can simplify it to (x+3)^2 = 8. When you finally get to a solution value for x using this approach, you may need to rationalize a denominator (take radicals out of it), and Professor Burger will review this in the lesson, too Completing the Square: An Example In this lesson, you will learn more advanced techniques to use when solving an equation by completing the square. This lesson will cover what to do when the initial x^2 term contains a coefficient, how to solve problems that involve fractions, how to handle denominators with fractions, etc. This technique is the basis for the quadratic formula, which can always been used to solve quadratic equationsving the Quadratic the Quadratic Formula
The quadratic formula is used to solve for x in quadratic equations, which come in the form ax^2+bx+c=0. This formula is most commonly used when the expression can't be easily factored for evaluation. Oftentimes, this is because the two solutions to the equation are not real numbers. In this lesson, Professor Burger will walk you through when to use the formula, what the alternatives to the formula are and how to apply the formula. He will also explain how and why the formula can give imaginary numbers as solutions and what that means Predict Solution Type by Discriminant
When working with quadratic equations and the quadratic formula, there is a way to determine what type of solutions you will find and how many there will be (2 real solutions or 2 complex solutions or 1 solution) by looking at the coefficients of the quadratic formula. In this lesson, you will learn how to do this by calculating and evaluating the discriminant (d) of the quadratic formula (equal to b^2-4ac, which is a component of the quadratic formula in a Squared Variable Real Number Fancy with him Quadratic Pythagorean Motion Projectile Effective Other Extraneous Roots Containing Radicals
When working with equations, you often end up with a radical of some sort (like a square root) on one side of the equation. These type of equations are called radical equations because they contain a square root. To evaluate this type of equation, you'll want to get rid of the radical. This lesson will show you how to approach and solve this type of equation by getting rid of the radical (by isolating the radical alone on one side of the equals sign and then squaring both sides of the equation). When evaluating this type of equation, you will always want to check your solutions in the original equation to make sure that you don't end up with an extraneous root as a solution. Even if the equation solves to give you an extraneous root, it is not a valid solution. An extraneous root is something that is a root to the quadratic but not to the original equation with Two Radicals
In this lesson, Professor Burger will show you how to solve equations that contain two radicals (roots). When you have an equation with two square roots, you'll want to have them on opposite sides of the equal sign. Then, you'll square both sides of the equation. If there is still a radical remaining, you'll have to isolate it on one side of the equation and then square both sides once again. There will be several examples included in this lesson that will show you how to approach this type of problem and then how to check your work.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Intermediate Algebra Exponent Vari Direct Proportion
In order to explain direct proportionality, Professor Burger uses a real-world example of a spring and Hooke's Law. Hooke's law states that the distance a spring stretches varies directly to the force applied. If force, f, is directly proportional to distance, d, then d~f or d=kf. This equation allows us to find the constant, k, of how much the spring stretches when force is applied. After we have found this number, we can determine the distance the spring will stretch with varying forces applied.
A lesson on inverse proportions can be found here unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Beg Algebra: Inverse Proportion
In this lesson, inverse proportionality is explained using light as a real-world example. The illumination of a light source varies inversely to the square of the distance from the source, or I=k/(d^2). So, to find the illumination of a particular light source, you will need to find the constant, k, of that source, and then divide by the distance squared.
An introduction to direct proportion can be seen here:
This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth! Inequalities
Professor Burger discusses solving inequalities for one variable. He begins with reminders about adding, subtracting, multiplying, and dividing with both positive and negative numbers and the effect on the inequality sign. Then he demonstrates solving for a variable within an inequality, using the inequality 2(x + 3) < 4x + 10. You will then review interval notation (covered in a previous lesson) and three different ways to write the answer On and Inequality Quadratic Inequalities
In this lesson, Professor Burger will teach you how to solve quadratic (non-linear) inequalities. In a quadratic inequality, there are things like x^2 included. To evaluate these inequalities, we once again start by factoring. Next, you'll find the values for x, for which the quadratic inequality is positive such that you will be able to make a sign chart and then determine the sign (positive or negative) for ech interval delineated on the sign chart. Once you have identified the intervals that satisfy the equation, Professor Burger will show how to properly denote the answer using correct notation Quadratic Domains of Number Lines & Absolute Values Equations
In this lesson, Professor Burger discusses solving problems with absolute values. Remember that the absolute value of a number includes both the positive and negative value of that number. This means that an equation involving an absolute value means that you will have to solve for two equations, one equal to a positive value, and one equal to the negative value a with 2 Absolute Values
In this lesson, you will learn how to solve an equation that has two absolute values. When beginning any equation with an absolute value, remember that, by definition, the absolute value of a number has both a positive and negative answer. You will also go over how to work an equation with a fraction inside an absolute value.
For a refresher on equations with one absolute value, see this lesson Inequalities
Reminding us of its definition, Professor Burger demonstrates how to work an inequality with an absolute value. You will need to convert the inequality from the absolute value to an inequality encompassing both the positive and negative points of that absolute value. This will look different, depending on whether the absolute value is < or >. Prof. Burger walks you through several examples.
For an introduction to inequalities, see this lesson:
And for more on absolute values Inequality Cartesian System rational Thinking Visually Find distance & midpoint betwn points
Professor Burger proves the distance formula (distance = square root [(x1-x2)^2 + (y1-y2)^2] ) using the pythagorean theorum. Using this formula, you can find the distance between two points on a line. Professor Burger goes on to prove the midpoint formula ( [x1 + x2]/2, [y1 + y2]/2). The midpoint formula is in the form of a point on a line and is the average of the points on the x and y axes 2nd Endpoint of a Segment Collinearity and Distancealities Triangles Circle - Center-Radius Form Circle Center and Radius Decoding the Circle Formula
In this lesson, you will learn how to find the (x, y) coordinates for the center of a circle graphed on the Cartesian coordinate system as well as the the radius of the circle from a formula or expression that doesn't easily lend itself to the standard circle formula (e.g. r^2 = (x-h)^2+(y-k)^2)). To do this, you'll generally use a math technique called, Completing the Square.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Involving Circles Locate Points to Graph Equation's x & y-Intercept Functions and the Vertical Line Test
A function is basically a machine that takes an input value (x) and processes it to produce an output value (y). With a function, if an x value is known, you can find the y value. When graphed, a curve is a function if it passes the vertical line test. In this lesson, Professor Burger will show you how the vertical line test means and how to recognize when a curve does not pass the vertical line test. The vertical line test looks to verify that, for every value of x, only one y value is produced. If something doesn't pass the vertical line test, it is called a relation and not a function Function Notation and Values
In this lesson, Professor Burger will show you how to correctly denote functions and values. By definition, a function has only one value of y for each value of x. A function can always be expressed using the term f(x) instead of y. This lesson will walk through when to use this notation and how to use it correctly to indicate what you want it to be. Additionally, Professor Burger will show you how to verbally say the new notation in addition to how to write it. Last, he'll walk you through a few examples involving functions and their notation and evaluation Increase Intervals That Functions
In this lesson, we will learn to define, recognize, write, graph and evaluate piecewise math functions. Piecewise-defined functions are unique in that they are defined to be equal to different things for different ranges of variable values. Thus, more than one expression defines the function (e.g. for x<2, f(x)=x^2 but for x>=2, f(x)=10x). Function Domain and Range
While a function always satisfies the vertical line test (for any value of x there is only one value of y), there are functions in which the domain of the function does not include all values of x. In this lesson, we look at the domain of a function (all of the values of x for which we can evaluate the function and find a value of y) and the range of a function (all the values of y that may be generated by evaluating the function for some value of x). In addition to learning about evaluating a function to find the domain and range, Professor Burger will graphically show you how to identify the domain and range Domain and Range: Anstems Satisfying the Domain of a Function
In this lesson, you will learn how to find all of the allowable x values for a particular function (the function's domain). An allowable x value is one in which you can evaluate the function. There are certain types of numbers which are not allowable, like square roots of negative numbers, numbers with 0 in the denominator, etc. If you evaluate a function and end up with one of these types of numbers, then the x value is deemed to be outside of the domain for the function. Professor Burger will also show you how to correctly denote the domain of a function once you determine what it is Slope the Slope Given Two Points
In this lesson, you will learn how to find the slope, or the relative increase (also known as a pitch), of a line if you are given two points on that line (x1, y1) and (x2, y2). The slope (denoted by the letter, m) of a line is defined by the change in y divided by the change in x. First, you must calculate the change in the two distances (or the change (x1 - x2) and the change (y1 - y2)). You will also learn the shorthand for writing the equation of a slope and the phrase 'rise over run.' After learning how to find the slope of a line, you will practice with several sets of points and lines with different slopes (including verticle lines and horizontal lines) and also practice graphing those lines to view the slope. Professor Burger also examines what it means when a slope is undefined (or the change in x = 0), and when a slope = 0 (or the change in y = 0 named Slope from Use Point & Slope to Graph Lines in Slope-Intercept Form
Professor Burger teaches the algebraic expression for lines, or the equation of a line. The standard form for a line is written Ax + By = C. More complex algebraic expression include the slope-intercept form, y = mx + b, where m=slope and b= the point where the line crosses (or intercepts) the y-axis. Professor Burger proves the validity of this expression, and shows you how to graph a line from the slope-intercept equation.
Learn how to determine the slope of a line here equations Given Two Points
Using the slope-intercept equation of a line, Professor Burger teaches you how to write the equation of a line if you are given two points on that line. Given two points, you can find the slope. Once you have found the slope of the line, you can input any point on that line into the equation with the slope to solve for b. Once you have found the slope and b, you have the slope-intercept equation (y = mx + b).
Learn how to find the slope of a line having Writing Point-Slope Form Equations
This lesson introduces another format for the equation of a line called the point-slope form. The point-slope form for the equation of a line is y - y1 = m(x - x1), where m=slope and x1 and y1 are the coordinates of a point on the line (x1, y1). Professor Burger proves the validity of this equation, which is derived from the formula for the slope.
Learn how to find the slope of a line in Slope-Intercept Form, Parallel & Perpendicular Line Slopes
Professor Burger explains parallel and perpendicular lines, teaching you how to identify if two lines are parallel or perpendicular, by looking at the formulas. Two lines are parallel if they have the same slope. Perpendicular lines are slightly more complicated, as they have slopes that are negative reciprocals. After demonstrating these principles, Professor Burger walks you through some example problems.
To learn more about slopes, visit Function Models
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are Cost and Revenue Important Equations with variety Operations on Composite Functions
In this lesson, you will learn about a method that you can use to combine functions. The composition of two functions is the way to combine two functions. In this lesson, you will learn how to combine functions (for example, to find f(g(x)) ). There are specific ways to denote these types of composite functions, and you will also learn how to correctly write composite functions (f(g(x)) or (f o g)(x) ). To compose a function (find the composition of functions), you'll have to take the answer of one function and plug it into the other function (to find something like, 'g composed of f of 3'. Professor Burger will also highlight why g(f(3)) is not always equal to f(g(3)).
This Composite Function Components Functions to Form Composite Difference Quotient Quadratic Function Graph
Taught by Professor Edward Burger, this lesson Nice-Looking Parabola Using Discriminant Max Height in Real World Find Vertex by Completing the Square
In this lesson, you will learn how to find the vertex of a parabola given the formula for the parabola. To do this, you will complete the square. By completing the square of the parabola equation, you will be able to get the equation into a standard form that can be more easily evaluated. A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. Once we've identified the vertex of a parabola, we can get a good sense for how the parabola is positioned on the Cartesian coordinate plane Write Quadratic Equation w Vertex Quadratic Maximum or Minimum entertaining and informative video lectures.
College Algebra: Shifting Curves along Shift or Translate Curves on Stretching a Quadratics Using Patterns Symmetry Reflections Reflecting Long Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will review with you how to long divide and then show you how to use long division with polynomials (to evaluate things like (x^4+3x^2-5x-10)/(X^2+3x-5) ). When long dividing, you often end up with a remainder, and this will be the case when using long division on polynomials, as well. This lesson will show you how to find both the quotient and the remainder when dividing two polynomials using long division's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
College Algebra: Long Division: Another Synthetic Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will show you how to eliminate several of the steps in long division by u sing synthetic division. Synthetic division only works when you are dividing by (x + ?) or (x - ?) where ? is a number. In synthetic division, you start by using the coefficients of the polynomial in the numberator with switched signs. In the end, you will end up with the same answer for both the quotient and remainder as you would using long division, but it will be a less harrowing path to get there Synthetic Division and on the Factor Theorem and Its Uses a Polynomials Given a Zero Zero and Considering Possible Solutions Polynomial from Zeroes, etc Polynomial Zeros & Multiplicities
The zeros of a polynomial are just the places where a polynomial crosses the x-axis, or those values for x, which if you plug into the polynomial, give zero as a result. In this lesson, we will define and discuss zeros and their multiplicity for a variety of different functions from the perspective of how to identify and count zeros using a mathematical formula or using a graph of the function. We'll cover zeros and multiplicity for parabolas and various formulas like (x^2-4x+4), (7x^3+x), and [(x+1)^2*(x-1)^3*(x^2-10)] a Polynomial's Real Zeros Descartes' Rule of Signs Zeros of Graphs to Sketch Basic Polynomial referees Basic Vertical Horizontal fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
College Algebra: Graph Rational Functions Horizontal Line Test Are Two Functions Inverses? the Inverse the Inverse of a Function
This lesson will teach you how to find the inverse of a function [f-1(x)] when you are given the function [f(x)] as a formula algebraically. Some functions, however, have no mathematically defined inverse. Professor Burger will show you how to recognize when a provided function has no inverse. For example, a parabola function cannot be inverted of Higher-Power ideal presenter of Thinkwell's entertaining and informative video lectures.
College Algebra: Exponentialonent Function Graphs-Pattern Exponential Exponent Properties
In this lesson, we'll examine how to solve exponential equations. These are equations in which the unknown variable (usually x) is found in the exponent (like 2^x = 4). One approach to this involves making the bases equivalent on both sides of the equation (given that this will mandate that the exponents are equivalent). Other equations we'll solve in this lesson include 8^x = 2, 8^x = 4, (1/3)^x = 27, 3^(-x)=27, and x^(1/3)=27 American Present Value & Future Interest Rate to Match Goals e Exponential Thinkwell's entertaining and informative video lectures.
College Algebra: Logarithmic to Log Functions
The lessons shows us how to go from exponents to logs and from logs to exponents. To start with, Professor Burger reviews bases and exponents in logarithmic functions and shows us how to convert one of these logarithmic functions to an exponential expression. For example, we'll learn how to express 2^5=32 as a log statement and we'll go over how to express log(base square root of 3)9 = 4 in exponential form Log Function Values
This lesson will show you how to find the value of a logarithm. We will also practice with different bases, logs with radicals, logs in exponents and logs of mixed numbers and fractions. You will go over problems like log (base 6) of 36 = ? Or 6^[log (base 6) 28] = ? x in Log Equations
This lesson shows you how to solve a log equation. Professor Burger begins by reviewing the relationship between a log expression and an exponential expression. Then, he walks you through solving a logarithmic expression that contains a variable in a number of different parts of the equation. We will solve problems like x=log (base 2) 32 and log (base 2) 128 = x and log (base x) 25 = -2 and log (base x) 1/16 = -2 Mathemat Logarithmic Log Function to its Logarithms
The lesson opens with a review of exponent properties. Next, Professor Burger shows you how to convert between exponential expressions and lograithmic formulas as a way to arrive at the fundamental properties of logs. He walks you through the logarithmic analog of exponent rules and explains how they are derived. You will learn about the log of a product [log (base b) xy] = ?, the log of a quotient [log (base b) x/y] = ?, logs of 0 [log (base b) 0] = ?, logs of 1 [log (base b) 1] = ?, logs of exponential expressions [log (base b) x^y] = ?. You will also be made aware of the most common mistakes made by math students when manipulating logs (which include the fact that the log of the sum is NOT equal to the sum of the logsanding Logarithmic Expressions
In this lesson, you will learn how to simplify logarithmic expressions by applying the fundamental properties of logs to the expressions. Professor Burger begins by walking through the different properties and rules of logs. Then, he illustrates how to apply these different laws of logs (which include logs of quotients, logs of products, logs of 1 and logs of 0). Burger will go through an assortment of problems in which bases and expressions vary.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course Combining Logarithmic Functions with Calculators Change of Base Richter Scale Distance Modulus Exponential Equations
In this lesson, you will learn to solve equations in which the unknown is an exponent. To do so, you will use logarithms. In simple problems, the exponential equation can be solved by simply converting both sides of the equation in such a way that the bases of each side match (e.g. with (3/4)^x = 16/9). When equations are more complex (like 3^(x-2) = 4^(2x+1)), Professor Burger will show you how to manipulate the equations using logs and the rules of logarithmic equations, which will allow you to change the exponents to coefficients of logarithmic expressions Logarithmic Equations
This lesson will teach you how to solve an equation with logs in it. To do this, you'll learn to use the properties of logs to combine all logs on one side of the equation. Once this is done, you'll convert the equation back to an exponential equation. Example problems you will work through in this lesson include log (base 2) x + log (base 2) (x-3) = 2 and ln x = 1/2* ln (2x+5/2)*x+ 1/2 ln 2 approximationarithmic Compound Predicting Change Growth and Decay
One of the most common applications of logs and exponentials is using e (2.718) to calculate rates of growth or rates of decay. In this lesson, we will go through the model for exponential growth (e.g. compounding interest, population growth, etc) and the model for exponential decay (e.g. half-life problems for radioactive decay or medicinal effectiveness declines). In evaluating many of these problems, you'll use the identity e^ln A = A because the log function and the ln function are inverse functions Half-Life Newton's Law of Cool Continuously Compounded continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Int Algebra: Solving a System by Substitution
In this lesson, Professor Burger will show you how to solve systems of equations using a technique known as substitution. In this approach, you will solve one equation for one of the variables (eg y) and then plug the value (what y is equal to) into into the other equation (anywhere a y appears). This substitution will allow you to solve for x and then in turn solve for y. In order to fully explain how this works, Professor Burger will walk you through several different types of examples System by Elimination
While you can often solve systems of equations using substitution, you may also find that elimination is a simple approach for some systems of equations. When evaluating a system of linear equations with two linear variables using elimination, you will look for ways to combine the equations (or multiples of the equations) such that the sum of the equations will eliminate one of the variables. Once you eliminate one variable, it should be easy to deduce the value of the other equation. Once you have this, you should be able to plug it in to one of the original equations to solve for the eliminated value Systems in 3 3-Variable Inconsistent Dependent Two Equation Systems
In this lesson, we start by reviewing three-equation sets that give us independent systems (meet at one point), inconsistent solutions (don't have a solution) and dependent systems (meet on a line). Next, you will move onto the instance In which you have three variables but only two equations. To solve dual-equation system problems, you first work to cancel out one of the included variables. Next, you start over to eliminate a different one of the two variables. In the end, you may come up with an answer that implies an infinite number of solutions (a line) or no solution (an instance when the two equations can never intersect - generally a situation where two planes are running parallel to each other Investmentsalities with Partial Fractions
In this lesson, you will learn about finding a solution using partial fractions, a technique which will be very useful in calculus. With partial fractions, you break an existing fraction into the sum or difference of two component fractions. This will allow you to take a fraction like (x-5)/[(3x+5)(x-2)] and turn it into (20/11)/(3x+5) - (3/11)/(x-2). This approach allows you to take one fact and turn it into two equations and two unknowns Systems and Elimination System and SubstitutionCollege Algebra: An Introduction to Arithmetic of by a Scalar
In this lesson, you will learn how to correctly multiply matrices. Professor Burger will walk you through how to multiple a 2X3 and a 3X4 matrix, a 2X3 and a 3X2 matrix and a 3X1 and a 1X3 matrix. You'll also learn why you can't multiply matrices that are the same shape and how to determine when you can multiply two matrices. To multiply two matrices, you need the number of columns in the left matrix to equal the number of rows in the right matrix. It is imprtant to remember that the order matters in multiplication of matrices. When you multiply matrices, you end up with a matrix that has the same number of rows as the first matrix and the same number of columns as the second (right) articles Gauss-Jordan Method
This lesson shows you how to use the Gauss-Jordan method to solve systems of equations. Professor Burger will walk you through how to create and use an augmented matrix based upon the system of equations in this gaussian approach. He also shows you the 'rules' of this methodology: you can flip the order of the equations, you can multiply through any of the equations by a constant (on both sides), and you can replace any row with the sum of other rows. Once the rules are established, you will learn what the goal for manipulating the augmented matrix representing the system of equations is and how to arrive at this end point Gauss-Jordan: 2x2 Determinants
In this lesson, you will learn about square matrices (a matrix in which the number of rows equals the number of columns - e.g. a 2X2 matrix or a 3X3 matrix, but this lesson focuses on 2X2). In a square matrix, you can associate a single number (a scalar) with the collection of numbers that describes the full matrix. This number is called the determinant, and this lesson will walk you through how to execute the matrix to identify what it is. For square matrix A, the determinant of A is denoted as det (A) or lAl (which looks like absolute value but isn't when A is a matrix). If the determinant of a square matrix is not equal to zero, the matrix is non-singular, and square matrices for which the determinant is zero are considered to be singular nxn Determinants
With larger square matrices, the calculation of the determinant gets more difficult. This lesson shows you a special method to use to identify the determinant of a 3X3 square matrix. You will also learn another technique to use to calculate the determinant of a 3X3 or larger square matrix. Professor Burger will go over the rules for identifying the determinant of any square Determinants in 3x3 Matrix Inverses
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full 2x2 Matrices
In this lesson, we will talk about finding the inverse of a matrix. You can only find the inverse of a matrix that is both square and non-singular. To start with, we will go through the formula for finding the inverse of a 2X2 square matrix. Then, we will apply the formula and walk through how to double-check that our answer is, indeed, the inverse of the 2X2 matrix we started with. To find the inverse, you will first find the determinant (or scalar) of the original 2X2 matrix and then take the reciprocal of the determinant multiplied across a manipulated form of the original matrix (which Professor Burger will walk you through).
For Professor Burger's lesson on finding inverses of 3X3 matrices, check out Another Look at 2x2 3x3 Matrices
This lesson will show you how to take the approach you would use for calculating the inverse of a 2X2 square matrix in finding the inverse of a 3X3 square matrix. Once you find the inverse matrix, you should be able to multiply the original matrix by the inverse matrix and get the identity matrix. The identification of the inverse of 3X3 square matrices begins with finding the determinant (or scalar) of the full 3X3 matrix followed by finding the determinant of sub components of that 3X3 matrix (finding the minor determinants). Once all determinants are found, you'll apply a sign chart to the resulting 3X3 matrix and flip the matrix across its diagonal. The last step will be to multiply your result by the reciprocal of the determinant of the original 3X3 matrix. You would be able to use this same approach to find the inverse of a larger square matrix (4X4 or larger), but the calculation thereof would be very cumbersome.
For Professor Burger's lesson on finding inverses of 2X2 matrices, check out sum System of Equations and Systems ofAlgebra: Graphing Linear & Nonlinear Inequalities
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra.
Algebra: Graph System of Inequalities Solution Set Maxima-Minima taught Linear Programming Conic Sections Info from a Parabola's Equ Writing an Equation for a Parabola
A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. To find the formula of this equation when given the vertex (h,k) and the distance from the focus (p), this lesson will show you how to find the equations for the parabola described by these criteria. There will be two formulas depending on whether p is positive or p is negative (which should indicate whether the parabola opens up or down).
This Ellips Ellipses
An ellipse is a collection of points whose combined distance from two fixed points (both called a focus) are the same. This lesson will show you how to find the equation of an ellipse if you know some information but not all of it. The equation for this type of conic section is typically written as: x^2/a^2 + y^2/b^2 = 1. We start with a situation where you know the x-intercepts and the foci (both focuses) but are looking for the equation of the ellipse. To approach this problem, we'll use triangle formulas and the Pythagorean Theorem to find the y-intercept Ellipse - Satellites Hyperb Hyperbolas
A hyperbola is a collection of points for which the difference in distance between two fixed points (both called a focus) is constant. This type of conic section is typically described by a formula that is written as: x^2/a^2 - y^2/b^2 = 1. In this lesson, we walk through how to find the equation for a hyperbola when we know the x-intercept and the foci (both focus points) of the hyperbola. We also work through a problem in which the y-intercept and both foci are provided and you are asked to find the equation for the hyperbola Hyperbolas in Navigation analysis a Conic Binomial Coefficients
This lesson answers the question, How do you find the binomial coefficients appearing in the binomial theorem? To do so, you'll use the factorial function (denoted as n! and called n-factorial). After walking through this information, you'll learn how to use the binomial coefficient (or binomial theorem). Thus, you'll learn to evaluate 'binomial coefficient n m' or 'n choose m.' Professor Burger also describes the relationship between the binomial coefficients and Pascal's triangle and walks you through an example of how to apply the binomial theorem. He solves (2A-B)^5 using both Pascal's triangle and binomial coefficients to arrive at 32A^5 - 80A^4B + 80A^3B^2 - 40A^2B^3 + 10AB^4 - B^5 Understanding Arithmetic Jazz Problems with Geometric Sequencesve Formulas Using Induction Examples of Induction Permutation Problems
In this lesson, you will learn about permutations and how to solve combinatorics problems that involve mathematical permutations. In math, permutations are distinct ways in which a set of numbers (or objects) can be ordered or sequenced. In evaluating permutations, factorials are used. Factorials in math are represented by the '!' sign (n-factorial is denoted by n!). You will learn to solve problems like, If there are 4 people in a race, how many different ways could these four people place? Also, you will be able to answer How many different ways could the top-2 finishers turn out (ignoring the sequencing for the third and fourth place finishers)? Combination Problems
In this lesson, you will begin by reviewing permutations. Then, you will learn about mathematical combinations and how to evaluate and solve combinatorics problems that involve combinations. Most often, the formula for the binomial coefficient is used to solve these problems. This is also called the choose function and read as 'n choose k.' Where order matters in permutations (e.g. A B C is distinct from A C B), combinations do not take sequence into account. Combination problems are things like, How many different sets of 6 numbers are there that can be selected from a broader set of 50 (to give you an idea of the odds that you'll win a Pick 6 Lottery game? Independentclusive and Exclusive Final Close atSupplementary Files:
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The authors are Gerald Rising and Ray Patenaude. The publisher is William R. Parks: wrparks.com There are about 12,500 new math teachers who enter school classrooms each year. This is the audience for "Letters to a Young Math Teacher." It is designed to help these young men and women to meet the real world of the school and classroomMathematical Formulas for Economics and Business: A Simple Introduction includes over 100 formulas in the field, alongside relevant definitions and explanations. The formulas cover the areas of supply and demand, market equilibrium, non-linear functions, financial mathematics, differentiation, functions of several variables, integration, and matrix algebra.
Proposes a system of methodical digit construction based upon readily perceived rules of glyph design. In other words, the number value can be calculated by observation based on simple rules of digit design. This is for easier operations when using large number bases.
Updated and revised edition of the most popular "cheating" guide to statistics! Everything you need to get you through elementary statistics. Expanded t-tests, f-tests and hypothesis testing sections, plus everything from calculating standard deviations to chi-square tests.
This tutorial is intended to help readers do four things: (1) Decide if their data gathering activity can yield numerical data that will permit a meaningful hypothesis test. (2) If it will, decide any of the tests described would be useful. (3) If so, apply that test, and (4) Adequately explain the results.
The book asks why people might believe that numbers 'exist', rather than simply being a concept of our minds? In particular, why should we believe that numbers that consist of the sum of an infinite number of other numbers added together exist? This book presents a convincing argument against the independent 'existence' of such concepts.
Fractal Delight is a collection of fractal based imagery with some 3D mixed in. These are the foundations for my video production whereby I play with colours and shapes before I embark on the task of creating an animation. They can be viewed on a tablet sideways or on a larger scale by downloading the PDF from Smashwords and rotating it 90 degrees as the pictures are mostly landscape. Kd.
This book comprises many mathematical problems suggested by the author to help the prospective contestants preparing for the Mathematical Olympiad competitions around the world as well as the general audience to learn the concepts and foundations of higher mathematics.
These problems are made and tailored in such a way to parallel those used in the past international and national competitions.
"Algebra, Trigonometry, and Statistics" helps in explaining different theorems and formulas within the three branches of mathematics. Use this guide in helping one better understand the properties and rules within Algebra, Trigonometry, and Statistics.
The integral (or antiderivative) has long been used to determine the area under a curve, but finding the antiderivative can be a challenge. Other methods of integration can be cumbersome and give only a crude estimate of the actual area. Standard-slope integration is a fast, easy, and accurate method of numerical integration with results that are on par with those of classical integration methods.
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Is real analysis helpful in physics?
I have tons of room for electives and I'm filling them up with math classes. I can see how complex analysis and even abstract algebra would be helpful, but would real analysis be helpful for research in the future? Other than getting a deeper understanding and proof based re-introduction to calculus, I don't see how it would help a physicist (especially when one can learn these proofs in their own time).
I'm interested in pursuing condensed matter physics or physical chemistry in grad school, and maybe even on the theoretical side. I was thinking maybe real analysis would be useful for getting more practice at mathematical writing for publishing papers, but is that about it?
By "Real analysis" you mean: the branch of mathematical analysis dealing with the real numbers and real valued functions of a real variable.
It will certainly help - though most physics courses include the specific math you'll need.
The way mathematicians and physicists approach math is a bit different. If you enjoy the formalism of pure math, then this will be good for you pretty much anywhere is physics.
mathwonk
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Jan26-13, 10:21 PM
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i only log in because it is late at night and i have nothing else to do, and i hope someone more knowledgable will chime in. but i think it depends which aspects of real analysis you refer to. i find it hard to believe that careful studies of how to complete the rational numbers to the real numbers by taking cauchy sequences has much value in physics, nor other foundational topics, but I do think it likely that integration theory and fourier analysis are very useful. in particular i think groups and symmetry are fundamental in physics and fourier analysis is about analysis on groups.
Robert1986
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Jan27-13, 01:47 PM
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Is real analysis helpful in physics?
Where I did my undergrad, there was a one year analysis sequence. The first half we did lots of stuff that made absolutely no sense to me at the time: a bunch of open sets, closed sets, closure operators, neighbourhoods (essentially very basic topology in R^n.) Then we started talking about continuous functions, series and sequences. None of this part was brand-new to me, but it was a deeper look at series and sequences than I did in calc. Essentially, all of the proofs that my calc book said were too advanced to calculus were proven in this class (at least the ones dealing with series and sequences.) The last three weeks or so was all about Fourier stuff.
The second semester we dealt with differentiation and integration. Both done in general R^p spaces (though we only integrated over R^p, not anything more general than that.) This was very useful to me for several reasons. For example, I never really understood the whole change of variables thing from calc 3, and the theory helped me understand it more. Also, you will really start to see the derivative as a linear approximation to the difference of a function evaluated at two points and this makes some numerical approximation theory a little easier to understand. Also, in the book we used, there were lots of "projects". The projects were harder than homework, and broken down into several parts and you proved "real math things". For example, one was proving that every ODE has a unique solution. (Well, it wasn't every ODE, it was a particular class of ODEs, I forget which, but the proof was non-trivial.) During the course, we re-visted some fourier stuff and the last three weeks was Lebesgueish stuff.
So, if this course is like the one you can take, then it seems like the second one might be helpful. The first one probably isn't as helpful, but you need it to do the second one.
bcrowell
#5
Jan27-13, 02:16 PM
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Quote by cytochrome
I have tons of room for electives and I'm filling them up with math classes. I can see how complex analysis and even abstract algebra would be helpful, but would real analysis be helpful for research in the future?
It might be useful for some theorists, but the chances are you would never use it. If you have tons of room for electives, why don't you take some liberal arts classes?
The biggest advantage of classes like Real Analysis, Abstract Algebra and Topology for physicists is not that the material in those classes is directly useful, but instead is necessary for the advanced stuff which is. For example, if you ever want to learn about the mathematics behind quantum mechanics rigorously i.e functional analysis, you will certainly need a background in real analysis. If you want to learn about Algebraic Topology and Differential Geometry which have applications in string theory (I hear at least) and general relativity a knowledge of general topology is very helpful. And obviously lie groups and representation theory is an important topic which requires knowledge of abstract algebra.
So if you're interested in mathematical physics it's a must. If you're interested in theory, you should still take them if you have the time, but don't give them preference over your physics courses. If you're going into experimental though, it's gonna be almost completely useless.
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Mathematical Reasoning for Elementary Teachers Fifth Edition of Mathematical Reasoning for Elementary Teachers,with new co-author Richard Millman,;focuses on ;mathematical knowledge needed for teaching demonstrating why future teachers are learning math content as well as when they will use it in the classroom. One of the most important aspects of teaching is being able to explain why students; methods and ideas are either right or wrong. Imparting this skill to future teachers the emphasis of this fantastic text.
Calvin Long received his B.S. in Mathematics from the University of Idaho. Following M.S. and Ph.D. degrees in Mathematics from the University of Oregon he worked briefly as an analyst for the National Security Agency and then joined the faculty at Washington State University. His teaching ran the gamut from elementary algebra through graduate courses and included frequently teaching the content courses for prospective elementary school teachers.
His other professional activities include serving on numerous committees of the National Council of Teachers of Mathematics and the Mathematical Association of America, and holding various leadership positions in those organizations. Professor Long has also been heavily engaged in directing and instructing in-service workshops and institutes for teachers at all levels, has given over one hundred presentations at national and regional meetings of NCTM and its affiliated groups, and has presented invited lectures on mathematics education abroad.
Professor Long has co-authored two books and is the sole author of a text in number theory. In addition, he has authored over ninety articles on mathematics and mathematics education, and also served as a frequent reviewer for both The Arithmetic Teacher and The Mathematics Teacher. In 1986, he received the Faculty Excellence Award in Teaching from Washington State University and, in 1991, he received a Certificate for Meritorious Service to the Mathematical Association of America.
Aside from his professional activities, Dr. Long enjoys listening to, singing, and directing classical music, reading, fly fishing, camping, and back packing.
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Duane DeTemple received his B.S. with majors in Applied Science and Mathematics from Portland State College. Following his Ph.D. in Mathematics from Stanford University, he joined the faculty at Washington State University, where he is now Professor of Mathematics. He has been extensively involved with teacher preparation and professional development at both the elementary and secondary levels. Professor DeTemple has been a frequent consultant to projects sponsored by the Washington State Office of the Superintendent of Public Instruction, the Higher Education Coordinating Board, and other boards and agencies.
Dr. DeTemple has co-authored three other books and over 80 articles on mathematics or mathematics materials for the classroom. He is a member of the Washington State University President's Teaching Academy, and in 2007 was the recipient of the WSU Sahlin Faculty Excellence Award for Instruction and the Distinguished Teaching Award of the Pacific Northwest Section of the Mathematical Association of America.
In addition to mathematics teaching and research, Duane enjoys reading, listening to and playing music, hiking, biking, canoeing, traveling, and playing tennis.
________________
Richard Millman received a B.S. from the Massachusetts Institute of Technology and a Ph.D. from Cornell University in Mathematics. He is the Outreach Professor of Mathematics at the University of Kentucky, which supports pre-service and in-service teacher training for PreK-12 mathematics teachers. He is Principal Investigator and Project Director for ALGEBRA CUBED, a grant from the National Science Foundation to improve algebra education in rural Kentucky.
Dr. Millman has co-authored three books in mathematics, co-edited two others, and received nine peer reviewed grants. He has published over 40 articles about mathematics or mathematics education and has taught a wide variety of mathematics and mathematics education courses throughout the undergraduate and graduate curriculum, including those for preservice teachers. He received, with a former student, an Excel Prize for Expository Writing for an article in The Mathematics Teacher.
Rich enjoys traveling, writing about mathematics, losing golf balls, listening to music, and going to plays and movies. He also loves and is enormously proud of his grandchildren with whom he enjoys discussing the conceptual basis of mathematics, among other topics.
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Description
Text meeting the need for a compact introduction to Mathematica for students enrolled in various standard mathematics courses using Mathematica. Presents concepts in an order closely following a standard mathematics curriculum, rather than along the features of the software. Provides a brief introduction to those aspects of the program most usefulto students. Includes a brief introduction to Versions 3 and 4, followed by discussions of functions and graphs, algebra, calculus, multivariate calculus, and linear algebra. Can be used as a supplementary text or as a tutorial introduction to Mathematica. Contents
Getting Started | Working with Mathematica | Functions and Their Graphs | Algebra | Calculus | Multivariable Calculus | Linear Algebra Related TopicsAlgebra, Calculus and Analysis
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Should Probability and Basic Stats Replace Calculus in the High School Curriculum?
Don't get me wrong, I love calculus. I use calculus every day. If you're a bright young student with dreams of becoming a mathematician, physicist, engineer, or economist, a good foundation in calculus is just what you need to get started. For everyone who isn't that kid, calculus may be something they learn once and then never use again.
Probability, on the other hand, is something that we all deal with all the time, and it's something that humans have a remarkably hard time grasping intuitiv…
drlorentz: Both calculus and statistics are important for someone in a scientific field. Calculus is more immediately useful, and indeed, prerequisite for any college-level physics. Statistics can wait for that purpose. As for the rest of the folks, most will take neither calculus nor stats, so it's a moot point. More specifically, the average juror (viz. prosecutor problem) will not take stats anyway so it won't help.
Math is my profession, and I have a different take on the issue of why one ought to learn math, and the corollary issue of which math to prioritize That math is useful in a myriad other, practical ways, is mere economic gravy. Hardly anyone thinks of math in this way, but I am convinced that is where its main value lies. But math is so vast we must choose. The choices that have stood the test of time are for those subfields with the most connections to other things
I don't dispute your point regarding math literacy in general. However, most students never reach calculus. I'd be happy if even a lower mathematical literacy were broadly attained. That would be a step up for most students.
The question originally posed is about calculus. Many of the students who take this class do have a very real use for it, at least as prerequisites for other classes they need. My point was simply that calculus is more valuable, perhaps even essential, for its target audience.
The cultural objective of mathematics education is addressed at a lower level, at least for now. While I would celebrate if most kids learned calculus, it's not going to happen soon. I remind you that there was a thread a few months back in which it was suggested that algebra was too much math for students. In that context, we're fortunate that kids even attain that level.
Facts don't matter much in politics because their authority is low in the hierarchy of authorities. Like religion, politics' highest authority is belief. And like most conservatives who disputed Nate Silver on the belief that Romney was going to win (he had to!), we all learned that belief endures contrary facts.
Indeed, belief-source authority is the most robust and enduring kind of authority, stronger even than facts and logic tools like calculus, probability, and statistics. Why? Many reasons for this, but the most obvious one is that beliefs operate at a meta-level above other authority sources (such as sensory perception) in a way that organizes, makes sense of, and lends purpose to their products.
I heard somewhere that when communism was unraveling in Poland, the following graffito become common: 2+2=4 What did this graffito really mean? It meant "We no longer believe in communism". Back when belief in communism was robust, no facts, reason or logic could refute it. Only when belief faded did facts, reason or logic reassert their authority.
There is a 95% chance you are right. Stats are more important than calculus. I have a Bachelor's of Arts, Master's of Science, and Medical Degree. I taught statistics at the college level as an instructor, never have had a calculus class. It worked for me.
Both are important fields. Calculus teaches you how to think about really big numbers and really small numbers and how math can be used to understand many parts of the world. It is the abstract way of dealing with reality, and this is good skill to have -even if you never do another derivative again.
Probability teaches you to consider patterns logically rather than to accept that what you see must result from the obvious pattern. This is another skill which is good to have -even if you never calculate another mean again.
Ideally, we'd learn both in High School.
As for Monty Hall, I don't know that the problem is statistical rather than verbal. Not everybody thinks Monty knows where the car is right away. If Monty is just opening a random door, he's not actually giving you information for a conditional probability.
There is a pretty good argument that we should drop a lot of subjects from the high school curriculum. It seems I read a professor of some science subject advocating exactly that recently. Why waste time on subjects that are only stepping stones to careers you aren't likely to pursue? I wish I could find a reference to that article. I'll have to go looking.
If it weren't for the fact that Paul Erdos, father of the probabilistic method in pure mathematics, confessed difficulty grasping the explanation for the solution to the Monty Hall Problem, then I would say your assertion that it "fools even very smart people" is nonsense, because as far as I'm concerned, the explanation is completely transparent. Erdos was unquestionably one of the smartest mathematical minds of the 20th century. I suspect what he meant was more along the lines that it violated intuition, and he was not prepared to entirely abandon that intuiton.
Well, if you like this problem so much, I have one that I consider superior to it, and it is every bit as elementary:
Two apparently indistinguishable envelopes contain perfectly negotiable blank cheques for large sums of money. Nothing is known about the actual amounts, except that it is known that one of the envelopes contains exactly twice as much money as the other.
You open one envelope. It contains a cheque for $1000. You are allowed to keep the $1000 or to switch to the other envelope. Which should you do, in order to maximize your expected profit from the venture?
To be clear, you now know that the other envelope contains either $500 or $2000. Perhaps it is obvious that there is a .5 probability of each, and also obviously, the two possibilities are mutually exclusive, comprising a complete set of possible outcomes. Thus, by elementary probability theory, if you switch to the other envelope your expected take is (.5)x2000 + (.5)x 500 = $1250, so by switching you could expect to enrich yourself, on average, by an extra $250.
Now wait a minute, your evil twin argues — this argument will work no matter how much money is found in the first envelope. Therefore it must always be true that switching is the better option for maximizing one's profit. Therefore, the moment you decide which envelope you want, why not just open the other one and walk away?
But, you now wonder, how would that be distinguishable, in practical terms, from deciding to select that envelope in the first place? And is switching back even better?
Clearly our analysis has gone astray. Where? And there still remains the original question … stay, or switch?
One last clue: Despite the superficial similarity, this problem is not isomorphic to the MHP.
DocJay: I like the idea. I have had a running argument about the Monty Hall problem with a Stanford computer geek for years. Since it is on You Tube I am finally going to slam that geek in to submission. · 47 minutes ago
Precisely the sort of person who should have no problem with the correct answer. In my work (math professor) I have met many people who have trouble with this. Some people can't be convinced by rational arguments. However, I have seen numerous computer scientists won over by seeing the evidence for themselves: They write a very simple code to model the game and run it, oh, say, a million times. Swapping wins the car 2/3 of the time; staying wins it only 1/3 of the time; they're convinced. This has led me to believe that, while such people may be perfectly rational, they are not particularly logical or analytical · 3 minutes ago
And if x is the larger amount switching gives an expected value of (3/4)x. Now there is a 50% probability of each …
There are no conditional probabilities in your example. Odds are 50% you'll get richer and 50% you'll get poorer, no matter which envelope you pick first. It's a coin toss. · 58 minutes ago
Avoiding the question? To maximize your expected profit you want a calculation determining your expected takes. For example, if we had different conditions: two different amounts and the only possible amounts are known to be: $100, $1000 and $1000000, and you get the $1000, I guarantee you that switching is a really good idea. It gives you a 50% chance to win the lottery, for a mere potential loss of $900. Your expected take would be (100+1000000)/2 = 500050.
In this variant you are still 50% likely to get richer and 50% likely to get poorer, but it is clear that you should take the wager.
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Core-Plus Mathematics, Course 2 - 08 edition
Summary: Core-Plus Mathematics, is a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence. Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations. Developed by the CORE-Plus Math Project at Western Michigan University with funding from the National Science Foundation (NSF),Core-Plus Mathematicsis w...show moreritten for all students to be successful in mathematics. Core-Plus Mathematicsis the number one high school NSF/reform program and it is published by Glencoe/McGraw-Hill, the nation's number one secondary mathematics company. ...show less
2007 Hardcover 2008
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You Do the Math -- K thru Calculus
Wednesday, August 6, 2014
I've been writing quite a bit on the work of George Pólya, particularly focusing on what strike me as some common misconceptions and overlooked aspects. I started with his emphasis on building self-confidence and making the experience pleasant since these things are so much at odds with the tough-talk rhetoric that has become so popular in education circles over the last few years.
Pólya also spends a great deal of time talking about the importance of "getting inside the student's head," but compared to the parts about self-confidence, I think the point here is less emotional and more cognitive. One of the main ideas of the book How to Solve It is that people who work with mathematics professionally have almost invariably mastered and internalized a number of useful problem-solving tools. Unfortunately, by internalizing these tools we have also in effect hidden them from our students.
When faced with a problem, we quickly and in many cases unconsciously run through a number of techniques that we have found over the years to be helpful. We examine the problem, determine the unknown, compare the problem to those we've encountered in the past, perhaps draw a mental picture and run through any number of similar steps before deciding on the proper strategy. To the student this gives an unrealistically linear appearance to the process, as if "let u equal X cubed minus 8 and then factor by substitution" was the first thing that popped into our mind .
Polya's point, and I think it's a profound one, is that to explain a process to someone who is unfamiliar with it, you have to be self-aware enough to explain the whole process, not just the parts you are still conscious of.
For the math people out there, this is not a bad explanation, but we aren't the target audience. For the target audience, this just terrible, particularly for a video. If you're working live, you can read the room. With a recorded medium, you have to anticipate the room.
Think of the world as being divided into two groups: people who can do this problem without help; and people who can't. The person doing this video is obviously in the first group, For the first group, setting up equations is second nature. It's obvious me, having been through this from every vantage, that the instructor took a few seconds to understand the problem and mentally outline the steps for solving problem, then he hit record and started filling that outline in.
The trouble is, for the overwhelming majority of the people in the second group, getting that outline is the part they were having trouble with. Very seldom do you see students who can effortlessly set up the equations for a word problem but who then get stuck on the basic algebra.
The students who need help look at this problem and see a lot of possible variables and equations. Maybe X should be the amount spent on the expensive paper. Maybe we should set up an equation to show the difference between the two amounts, cheap and expensive. You and I know these are dead ends because we've seen this show before. The key to explaining this type of problem is to imagine what it would look like if you were seeing it for the first time.
George Pólya was, of course, big on word problems. Here's a relevant passage from How to Solve It:
Monday, August 4, 2014
What's a MacGuffin? A MacGuffin is the key or stolen diamonds or secret code or NOC list that the characters desperately pursue. Audiences, pretty much by definition don't care about MacGuffins, but they do enjoy watching characters pursue them. Sometimes the audience isn't even clear on what the MacGuffin is.
Do you know what a NOC list is?
A pedagogical MacGuffin is a type of problem we pretend to care about even though we really don't. Like its fictional counterpart, what's important with a mathematical MacGuffin is not the thing but the pursuit.
The classic example is factoring polynomials. A standard part of most algebra classes is to learn how to take a trinomial like
2x^2 - x - 15
and find two binomials you can multiply together to get it
(2x+5)(x-3)
Every once in a great while, you'll get a trinomial that won't factor but the rest of the time you'll get a nice clean answer where each binomial consists of an integer times x plus another integer. At least, that's how it works with the assignments. You may even be told that polynomial factoring is useful because it can help you solve equations. That part is a lie.
With a couple of notable exceptions (differences between two squares and perfect square trinomials), you will probably never even try to solve a problem by factoring a quadratic for the simple reason that most don't factor.
Not only does solving by factoring usually not work; we already have a simpler method that always works, the quadratic formula.
The truth is, we don't care whether or not you know how to factor a trinomial; we care about what you learned in the pursuit, things like problem solving skills and insights into how numbers work.
Thursday, July 31, 2014
In his book Mastery, George Leonard has some interesting thoughts about slow learners.
My experience as an instructor has shown me, for one thing, that the most talented students don't necessarily make the best martial artists. Sometimes, strangely enough, those with exceptional talent have trouble staying on the path of mastery. In 1987, my colleagues at Esquire and I conducted a series of interviews with athletes known as masters of their sports, which tended to confirm this paradoxical finding. Most of the athletes we interviewed stressed hard work and experience over raw talent. "I have seen so many baseball players with God-given ability who just didn't want to work," Rod Carew said. "They were soon gone. I've seen others with no ability to speak of who stayed in the big leagues for fourteen or fifteen years."
Good Horse, Bad Horse
In his book Zen Mind, Beginner's Mind, Zen master Shunryu Suzuki approaches the question of fast and slow learners in terms of horses. "In our scriptures, it is said that there are four kinds of horses: excellent ones, good ones, poor ones, and bad ones. The best horse will run slow and fast, right and left, at the driver's will, before it sees the shadow of the whip; the second best will run as well as the first one, just before the whip reaches its skin; the third one will run when it feels pain on its body; the fourth will run after the pain penetrates to the marrow of its bones. You can imagine how difficult it is for the fourth one to learn to run.
"When we hear this story, almost all of us want to be the best horse. If it is impossible to be the best one, we want to be the second best." But this is a mistake, Master Suzuki says. When you learn too easily, you're tempted not to work hard, not to penetrate to the marrow of a practice.
"If you study calligraphy, you will find that those who are not so clever usually become the best calligraphers. Those who are very clever with their hands often encounter great difficulty after they have reached a certain stage. This is also true in art, and in life." The best horse, according to Suzuki, may be the worst horse. And the worst horse can be the best, for if it perseveres, it will have learned whatever it is practicing all the way to the marrow of its bones.
Suzuki's parable of the four horses has haunted me ever since I first heard it. For one thing, it poses a clear challenge for the person with exceptional talent: to achieve his or her full potential, this person will have to work just as diligently as those with less innate ability. The parable has made me realize that ifl'm the first or second horse as an instructor of fast
Wednesday, July 30, 2014
Most normal people (a.k.a. non-statisticians) tend to think in linear terms. The trouble is most normal behavior doesn't tend to be very linear. As a rule, you're better off thinking in terms of of U-curves (things go either up or down then come back) and S-curves (things are level, they move either up or down, then they level off again). These are still approximations, but they are usually more reasonable approximations.
This is particularly true in education. Arguably the best way to model learning is with a series of S-curves. We work and study with little progress, then we have a period of improvement, then we hit another plateau.
If we think in terms of straight lines, ranking students is relatively easy.
But if we think in terms of S-curves, which is a great deal more realistic, things get more complicated.
The x-axis doesn't actually mean anything (this is made-up data), but let's say it represents months studying a language and the lines represent daily test scores. Now, who's the best student depends on when you ask, and that raises some troubling points.
We tend to put too much faith both in the metrics we use to evaluate students and in the linearity of human behavior. We are not straight -line animals but we have a bad habit of making straight line decisions. In this case, think of what would happen if we made a decision on who to drop from a program after two months.
Monday, July 28, 2014
Having hammeredaway at the importance of student self-confidence and positive attitude as a condition for success in math (part of the larger discussion of applying Pólya's teaching principles), it's important to step back and point out that a lot of people have made horrible, costly mistakes thanks to positive thinking and the influence of motivational speakers (for example).
With fantastic successes on one side and horror stories on the other, it is tempting to call this a wash, but if you think like a statistician (and you should always think like a statistician) and start breaking things down, you'll find that a few common sense rules can tell you when to assume the best and when to prepare for the worst.
Being pragmatic about being positive
For the purposes of this discussion, let's decide on a fairly precise definition of what we mean by positive thinking:
To apply positive thinking to a task, you act under the assumption that, given reasonable and intelligently applied effort, the probability of success is close to one;
Furthermore, this assumption will not be reassessed unless there is a major change in the situation.
The advantages to this approach are: we can waste a great deal of time and energy worrying; overestimating risk can cause us to prematurely abandon projects; thoughts of failure can cause us to "flinch," to hold back and not give the task our best effort. Avoiding these things can allow positive thinking to create self-fulfilling prophecies.
The disadvantages are that underestimating the probability of failure can cause us to waste resources on projects with negative expected value and, more importantly, failing to pay attention to warning signs can leave us vulnerable to otherwise avoidable disasters.
We could have a general discussion at this point about the relative weight of these advantages and disadvantages but it wouldn't be very productive because neither risk nor reward are evenly distributed. In many if not most situations, a fairly clear case can be made for either positive or cautious thinking. To determine which approach is best for a given situation, think about these rules of thumb:
Before you commit yourself, try to think realistically about the expected value in terms of other people's success rates;
Never bet more than you're willing to lose;
Consider collateral damage (are you putting your spouse and children at risk of hardship?);
Is there incremental payoff? This last one is extremely important. If you decide to start a restaurant or move to NYC to make it on Broadway, and you fail, then you will probably have very little to show for the effort. If, on the other hand, you decide to lose forty pounds through diet and exercise or to go from being a C student to an A student, then there is incremental pay off for your hard work even if you fail to achieve your goal.
All of this leads us back to the original point. We often associate positive thinking with business and entrepreneurship where it is, more often than not, a bad idea, while in education, where we have every reason to encourage positive thinking, we are constantly hearing people like Michele Rhee complain that we spend too much time building up kids' self-esteem.
Don't let the posturing and tough talk fool you. Self-esteem is good for kids and you should do everything you can to convince them that they are capable of doing every problem their teacher gives them, as long as they put in the effort.
Thursday, July 24, 2014
And according to this article from Tim Walker, I might have been onto something.
Like a zombie, Sami—one of my fifth graders—lumbered over to me and hissed, "I think I'm going to explode! I'm not used to this schedule." And I believed him. An angry red rash was starting to form on his forehead.
Yikes, I thought. What a way to begin my first year of teaching in Finland. It was only the third day of school and I was already pushing a student to the breaking point. When I took him aside, I quickly discovered why he was so upset.
Throughout this first week of school, I had gotten creative with my fifth grade timetable. Normally, students and teachers in Finland take a 15-minute break after every 45 minutes of instruction. During a typical break, students head outside to play and socialize with friends while teachers disappear to the lounge to chat over coffee.
I didn't see the point of these frequent pit stops. As a teacher in the United States, I'd spent several consecutive hours with my students in the classroom. And I was trying to replicate this model in Finland. The Finnish way seemed soft and I was convinced that kids learned better with longer stretches of instructional time. So I decided to hold my students back from their regularly scheduled break and teach two 45-minute lessons in a row, followed by a double break of 30 minutes. Now I knew why the red dots had appeared on Sami's forehead.
Come to think of it, I wasn't sure if the American approach had ever worked very well. My students in the States had always seemed to drag their feet after about 45 minutes in the classroom. But they'd never thought of revolting like this shrimpy Finnish fifth grader, who was digging in his heels on the third day of school. At that moment, I decided to embrace the Finnish model of taking breaks.
Once I incorporated these short recesses into our timetable, I no longer saw feet-dragging, zombie-like kids in my classroom. Throughout the school year, my Finnish students would—without fail—enter the classroom with a bounce in their steps after a 15-minute break. And most importantly, they were more focused during lessons.
At first, I was convinced that I had made a groundbreaking discovery: frequent breaks kept students fresh throughout the day. But then I remembered that Finns have known this for years; they've been providing breaks to their students since the 1960s.
Monday, July 21, 2014
Note: Though the connection may not be immediately obvious, the following thoughts on teaching will eventually tie in with a larger piece on George Pólya.
Though it varied someone from class to class and situation to situation, my preferred method was to reserve the last part of the class for students to work individually while I went around the room and checked each student's work. Generally, I would give the students a couple of worksheets to be handed in at the end of class. After completing those worksheets, they were instructed to spend the rest of the hour working on their homework. I wasn't always able to get to every student every day, but I came close, and I never let more than a couple of days go by without making sure that I had personally observed a student doing problems in my class.
If a lots of the students were having trouble doing the assignment, I would sometimes interrupt the routine, go back up to the board, and reteach some of the material. That was fairly rare. Most of the time, two or three students would need real help and the rest only needed either a couple of quick suggestions or simply confirmation that they were doing the problems correctly.
The personal help was important, as was the knowledge on the students' part that if they needed help in the future I would be there. This approach also let me make sure that neither the class or any of the students got into a death spiral where confusion and failure started causing a cascading effect. By personally watching students successfully completing assigned problems, I could make sure that everyone was keeping up. Grading was also an important part of that process but for assessment there is no substitute for actually watching how a kid going through a problem.
In some cases, particularly with advanced classes, I might stray from this approach, but if we are talking about at-risk kids in tough environments who need to make up ground academically, I believed then and believed now this is the best way to teach high school math.
If I sound a little over emphatic with that last sentence and perhaps even a little bitter it's because I am more than a little bitter about the direction our schools have headed. I enjoyed that kind of teaching and I got excellent results with it, but if I were to go back into the profession now, there is almost no way I could give that kind of personal attention nor could I take the same level of accountability for students' success. Class sizes have simply gotten too large.
Many.
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Starting at $0Beginning Algebra with Applications and Visualization offers an innovative approach to the beginning algebra curriculum that allows students to gain both skills and understanding. This text not only prepares students for future mathematics courses, but it also demonstrates to students the relevance of mathematics. Real data, graphs, and tables play an important role in the course, giving meaning to the numbers and equations that students encounter. This approach increases student interest, motivation, and the likelihood for success. Many students think in visual, concrete terms and not abstractly. This text helps students learn mathematics better by moving from the concrete to the abstract. It makes use of multiple representations (verbal, graphical, numerical, and symbolic), applications, visualization, and technology.
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Abstract: Students' work with linear and nonlinear relationships illustrates algebra skills and understandings important to introductory algebra. Attending carefully to students' language helps us appreciate and support their early insights.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Diablo Precalculus of teaching is to break a problem into smaller parts. I explain each of these smaller parts by teaching a lesson of a particular problem. I will check for understanding as I explain these smaller parts.
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Read and Do Proofs: An Introduction to Mathematical Thought Processes, 5th Edition
How to Read and Do Proofs has been teaching students how to do proofs for over 20 years!
This text provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to catagorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem. Students are taught how to read proofs that arise in textbooks and other mathematical literature by understanding which techniques are used and how they are applied. It shows how any proof can be understood as a sequence of the individual techniques. The goal is to enable students to learn advanced mathematics on their own. This book is suitable as: (1) a text for a transition-to-advanced-math course, (2) a supplement to any course involving proofs, and (3) self-guided teaching.
The inclusion in practically every chapter of new material on how to read and understand proofs as they are typically presented in class lectures, textbooks, and other mathematical literature. The goal is to provide sufficient examples (and exercises) to give students the ability to learn mathematics on their own.
The Instructor's Solutions Manual contains the solutions to all of the exercises and is available as a download from the websiteon the Instructor Book Companion Site. Not only short answers, these solutions are often given in detail, with a full explanation of the thinking process that goes into the solution.
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Use both English and Metric measurements, conversions, temperature, and to write, manipulate, interpret, and solve applications and formula problems. Concepts will be introduced numerically, graphically, symbolically, and in oral and written form. Scientific calculator with fraction capabilities required. Prerequisite: placement into MTH 20 and RD 90. Audit available.
Surveys mathematical topics for those interested in the presentation of mathematics at the K-9 levels. Various manipulatives and problem solving approaches are used to explore rational numbers (fractions, decimals, percents), integers, the set of irrational numbers, the set of real numbers, and simple probability and statistics. Prerequisite: MTH 211 and its prerequisite requirements. Audit available.
Surveys mathematical topics for those interested in the presentation of mathematics at the K-9 levels. Various manipulatives and problem solving approaches are used to explore informal geometry, transformational geometry, and measurement systems. Prerequisite: MTH 211 and its prerequisite requirements. Audit available.
Includes infinite sequences and series (emphasis on Taylor series), an introduction to differential equations, and vectors in three space. Graphing calculator required. Prerequisites: MTH 252 and its prerequisite requirements. Audit available.
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Precalculus - With 2 CDS - 4th edition
Summary: Bob Blitzer's background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets students engaged and keeps them engaged. Presenting the full scope of mathematics is just the first step. Blitzer draws students in with applications that use math to solve real-life problems.
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall.
View Table of Contents
Table of Contents
Preface
Acknowledgments
To the Student
About the Author
Applications Index
P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Exponents and Scientific Notation
P.3 Radicals and Rational Exponents
P.4 Polynomials
P.5 Factoring Polynomials
Mid-Chapter Check Point
P.6 Rational Expressions
P.7 Equations
P.8 Modeling with Equations
P.9 Linear Inequalities and Absolute Value Inequalities
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER P TEST
1. Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and Their Graphs
1.3 More on Functions and Their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
Mid-Chapter Check Point
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
1.10 Modeling with Functions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 1 TEST
2. Polynomial and Rational Functions
2.1 Complex Numbers
2.2 Quadratic Functions
2.3 Polynomial Functions and Their Graphs
2.4 Dividing Polynomials; Remainder and Factor Theorems
2.5 Zeros of Polynomial Functions
Mid-Chapter Check Point
2.6 Rational Functions and Their Graphs
2.7 Polynomial and Rational Inequalities
2.8 Modeling Using Variation
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-2)
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Properties of Logarithms
Mid-Chapter Check Point
3.4 Exponential and Logarithmic Equations
3.5 Exponential Growth and Decay; Modeling Data
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-3)
4. Trigonometric Functions
4.1 Angles and Radian Measure
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
Mid-Chapter Check Point
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications of Trigonometric Functions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-4)
5. Analytic Trigonometry
5.1 Verifying Trigonometric Identities
5.2 Sum and Difference Formulas
5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Mid-Chapter Check Point
5.4 Product-to-Sum and Sum-to-Product Formulas
5.5 Trigonometric Equations
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-5)
6. Additional Topics in Trigonometry
6.1 The Law of Sines
6.2 The Law of Cosines
6.3 Polar Coordinates
6.4 Graphs of Polar Equations
Mid-Chapter Check Point
6.5 Complex Numbers in Polar Form; DeMoivre's Theorem
6.6 Vectors
6.7 The Dot Product
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 6 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-6)
7. Systems of Equations and Inequalities
7.1 Systems of Linear Equations in Two Variables
7.2 Systems of Linear Equations in Three Variables
7.3 Partial Fractions
7.4 Systems of Nonlinear Equations in Two Variables
Mid-Chapter Check Point
7.5 Systems of Inequalities
7.6 Linear Programming
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 7 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-7)
8. Matrices and Determinants
8.1 Matrix Solutions to Linear Systems
8.2 Inconsistent and Dependent Systems and Their Applications
8.3 Matrix Operations and Their Applications
Mid-Chapter Check Point
8.4 Multiplicative Inverses of Matrices and Matrix Equations
8.5 Determinants and Cramer's Rule
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 8 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-8)
9. Conic Sections and Analytic Geometry
9.1 The Ellipse
9.2 The Hyperbola
9.3 The Parabola
Mid-Chapter Check Point
9.4 Rotation of Axes
9.5 Parametric Equations
9.6 Conic Sections in Polar Coordinates
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 9 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-9)
10. Sequences, Induction, and Probability
10.1 Sequences and Summation Notation
10.2 Arithmetic Sequences
10.3 Geometric Sequences and Series
Mid-Chapter Check Point
10.4 Mathematical Induction
10.5 The Binomial Theorem
10.6 Counting Principles, Permutations, and Combinations
10.7 Probability
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 10 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-10)
11. Introduction to Calculus
11.1 Finding Limits Using Tables and Graphs
11.2 Finding Limits Using Properties of Limits
11.3 Limits and Continuity
Mid-Chapter Check Point
11.4 Introduction to Derivatives
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 11 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS P-11)
Appendix A: Where Did That Come From? Selected Proofs
Appendix B: The Transition from Precalculus to Calculus
Answers to Selected Exercises
Subject Index
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Additional Sellers for Precalculus - With 2 CDSU.S.A. 2010 Hard Cover ACCEPTABLE BOOK LOOKS TERRIBLE ON THE OUTSIDE WITH WEAR TO THE BOARDS AT THE CORNERS. THERE ARE SEVERAL PAGES WITH THE CORNERS DOG EARED AT ONE TIME. THE FIRST AND LAST PAGES...show more ARE VERY WRINKLED. TEXT IS CLEAN. NO HIGHLIGHTING OR UNDERLINES. HEAVY BOOK, USA ONLY PLEASE. ...show less
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Lazy Lake, FL Statistics students with a thorough and extensive study of linear and quadratic functions and graphing on the xy-coordinate system. By the end of thier lessons, students will have all the knowledge necessary to solve and graph equations and inequalities. They will also be able to apply this knowledge to other areas of math, such as word problems, ratios and proportions
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The engaging Martin-Gay workbook series presents a user-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances readers' perception of math by exposing them to real-life situations through graphs and applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills.
Review:
Real-life applications— unparalleled in terms of quantity, quality, degree of integration, nontrivial use of real data, variety of fields, and level of interest, and many based on real data from a variety of fields— highlight the relevance of math to various careers. The Whole Numbers, Multiplying and Dividing Fraction, Adding and Subtracting Fractions, Decimals, Ratio and Proportion, Percent, Statistics and Probability, Measurement, Geometry, The Real Numbers, Introduction to Algebra. Includes approximately 550 worked examples, and 4000 exercises. For a variety of business, science, math, and technology careers30676993GOA
Book Description:Prentice Hall, 2002164173
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Probability : An Introduction - 87 edition
Summary: Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, and other key concepts and methods essential to a thorough understanding of probability. Designed for use by math or statistics departments offering a first course in probability. 360 illustrative problems with answers for half. Only high school algebra needed. Chap...show moreter bibliographies. ...show less
PAPERBACK Fair 048665252198McKinney McKinney
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"Admirably meets the topology requirements for the pregraduate training of research mathematicians."--American Mathematical Monthly Crucial to modern mathematics, topology is equally essential to many other disciplines, from quantum mechanics to sociology. This stimulating introduction employs the language of point set topology to define and discuss topological groups. The text examines set-theoretic topology and its applications in function spaces, as well as homotopy and the fundamental group. This new theoretical knowledge is applied to concrete problems, such as the calculation of the fundamental group of the circle and a proof of the fundamental theorem of algebra. The abstract development concludes with the classification of topological groups by equivalence under local isomorphism. Throughout this text, a sustained geometric development functions as a single thread of reasoning that unifies the topological course. Well-chosen exercises, along with a selection of problems in each chapter that contain interesting applications and further theory, help solidify students' working knowledge of topology and its applications.
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Hardcover, ISBN 0486450821 Publisher: Dover Publications, 2006 Used - Very Good, Usually ships in 1-2 business days, Publisher overstock with possible minor shelfwear, remainder mark. Leaves our warehouse same or next business day. Most continental U.S. orders lead time 4-10 days. International - most countries 10-21 days, others 4 weeks.
Hardcover, ISBN 0486450821 Publisher: Dover Publications, 2006
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Solving Equations with a Variable on Both Sides In order to figure out where to start when solving equations with a variable on both sides of the equals sign, we will need some useful methods and practice. There are many methods we use to solve for the variable when it appears in more than one place. This video explains how to combine like terms when solving multi-step equations. (00:41) Author(s): No creator set
Khul Khul , directed by Lucy Bennett, and the latest film coming out of the Real World scheme, examines the contested Islamic legal right 'Khul', which allows Egyptian women to unilaterally end a marriage in exchange for forgoing financial rights. It asks to what extend this law can be seen as a pathway to women's empowerment. Author(s): No creator set
Harriet Tubman and the Underground Railroad (3:07) Born a slave, Harriett Tubman became a famous "conductor" on the Underground Railroad, leading hundreds of slaves to freedom. This video tells about her actions and how she returned to free other slaves even after she had escaped to the North. A good video that shows what determination can create to help others. A good quote at the end about saving more slaves well worth a discussion in itself. Author(s): No creator set
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How to Understand the Vocabulary Of Algebra How to Understand the Vocabulary Of Algebra - Mathematical tutorial: in this tutorial you will learn how to understand the vocabulary of algebra. (02:41) Author(s): No creator set
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John Locke and His Philosophy John Locke was an English philosopher and a part of the Enlightenment
movement. He thought a government should provide life, liberty and
private property to its citizens. This forty second video deals with Locke's feelings that government must protect and exist for the people. It is too short to be used except as an introduction to Locke's influence on the Founding Fathers. Author(s): No creator set
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Recreation Finance My report studies the financing of recreation improvements and examines the differences in financing between wealthy and poor neighborhoods. Author(s): No creator set
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MathWORKS! reaches out to high school math and science instructors, introduces them to operations research methods that help solve real-world problems, and excites them into teaching math in ways that help improve student learning. Instructors and undergraduates at the United States Military Academy conduct workshops that relate mathematical ideas to familiar context - such as reducing waiting time in a fast food restaurant, maximizing profit for a manufacturing company, or choosing of the most appropriate college upon graduating from high school - so that high school instructors can then incorporate the material into their classrooms. MathWORKS! seeks to introduce practical methods and tools that help promote the love of learning, dispel the notion that mathematics is incomprehensible, and empower teachers and students alike with the capacity and imagination to leverage math in the solution of everyday problems. In short, MathWORKS! aims to show that math does actually work
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Valley Ford Precalculus I score readability based on 5-7 specific measures for a PowerPoint or OpenOffice slide presentation.
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supportive environment to help students successfully learn the content of a standard algebra and trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success.Prerequisite review is included in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge.Integrated Review Notes provided next to examples throughout the text help students see the key prerequisite skills used within the example. For added convenience, these example-specific notes direct students to the page(s) where they can practice and review skills.Prepare for the Next Section Exercises, found at the end of the exercise sets, have been carefully selected to review the prerequisite skills students will need in the next section. Next to each exercise is a reference to a section of the text where students can go to review topics they don't understand.Interactive reading and study support is provided through careful placement of a Question/Answer feature throughout the exposition of the text so that students can check their understanding of concepts, think more critically about the mathematics, and more actively engage in learning mathematics. To support students studying independently, the answer to each question is conveniently provided as a footnote on the same page as the question.To create a link between the algebraic and visual representations of a solution, increase students' understanding of the concept presented, and accommodate different learning styles, the authors have provided both an algebraic solution and a graphical solution (represented by either a coordinate grid graph or a graphing calculator screen) for appropriate examples.Focus on Problem Solving at the beginning of every chapter reviews and demonstrates various strategies used by successful problem-solvers.Special modeling sections throughout the text, which rely heavily on the graphing calculator, provide an opportunity to motivate students with relevant, modern applications. These special sections introduce the idea of mathematical modeling of data through linear, quadratic, exponential, logarithmic, and logistic regression. Students are often required to work with tables, graphs, and charts using data drawn from a variety of disciplines.
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23.85Complex analysis is one of the most beautiful subjects that we learn as graduate students. Part of the joy comes from being able to arrive quickly at some "real theorems". The fundamental techniques of complex variables are also used to solve real problems in neighboring subjects, such as number theory or PDEs. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors. All the material usually treated in such a course is covered here, but following somewhat different principles. To begin with, the authors emphasize how this subject is a natural outgrowth of multivariable real analysis. Complex function theory has long been a flourishing independent field. However, an efficient path into the subject is to observe how its rudiments arise directly from familiar ideas in calculus. The authors pursue this point of view by comparing and contrasting complex analysis with its real variable counterpart. Explanations of certain topics in complex analysis can sometimes become complicated by the intermingling of the analysis and the topology. Here, the authors have collected the primary topological issues in a separate chapter, leaving the way open for a more direct and less ambiguous approach to the analytic material. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painlevé's theorem on smoothness to the boundary for conformal maps. A large number of exercises are included. Some are simply drills to hone the students' skills, but many others are further developments of the ideas in the main text. The exercises are also used to explore the striking interconnectedness of the topics that constitute complex analysis.
Editorial Reviews
Review
"I can say that I have read this book with great pleasure and I do recommend it for those who are interested in complex analysis." ---- Zentralblatt MATH
--This text refers to an alternate
Hardcover
edition.
From the Publisher
Rather than using the traditional approach of presenting complex analysis as a self-contained subject, the authors demonstrate how it can be connected with calculus, algebra, geometry, topology, and other parts of analysis. They emphasize how complex analysis is a natural outgrowth of multivariable real calculus by comparing and contrasting complex variable theory with real variable theory. The text relates the subject matter to concepts that students already know and motivates these ideas with numerous examples. Special topics in later chapters deal with current research including the Bergman kernel function, Hp spaces, and the Bell-Ligocka approach to proving smoothness to the boundary of biholomorphic mappings. Features many examples as well as 75 illustrations, which is provided through exercise sets.
--This text refers to an out of print or unavailable edition of this title.
Most Helpful Customer Reviews
This book is rather unorthodox in a number of respects, but it has become one of my favourite texts in complex analysis. The authors claim that their motivation for their presentation of the subject is to emphasize the interconnectedness of complex function theory with multivariable calculus, and de-emphasize the connection with topology. While I do not exactly agree with these goals, I think they do an excellent job of acheiving them. My only complaint about the book is that a few proofs in early chapters result in a sea of differential operators that is resolved by a plug-and-chug computation, something I'd always rather avoid.
The level of the book is elementary, especially for a graduate text, and I appreciate the authors for making honest and reasonable claims about the accessibility of their book. This book would probably even work well for someone who has not had a prior course in complex analysis, such as senior undergraduates. Some of the more advanced topics are presented in clearer ways in this book than I have seen elsewhere.
This book has a wealth of exercises, and the difficulty level is somewhat inconsistent. Some of the exercises are outright inane--possibly inappropriate for a graduate-level text, but useful for rote practice. Others are more interesting. I appreciate, however, the inclusion of more elementary exercises: many graduate texts have the problem of not including enough such exercises, which can make it hard for students to master the fundamentals. This book avoids this pitfall.
The best part about this book is the prose. This book is well-written and is a pleasure to read. Theorems and results are well-motivated, and necessary nuances are effectively communicated through the text.Read more ›
I used this book as the text in a two semester graduate course on complex analysis that I taught recently. I found this to be a rather traditional introduction to a very classical core area of pure mathematics. (It is true that the authors originally define analyticity via the Cauchy-Riemann equations, but this is a very minor aspect of the book, and of course the connection with the existence of complex derivatives is quickly made.) Greene-Krantz move at a rather gentle pace, especially when compared to other, more classical texts (take Ahlfors, for example); this can be a major advantage, depending on your tastes.
However, if it was ever true that the devil is in the details, then this certainly applies to a mathematics book. I found the present book to be rather disappointing in this respect. I probably shouldn't have been surprised as Krantz has acquired some notoriety as a mass producer of math books. Few of the proofs can be called polished, and occasionally there are minor gaps (usually easy to fix, though) in the arguments. Cross references are often done awkwardly; sometimes, essentially the same argument is presented several times at different places without clarifying comment, setting the reader's head spinning unnecessarily.
The quality of the writing gets successively worse as we approach the end of the book. For example, I cannot shake off the suspicion that the treatment of the analytic continuation of Riemann's zeta function in Ch. 15 was hastily copied, with errors, from some other book; definitely, very little can be taken at face value here and the authors manage to completely obscure the main point behind the procedure used (which is essentially Riemann's original argument). Curiously, the following (final) Ch. 16 is independent of Ch.Read more ›
This book is reasonably accessible to those who may not have had any previous exposure to complex analysis. Many parts of the text are well written and easy to read and I really enjoyed the exposition on harmonic functions. With that being said, however, there are some things that I did not particularly like.
I thought it was strange that the author discusses the Cauchy integral formula for a disk, develops more aspects of the theory, and then later comes back to deal with homotopy theory and topology insofar as integration is concerned. In this aspect, Conway's treatise on the subject is superior, in my opinion.
I also prefer Conway's proof of Mittag-Leffler's theorem which is eloquent and a good application of Runge's Theorem. Additionally, I prefer Conway's proof of the Picard theorems as well (Conway uses Montel-Caratheodory which in and of itself is interesting while Greene and Krantz use the modular function and there are a few choice spots when Krantz is a bit vague).
Finally, some of the proofs and exercises contain errors (most of them minor, some of them not so minor) and a few of the proofs are quite difficult to follow at times while Conway's book seems more readable in these areas. This comment mainly applies to the 2nd edition and it is quite conceivable that the author has remedied these errors in the 3rd edition.
Overall, this book has some value. I believe that this book, coupled with Conway's book is a good combination. There are many things that Greene and Krantz do that I prefer over Conway and vice versa although if I had to compare the two, I would prefer Conway.
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Thank you for visiting us. We are currently updating our shopping cart and regret to advise that it will be unavailable until September 1, 2014. We apologise for any inconvenience and look forward to serving you again.
Math Survival Guide: Tips for Science Student, 2nd Edition
This book is specifically designed as a study guide and resource for science students confronted with mathematics that they need extra help on. This math skills review and practice guide is written in a clear, accessible manner to bring readers up to speed quickly on basic math principles.
Offering the right amount of depth on the right selection of topics, the book provides quick, clear, and accessible guidance on basic algebraic methods, right when students need it most. In addition to a full range of mathematics topics, Math Survival Guide includes special chapters focused on helping students improve their problem solving and study skills.
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Intermediate Algebra With Early Functions and Graphing
9780321064592
0321064593
Summary: The Lial/Hornsby developmental mathematics paperback series has helped thousands of students succeed in math. In keeping with its proven track record, this revision includes a sharp new design, many new exercises and applications, and several new features to enhance student learning. Among the features added or revised include a new Study Skills Workbook, a Diagnostic Pretest, Chapter Openers, Test Your Word Power, F...ocus on Real-Data Applications, and increased use of the authors' six-step problem solving process.
Lial, Margaret L. is the author of Intermediate Algebra With Early Functions and Graphing, published 2001 under ISBN 9780321064592 and 0321064593. Thirty two Intermediate Algebra With Early Functions and Graphing textbooks are available for sale on ValoreBooks.com, thirty used from the cheapest price of $0.45, or buy new starting at $151.93
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1111429480
9781111429485
Student Solutions Manual for Van Dyke/Rogers/Adams' Fundamentals of Mathematics, 10th:Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
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Get the math you need for framing a wall, spacing beams, figuring water flow, sizing wiring, mixing concrete, preparing estimates, determining loan costs—just about any calculation in the building trades. A complete, compact self-study ...
Get the math you need for framing a wall, spacing beams, figuring water flow, sizing wiring, mixing concrete, preparing estimates, determining loan costs—just about any calculation in the building trades. A complete, compact self-study course, Mastering Math for the Building Trades even helps with tools, from steel square and surveyor's transit to calculators and computers.
Here to help you meet deadlines, avoid costly and wasteful errors, write better estimates and plans, and have happier customers, this self-teaching tool provides the answers you want, in the office or in the field.
Related Subjects
Meet the Author
James Gerhart is experienced in residential construction, working for a number of years as a project coordinator. He built his reputation, however, teaching subjects such as math, estimating, scheduling, blueprint reading, and surveying to vocational and construction management studies
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Descriptions and Ratings (1)
Date
Contributor
Description
Rating
6 Nov 2012
Krister
This book introduces you to the basics of Matlab without requiring any previous experience of programming. Through a series of easily followed examples, the book builds your knowledge step-by-step so that, at the end, you will master all the fundamentals of the program.
Topics include how to import data, mathematical operations, graphics, and programming. Special attention has been given to debugging techniques and how to find further help. Examples include linear regressions, solving equations, and numerical integration.
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Beginning and Intermediate Algebra - With CD - 2nd edition
Summary: A worktext format for basic college math or arithmetic courses including lecture-based, self-paced, and modular classes.
John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. The Tobey approach focuses on building skills one at a time by breaking math down into manageable pieces. This building block organization is a practical approach to basic math skill development that makes it easier for students to underst...show moreand each topic, gaining confidence as they move through each section. Knowing students crave feedback, Tobey has enhanced the new edition with a "How am I Doing?" guide to math success. The combination of continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the second edition of Tobey/Slater Beginning and Intermediate Algebra even more practical and accessibleAcceptable
BridgePointe Books Clarksville, IN
Acceptable
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In this lesson you will learn how Algebra is used in everyday life and how to solve basic problems using multiplication and division along with addition and subtraction from Algebra 101. This application includes a detailed description of basic algebra functions, an unlimited number of practice problems and a step by step solution to each
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...Discrete math is defined less by what topics are included than by what is excluded. Excluded are notions of continuity upon which calculus is built. Consequently, discrete math is described as "non-calculus" math
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Attack of the math software clones
Authored by: Leland Teschler Editor leland.teschler@penton.com Key points: • It is relatively easy to find math packages devised for college coursework and research that can be repurposed to do meaningful tasks in engineering. • Some kinds of academic software is flexible enough to handle engineering simulations. Resources: MathWorks
When math professors get frustrated, the result can sometimes be mathematical-analysis software that is free for the asking. Picture this: The instructor of a calculus or higher-level math class realizes that students would benefit greatly from access to mathematical-analysis software. But commercial packages are too expensive for every student to have a copy. So the professor sets out to create a math package to be used as free course material. The resulting software becomes open source, and the rest is history.
The above scenario has played out several times over the past few years. Free math packages that include Octave, Sage, and Ptolemy II, as well as several others, began as classroom aids, then were expanded either by their original authors and collaborators or by independent contributors who took advantage of the open-source nature of these packages.
The point of these packages is to mimic the environment of commercial packages, often the Matlab package from MathWorks, Natick, Mass. For example, consider GNU Octave, a high-level language for numerical computations now used by thousands of people worldwide. Entering data in a command line lets the user solve linear and nonlinear problems numerically, using a language that is mostly compatible with Matlab. It can solve common numerical linear-algebra problems, find the roots of nonlinear equations, integrate ordinary functions, manipulate polynomials, and integrate ordinary differential and differential-algebraic equations.
Octave was written by Dr. John W. Eaton and originally conceived around 1988 as companion software for an undergraduate-level textbook on chemical reactor design. Octave authors say they originally set out to create specialized tools for solving chemical-reactor design problems but eventually realized that approach was limited and opted to create something more flexible.
Over the years, other packages have been developed that augment Octave's capabilities. For example, one called pMatlab enables parallel programming by providing distributed arrays and functions.
Another package that began life in academia is called Sage. It is built out of nearly 100 open-source packages and can be used for basic algebra, calculus, elementary to very-advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra, and more. The user interface is a notebook in a Web browser or a command line. Using the notebook, Sage connects to a Sage server on the network. Inside the Sage notebook users can create embedded graphics, mathematical expressions, add and delete input, and share work across the network.
Sage was originally the vision of Dr. William A. Stein, now a mathematics professor at the University of Washington. Over 200 people have contributed to its creation. It contains over 90 open-source packages that have been smoothly tied together and which can be accessed through a single user interface. The program is also somewhat different from Octave in that it provides capabilities of programs like Matlab but doesn't attempt to run their code. You need a special translation program to do that. Originally created in 2005, Sage is written in open-source languages called Python, PARI, and GAP.
Another math program with academic roots is Maxima. It is a descendant of Macsyma, a well-known computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It was maintained by University of Texas math professor William Schelter who, in 1998, released the source code under the GNU General Public License. Schelter passed away in 2001, and since then a group of users and developers continues to work on the program.
Another package with academic roots is called R. Basically a statistics package, R was initially written by Ross Ihaka and Robert Gentleman at the University of Auckland in New Zealand. Since 1997, a large group of individuals has contributed to R.
R handles such statistical tasks as linear and generalized linear modeling, nonlinear regression modeling, time-series analysis, classical parametric and nonparametric tests, clustering, and smoothing. There is also a large set of functions which provides a graphical environment for creating various kinds of data presentations. Additional modules are available for a variety of specific purposes. R consists of a language plus a run-time environment with graphics, a debugger, access to certain system functions, and the ability to run programs stored in script files. The core of R is an interpreted computer language which allows branching and looping. It is possible to interface R to procedures written in the C, C++, or Fortran languages for efficiency.
The birth of a numerical computation program called Scilab differs from that of Octave and Sage in that it came out of a 1980s effort at a French research institute. The free version was developed in the 1990s by researchers at the French National Institute for Research in Computer Science and Control. A consortium was eventually created to support the package, which since 2008 has been distributed under an open-source license.
Scilab includes hundreds of mathematical functions as well as a high-level language that helps construct advanced data structures, and 2D and 3D graphical functions. Users can also use the package to solve problems in statistics, control-system design and analysis, signal processing, and optimization. There are about 1,700 mathematical functions useful for linear algebra, solving sparse matrices and systems of differential equations, polynomials and rational functions, and so forth.
Another academic project at the University of California, Berkeley resulted in a program called Ptolemy II. The program is more of a simulation engine than a mathematical package. It can model systems as state machines and show how they behave with different inputs. For example, it might model a simple thermostat as a heating and cooling state with temperature as an input. The program would plot outputs, a heating or cooling rate in this example, as results. But Ptolemy II is capable of handling systems that are much more complicated than a simple thermostat. More-sophisticated tasks for which it has been used include applications involving blended continuous and discrete dynamics, models of time, and models of computation for orchestrating real-time tasks across a network.
A second free package with simulation in mind is FlowDesigner. It is an open-source data-flow-oriented development environment rather than a simulation package. In that regard, it can be viewed as a sophisticated spreadsheet that uses building blocks rather than cells. It can be used to build complex applications by combining small, reusable building blocks. Its developers say that in some ways, it is similar to both Simulink and LabView, but is hardly a clone of either. Its developers also say FlowDesigner can be used both as a rapid-prototyping tool for building end-application controls, or to help build real-time applications such as audio-effects processing.
FlowDesigner is not really an interpreted language, which makes it fast. It is written in C++ and features a plug-in mechanism that allows plug-ins/toolboxes to be easily added. Currently there are toolboxes available in signal processing, audio processing, vector quantization, neural networks, fuzzy logic, robotics, linear algebra, and an interface to let the program work in conjunction with the Octave mathematics program mentioned earlier.
Then there is Freemat, whose author calls it an environment for rapid engineering and scientific processing. Freemat author Samit Basu says he developed the program over a period of four years with help from a number of contributors. The program is said to be similar to commercial systems such as Matlab and IDL from Research Systems, Australia, but is open source. FreeMat is intended to go beyond Matlab to include features such as a codeless interface to external C/C++/Fortran code, parallel/distributed algorithm development (via MPI), and advanced volume and 3D visualization capabilities.
Basu says FreeMat supports roughly 95% of the features in Matlab, including N-dimensional array manipulation, support for solving linear systems of equations, arbitrary size FFT support, sparse matrix support, and numerous others. Right now, FreeMat doesn't support Matlab GUI/widgets building, though Basu says that feature is in development.
SciPy is another open-source software package for mathematics, science, and engineering. The SciPy library depends on NumPy, a program for N-dimensional array manipulation built using a programming language called Python. The SciPy library is built to work with NumPy arrays, and provides many user-friendly numerical routines such as those for numerical integration and optimization. Because it is based on the widely used Python language, scientific applications written in SciPy benefit from the development of additional modules in numerous niches of the software landscape. Everything from parallel programming to Web and data-base subroutines and classes are available in addition to the mathematical libraries in SciPy.
It is also possible to find free versions of commercial packages. The free versions typically target students and educators and come with slightly diminished capabilities. That is the case with a commercial package called SysQuake and a free version called SysQuake LE. Created by Calerga in Switzerland, SysQuake's claim to fame is its interactive graphics, which help in understanding and solving complicated problems in mathematics, physics, and engineering. The free version excludes an integrated development environment, programming functions to read and write files, extension plug-ins (such as serial I/O, image files, and long integers), and a way to add extensions written in C or other languages.
Recast commercial software In at least one case, a failed commercial program wound up as an open-source free program. That is the case with Axiom, a general-purpose computer-algebra system. It targets users engaged in research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy and has a programming language and a built-in compiler.
Axiom has been in development since 1971, at which time it was called Scratchpad. Scratchpad was originally developed by IBM, Armonk, N. Y., and was basically considered as a research platform for developing new ideas in computational mathematics. In the 1990s, the program was renamed Axiom, was sold to another company, but never became commercially successful. It was eventually released as a free program.
Axiom has both an interactive language for user interactions and a programming language for building library modules. Users can build polynomials of matrices, matrices of polynomials of power series, hash tables with symbolic keys and rational function entries, and so on with the programming language. The Axiom interactive language is oriented towards ease of use. The Axiom interpreter uses type inferencing to deduce the type of an object from user input, so users need not specifically declare the type of variables they are using. Type declarations can generally be omitted for common types in the interactive language.
A program called CompPad has roots in an old commercial package as well. CompPad is part of the Open Office suite of open-source programs which mimic some of the capabilities of the Microsoft Office suite. The original package was a commercial product called StarOffice suite, which Sun Microsystems, Santa Clara, Calif. (now Oracle), acquired and eventually released as Open Office software. The software firm Oracle is now the principal contributor of code to Open Office, which has an estimated user base exceeding 100 million people.
CompPad is an OpenOffice.org extension that provides live mathematical and engineering calculations within an Open Office word processing document. It is intended to provide a free/open-source alternative to Mathcad. CompPad creates technical calculations in the form of conventional-looking mathematical expressions using the OpenOffice.org equation editor. With the click of a toolbar icon, CompPad will evaluate expressions and display the results, embedded in a word-processing document.
CompPad is currently in alpha release. Developers say it is quite usable and reportedly has evaluated documents with hundreds of formulas. Among the features supported in the most-recent version are support for real and complex numbers, Booleans, vectors and matrices; handling of measurement units in all quantities and calculations; use of basic operators, including arithmetical, exponential, comparison, rounding, trigonometric, logarithmic, exponential; and support for vector/matrix operators, including transpose, multiply, min, max, sum, and product.
SysQuake targets automatic control problems that involve feedback. Its claim to fame is the ability to display plots of system performance interactively so that the user can, for example, move poles around in the S plane and see what happens to system performance. It graphs performance curves simultaneously in the frequency, time, and complex plane domain.
Smath is a mathematical program with a "paperlike" interface and numerous computing features. Basically, the screen looks like a ruled sheet of paper. It has been integrated with a mathematical reference book that provides a level of tutorial help. It was developed by Andrey Ivashov for Windows, Linux and Windows Mobile — it works on smart phones.
Finally, there is Jasymca, an interactive system for solving math problems. As with many math programs, it was devised with teaching in mind. It supports arbitrary precision numbers and symbolic variables. Users can build scalars, vectors, and matrices and perform such operations as computing the pseudoinverse of symbolic matrices over trigonometric simplifications to symbolic solutions of integrals and systems of equations. The user interface can be selected from either an Octave/Matlab/SciLab-like language, or a GNU-Maxima style. There are three versions of Jasymca: A Midlet version for portable devices like cell phones or PDAs; a java application for desktop PCs, laptops, and workstations; and an applet which can be integrated in Web pages.
Free alternatives Sage 4.1 – Open source math software for studying number theory, algebra, group theory and more. It includes interfaces to Matlab and to other free math programs. Octave 3.3 – Uses a language compatible with Matlab. It is customizable with user-defined functions written in Octave's language or C++, C, Fortran or others. Scilab 4.1.2 – Handles linear algebra, matrices, polynomials, simulation based on solving differential equations. Maxima – Manipulates symbolic and numerical expressions, including differentiation, integration, Taylor Series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Smath – Math program with "paperlike" interface and numerous computing features, with integrated mathematical reference book. CompPad – OpenOffice.org extension that provides live mathematical and engineering calculations within a document. Intended as a free/open-source alternative to Mathcad. Axiom – General-purpose computer algebra system useful for research and development of mathematical algorithms. Has a programming language and a built-in compiler. Ptolemy II – Open-source software framework supporting simulation. Sysquake 4 LE – Programming language designed with functions that accept arrays as well as scalar arguments. Freemat – Free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as Matlab and IDL but is open source. R – Free software environment for statistical computing and graphics. Flow Designer – Free data flow-oriented development environment. Can be used to build complex applications by combining small, reusable building blocks. In some ways, it is similar to both Simulink and LabView. SciPy – Open-source software for mathematics, science, engineering, and scientific computing. Jasymca – Java Symbolic Calculator, also available for cell phones or PDAs, as a java application for desktop PCs, laptops and workstation, and an applet which can be integrated in Web pages
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Mu Alpha Theta is an organization whose purpose is to stimulate Colleges. There are now over 1700 chapters in the United States
interest in mathematics by providing public recognition of and eleven foreign countries. Colleges and major universities
superior mathematical scholarship and by promoting various recognize membership in Mu Alpha Theta as an important part of
mathematical activities. It is co-sponsored by the Mathematical a student's academic resume. Topics presented during club
Association of America, the National Council of Teachers of meetings, participation in our free mathematics competitions,
Mathematics, the Society for Industrial and Applied Mathematics, and the interest generated by these activities help members to
and the American Mathematical Association of Two-Year gain a greater understanding and enjoyment of mathematics.
I. Purpose of the Organization
The National High School and Junior College Mathematics Club, 4. The Spring and Fall Newsletter containing current chapter
Mu Alpha Theta, was formed in 1957 to engender keener interest news, news of regional and national meetings, ideas from
in mathematics, to develop sound scholarship in the subject and chapter meetings, and similar items of interest to the
promote enjoyment of mathematics among high school and two- membership.
year college students.
5. Insignia pins, buttons, charms, patches, banners, small seals,
National policy is determined by a twelve-person Governing medallions, ID holder and key chain, tassels, graduation honor
Council consisting of three national officers (President, cords, t-shirts, and a tote bag are available from the National
President-Elect or immediate Past -President, and Secretary- Office.
Treasurer), four governors elected for four year terms, and
representatives appointed by our sponsoring partners. An 6. Free mathematics competitions are offered by the National
Executive Director runs the day-to-day functions of the Office throughout the year for participation right at your school.
organization and is an Ex-Officio member of the Governing Regional and state meetings are frequently arranged by
Council. Officers and Governors serve without remuneration. chapters.
7. A National Convention is held annually during July with
Mu Alpha Theta provides the following: lectures by outstanding mathematicians, as well as by students.
Many individual and group math contests are held during the
1. Individual Membership Certificates, membership cards and National Convention.
School Charters issued by the National Secretary-Treasurer.
Member names remain in the National Database for membership 8. Chapters are encouraged to make suggestions to the national
verification. officers concerning additional projects which they would like to
see carried out. A sincere effort is made to be as helpful as
2. Full members are eligible for Scholarships, Awards and possible.
Grants. Active chapters and their Sponsors are also eligible for
Awards and Grants. 9. Math Horizons, an MAA publication, is available at reduced
prices to chapters. The magazine includes articles, math
3. A Handbook for Sponsors is sent free to new chapters. puzzles and problems of interest to high school and college
students interested in Mathematics.
II: School Qualifications for Chapters
Any high school may petition to have a chapter, providing it 4. An initial charter fee of $15.00, along with a one-time
meets the following minimum requirements: Registration Fee of $10.00 for each full member, must
accompany the petition for a charter. (These fees will be returned
1. At least six semesters of mathematics including geometry and if the institution is ineligible for membership.) Applications are
more advanced topics must be offered. These requirements can approved by the President and the Governor of the appropriate
not be fulfilled by courses in general mathematics, business region. Should a chapter fail to be approved; the chapter can still
mathematics, shop mathematics, or arithmetic. be approved by a favorable two-thirds vote of the Governing
Council. Each petitioning institution will be notified as soon as
2. During the two semesters preceding that in which a petition is possible whether or not a charter has been granted. This takes a
submitted, the school must have employed at least one teacher week or less.
whose primary teaching field is mathematics and who has
completed an undergraduate mathematics major or its equivalent 5. The petition should be submitted on the form provided by the
at an accredited college or university. National Office. A list of mathematics courses offered by your
school, including textbooks used, and a brief description of topics
3. The Principal, or other chief administrative officer of the covered in each course must be submitted with each petition.
institution, must approve the petition.
III. Qualifications for Individual Membership
Each chapter shall have a faculty-student committee which will distinction (on a 4 point grading scale this shall mean at least a
recommend possible members for the chapter's consideration. 3.0 average).
No student shall be recommended for consideration who does
not meet the minimum qualifications. Additional requirements (b) Associate Membership: High school students in grades 9
may be imposed by individual chapters; however, no student will through 12, at the school where their permanent record resides,
be denied membership on account of race, religion, color, creed, who have completed two semesters of algebra or their equivalent
ethnicity, national origin, gender, sexual preference and/or with distinction and who have enrolled in a third semester of
physical disability. mathematics are eligible for associate membership. Associate
members do not pay the $10.00 Registration Fee but should be
(a) Full Membership: High school students in grades 9 through registered with the National Office, if they wish to compete in
12, at the school where their permanent record resides, who national contests or our convention. They are not entitled to vote
have completed the equivalent of four semesters of on national policy. They are entitled to attend and be heard at
mathematics, Algebra 1 and up, and in addition have completed meetings and, presumably, are likely candidates for full
or are enrolled in a still more advanced course, are eligible for membership.
full membership providing their mathematical work was done with
IV. National Finances
There shall be no national annual dues. A one-time issued to the school. Finances are supervised by the
Registration Fee of $10.00 per full member shall be paid to the Controller's Office of the University of Oklahoma. Council
national Secretary-Treasurer for each person initiated into full approval is required for expenditures, and the Secretary-
membership, whereupon the Secretary-Treasurer shall issue a Treasurer must make a complete accounting to the Governing
membership certificate to that member and place his name in the Council twice yearly.
National Database of members. A $15.00 charter fee shall be
charged each new chapter at the time the official charter is first
V. Local Organizations, Officers, and Finances
Each chapter is free to set up its own by-laws, regulate its Office of new members in a timely manner can lead to
finances, and select its officers with the following restrictions: cancellation of the chapter's charter.
1. Each chapter must have a semi-permanent faculty-sponsor 4. Each chapter must hold regular meetings at periodic
and the National Office (Secretary-Treasurer) must be kept intervals and not merely consider itself an honor society for high
informed of the current faculty sponsor's name, address, and grades. At the minimum, we recommend one meeting every
email address. month.
2. The minimum membership requirements set forth by the 5. Local chapters are encouraged to participate actively in the
National Office must be met by all initiates. life of the school, providing stimulation of an interest in, and
appreciation of, mathematics for all students.
3. A complete and accurate list of all full member initiates,
accompanied by their $10.00 Registration Fee, must be received 6. Either the name National High School and Two-Year
by the office of the Secretary-Treasurer within one month of the College Mathematics Honor Society or Mu Alpha Theta may be
date when initiation takes place. Failure to notify the National used as desired by a chapter, as long as it submits new
members at least once every two years.
Petition for Charter
Email, fax or mail everything to us. (Addresses and numbers listed above.) Since we must see the original signatures on this page, please
scan, fax or print and mail with check. Check should be sent with the Petition or arrangement for payment must be made so that once the
chapter is approved, certificates and materials can be sent out.
The undersigned hereby petitions that
(School Name)
(Address)
(City) (State) (Zip Code)
(Phone Number) (Fax Number) (Email Address)
be granted a charter. The following information is submitted to guide the President and Governor in determining the eligibility of the school.
1. On separate sheets, list all mathematics courses from Algebra 1 and above, a paragraph summary of topics covered in each course,
and the textbooks used for each, including the authors and year of publication. Also include a few sentences telling us how you heard about
th
Mu Alpha Theta. As a student, were you ever a member? What grades does your school serve? Mu Alpha Theta membership is for 9 –
th
12 grade students.
2. Approximate school enrollment and the total number of students graduated from the high school in the last three years.
Year Total Students in the School Total Graduating
3. Name of sponsoring faculty member whose primary teaching field is mathematics and who has completed an undergraduate
mathematics major or its equivalent.
Major Field of teacher: Highest degree completed: Year:
Graduated from:
List courses by title this teacher has taken above the calculus sequence: (If more than six courses are involved list only six)
Courses above calculus:
4. Attached is a certificate order blank giving names of all full-member initiates. The Charter fee of $15.00, plus $10.00 initiation fee for each
full member, totaling , is enclosed.
_________________________________________________
(Signature of Faculty Sponsor)
This petition is approved by the principal of the school.
_________________________________________________
(Signature of Principal or Chief Administrative Officer)
Order Blank for
Membership Certificates
(Allow two weeks for processing)
Date of Order
(School Name)
Teacher's Email Address
Number of Initiates:
Amount Enclosed ($10/student):
Names can be emailed to matheta@ou.edu or typed below. Type them exactly as you want them to
appear on the certificates. Group by year of graduation.
I hereby certify that the above named students meet all of the qualifications for full membership in Mu Alpha Theta and have been
declared Charter Members
Faculty Sponsor
Please make sure all of the following are included with your charter:
School Statistics
Principal or Chief Administrative Officer's Signature
Paragraph description of Math classes with textbook information
List of Charter Student Members with year of graduation
Your signature certifying student's eligibility
Check for $15 Charter fee plus $10 per member
Answers to two questions in #1 of the petition
| 677.169 | 1 |
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