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The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. ?Math Across the Community College Curriculum? is the...
How will various institutions respond to global warming? It's a multifaceted question, and one that forms the basis of this thoughtful course offered by MIT's Sloan School of Management. Materials for the course are...
Created by Tony R. Kuphaldt, this web site from the Open Book Project provides educational resources for learning and teaching electronics. It is promotes student discussion and individual research. The web site...
This course, created by Wen Xiao-Geng of the Massachusetts Institute of Technology, is the second in the series of undergraduate Statistical Physics courses and features comprehensive lecture notes and assignments....
Created by Richard Dudley of the Massachusetts Institute of Technology, this lesson, Mathematical Statistics, is a graduate-level course featuring book chapters and sections presented as lecture notes, problem sets,...
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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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9780471089759
ISBN:
0471089753
Publisher: Wiley & Sons, Incorporated, John
Summary: Combining standard Volumes I & II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression. It shows how to think about a problem, how to look at special cases, & how to devise an effective strategy to attack & solve the problem. Covers arithmetic, algebra, geometry, & some elementary combinatorics. Includes an updated bibliography & newly expande...d index.
Pólya, George is the author of Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving, published under ISBN 9780471089759 and 0471089753. Two hundred ninety eight Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred twenty one used from the cheapest price of $4.12, or buy new starting at $22.50.[read more
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Course Information
Overview
In MCS 118, we will study polynomial and power functions. In particular, we will learn how to find limits, calculate instantaneous rates of change, and compute the area bounded by graphs of these functions. We will use these ideas to model various real world problems. At the same time, we will review the algebra and pre-calculus skills that are useful in understanding this material.
In MCS 119, we will continue our study of calculus by extending the ideas from MCS 118 to exponential, logarithmic, and trigonometric functions. Students who complete both MCS118 and MCS119 may use MCS119 to substitute for MCS121.
Prerequisites
Two years of high school mathematics beyond plane geometry, including trigonometry.
Text:
We will use Calculus I with Precalculus, 2nd Edition by Larson, Hostetler, and Edwards. Be sure you have the second edition, not the third. (The third edition is considerably more expensive.)
Calculators
You should have a graphing calculator available for use in class and on exams. If you are buying a new one, the MCS department encourages the use of Texas Instruments calculators, in particular the TI86, or the TI89 (though the use of some of the TI89 features may be restricted, so that I will want you to use another calculator on quizzes and tests). If you have the standard version of any of these calculators there is no need to purchase a new calculator. If you have another brand of calculator please see me before purchasing a new one as you may be able to continue using it. A limited number of calculators are available in the Diversity Center for students who have financial difficulties buying one.
Class Web Site
Classes
Classes will be used for lectures, problem solving, discussions, and other fun activities. You should prepare for
classes by doing the reading beforehand (reading assignments are posted on the Web), thinking about
the problems in the text, and formulating questions of your own. You should also participate as much as possible in
class. Class meetings are not intended to be a complete encapsulation of the course material. You will be responsible
for learning some of the material on your own.
Attendance, both physical and mental, is required.
Should you need to miss a class for any reason, you are
still responsible for the material covered in that class. This means that you will need to make sure that you
understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that
you understand what was covered. You may not make up any in-class work, unless you have accommodations for a disability (see below). If there is a homework assignment due that day, you should be sure to have a friend hand
it in or put it in my departmental mailbox (in Olin 324). You do not need to tell me why you missed a class unless
there is a compelling reason for me to know.
Should you miss more than four classes, no matter what the reason, I reserve the right to make your class participation grade a 0.
Texting (reading or sending messages) in class is prohibited.
If you are expecting an urgent call or text message, you should notify me before class. When you get the call, you should quietly leave class and deal with it in the hall. If you are not expecting an urgent call, your cell phone should be turned off and stored in your backpack.
Homework
You will need to read a section of the book and do problems for each day that we have class.
Homework problems are designed to help you learn the material we cover in class and in the reading. You should read the material and attempt the problems before coming to class. You should finish the problems after class. You may work with other students on these problems; but be sure to give credit. Once or twice a week, you will hand in your solutions to the problems you did. These should be neatly written on standard sized paper, and with all of the pages stapled together. The sections and problem numbers should be clearly labeled. Once you've completed the homework, fill out a homework reflection sheet and then staple all of your solutions together with the homework reflection sheet on top. The grader will only grade a few sample problems.
On the day that homework problems are due, you will be asked to place your work in a homework folder. After class, I place the folder outside my office door for the grader. Any homework that is not in this folder when the grader gets it is considered late. Late homework will be accepted as long as I get it before my grader hands back the graded assignments. (Alternatively, you can put it in the folder for late homework that is outside my office door.) In that case, the homework will be graded but you will lose 30% of the points on that assignment.
Quizzes and Exams
We will have four quizzes, one mid-semester exam, and and a final exam. The mid-semester exam will be given in the evening, on Tuesday, Oct. 15, from 5:00 -7:00 or from 7:00 - 9:00. The final is scheduled for . Be sure to make appropriate travel plans.
Course grade
Your grade is a measure of your learning and growth in the course, rather than a set of points to be "earned" or "lost." Viewed this way, a grade shows the extent to which you have mastered and can communicate important concepts and ideas. Not all work is graded – you do many things in a course that contribute to your learning: reading, writing, revising, thinking, talking, and listening. It is useful to think of work, then, as the set of activities that contribute to learning. Graded work is that subset of activities where you show how well you have learned to reason mathematically and how well you can communicate your reasoning to others.
The graded course components will contribute to your grade in the following proportion:
Class participation
5%
Homework problems
15%
Quizzes
30%
Mid-term exam
20%
Final exam
30%
Letter grades are assigned using the following table.
A 93-100
A- 90-92.9
mastery of the material with developed insight
B+ 87 -89.9
B 83-86.9
B- 80 -82.9
mastery with limited insight
C+ 77-79.9
C 73 -76.9
C- 70-72.9
basic knowledge with limited mastery
D+ 67-69.9
D 60- 66.9
F 0-59.9
minimal to unacceptable performance
Disability Services
Gustavus Adolphus College is committed to ensuring the full participation of all students in its programs. If you
have a documented disability (or you think you may have a disability of any nature) and, as a result, need reasonable
academic accommodation to participate in class, take tests or benefit from the College's services, then you should
speak with the Disability Services Coordinator, for a confidential discussion of your needs and appropriate plans.
Course requirements cannot be waived, but reasonable accommodations may be provided based on disability documentation
and course outcomes. Accommodations cannot be made retroactively; therefore, to maximize your academic success at Gustavus,
please contact Disability Services as early as possible. Disability Services
is located in the Advising and Counseling Center.
Academic Integrity
You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and
to abide by the Academic Honesty Policy. A copy of the honor code can be found in the
Academic Bulletin and a copy of the academic
honesty policy can be found in the Academic
Polices section of the Gustavus Guide.
On homework problems, I encourage you to discuss problems and their solutions with each other.
However, each of you should first make a real effort to solve each problem by yourself.
On quizzes and tests, you are expected to work completely by yourself, and to sign the honor pledge on each of
these assignments. The first violation of this policy will result in a 0 on that assignment and notification of the
Dean of Faculty. Further violations will result in failing the course.
Help for Students Whose First Language is not English
Support for English Language Learners and Multilingual students is available through the Academic Support Center and the Multilingual/English Language Learner Academic Support Specialist, Laura Lindell (x7197). She can meet individually with students for tutoring in writing, consulting about academic tasks and helping students connect with the College's support systems. When requested, she can consult with faculty regarding effective classroom strategies for ELL and multilingual students. Laura can provide students with a letter to a professor that explains and supports appropriate academic arrangements (e.g. additional time on tests, additional revisions for papers). Professors make decisions based on those recommendations at their own discretion. In addition, ELL and multilingual students can seek help from peer tutors in the Writing Center.
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MATHEMATICS
A scientific calculator is recommended for each student. It is important that students retain their instruction manual for reference.
Due to the complexity of the pathways in Mathematics, we have included this flowchart for
clarification.
While the bolded pathways MCV4U
Grade 12
illustrated are the most likely to The NEW Advance Functions course
Vectors & Calculus
occur, other pathways are possible. can be taken concurrently with or
can precede Calculus and Vectors.
Consult your guidance counsellor
and mathematics teacher for more
information.
To qualify for the Ontario MHF4U
Secondary School Diploma, a MCR3U Grade 12
Grade 11 Advanced Functions
student must have 3 compulsory
credits in mathematics. Functions
University Prep.
MDM4U
Grade 12
Mathematics of
Data Management
MPM1D MPM2D
Grade 9 Grade 10
Academic Academic MCF3M
Math Math Grade 11 MCT4C
Functions & Grade 12
Applications Mathematics for College
Univ./College Technology
MBF3C MAP4C
Grade 11 Grade 12
MFM1P MFM2P Foundations for Foundations for College
Grade 9 Grade 10 College Math Math
Applied Applied
Math Math
MEL3E MEL4E
Grade 11 Grade 12
Mathematics for Mathematics for
Everyday Life Everyday Life
Indicates completion of a supplementary course is required
Principles of Mathematics, Grade 9, Academic MPM1D1
This course enables students to develop understanding of mathematical concepts related to algebra, analytic geometry,
and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students
will investigate relationships, which they will then generalize as equations of lines, and will determine the connections
between different representations of a relationship. They will also explore relationships that emerge from the
measurement of three-dimensional objects and two-dimensional shapes. Students will reason mathematically and
communicate their thinking as they solve multi-step problems. Successful completion of this course prepares students for
Principles of Mathematics, Grade 10, Academic (MPM2D) or Foundations of Mathematics, Grade 10, Applied (MFM2P).
Learning through abstract reasoning is an important aspect of this course.
Foundations of Mathematics, Grade 9, Applied MFM1P1
This course enables students to develop understanding of mathematical concepts related to introductory algebra,
proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and
hands-on activities. Students will investigate real-life examples to develop various representations of linear relationships,
and will determine the connections between the representations. They will also explore certain relationships that emerge
from the measurement of three-dimensional objects and two-dimensional shapes. Students will consolidate their
mathematical skills as they solve problems and communicate their thinking.
Successful completion of this course prepares students for Foundations of Mathematics, Grade 10, Applied (MFM2P).
Learning through hands-on activities and the use of concrete examples is an important aspect of this course.
Principles of Mathematics, Grade 10, Academic MPM2D1
PREREQUISTE: Principles of Mathematics, Grade 9, Academic
This course enables students to broaden their understanding of relationships and extend their problem-solving and
algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore
quadratic relationships and their applications; solve and apply linear systems; verify properties of geometric figures using
analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically as
they solve multi-step problems and communicate their thinking.
Foundations of Mathematics, Grade 10, Applied MFM2P1
PREREQUISTE: Principles of Mathematics, Grade 9 Academic or Applied
This course enables students to consolidate their understanding of relationships and extend their problem-solving and
algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and
graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret
graphs of quadratic relationships. Students will investigate similar triangles, the trigonometry of right-angled triangles, and
the measurement of three-dimensional objects. Students will consolidate their mathematical skills as they solve problems
and communicate their thinking.
Functions, Grade 11, University MCR3U1
PREREQUISTE: Principles of Mathematics, Grade 10, Academic
This course introduces the mathematical concept of the function by extending students' experiences with linear and
quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and
exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving
applications of functions; and develop facility in simplifying polynomial and rational expressions. Students will reason
mathematically and communicate their thinking as they solve multi-step problems. A mark of at least 70% from Grade
10 Academic is strongly recommended.
Functions and Applications, Grade 11, University/College MCF3M1
PREREQUISTE: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied
Note: This is the required Prerequisite for Mathematics for College Technology, MCT 4C1.
This course introduces basic features of the function by extending students' experiences with quadratic relations. It
focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students
will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve
problems relating to financial and trigonometric applications. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
Foundations for College Mathematics, Grade 11, College MBF3C1
PREREQUISTE: Foundations of Mathematics, Grade 10, Applied
This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world.
Students will extend their understanding of quadratic relations, as well as of measurement and geometry; investigate
situations involving exponential growth; solve problems involving compound interest; solve financial problems connected
with vehicle ownership; and develop their ability to reason by collecting, analysing, and evaluating data involving one and
two variables. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Mathematics for Work and Everyday Life, Grade 11, Workplace MEL3E1
PREREQUISTE: Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a
ministry-approved locally developed Grade 10 mathematics course
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily
life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations
of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel
in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their
thinking.
Calculus and Vectors, Grade 12, University Preparation MCV4U1
Note: The new Advanced Functions can be taken concurrently with or can precede Calculus and Vectors.
This course builds on students' previous experience with functions and their developing understanding of rates of change.
Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines
and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of
polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to the modelling of real-
world relationships. Students will also refine their use of the mathematical processes necessary for success in senior
mathematics. This course is intended for students who plan to study mathematics in university and who may choose to
pursue careers in fields such as physics and engineering.
Advanced Functions, Grade 12, University Preparation MHF4U1
PREREQUISITE: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12,
College Preparation
This course extends students' experience with functions. Students will investigate the properties of polynomial, rational,
logarithmic, and trigonometric functions; broaden their understanding of rates of change; and develop facility in applying
these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in
senior mathematics. This course is intended both for students who plan to study mathematics in university and for those
wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university
programs.
Mathematics of Data Management, Grade 12, University Preparation MDM4U1
PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11,
University Preparation
This course broadens students' understanding of mathematics as it relates to managing data. Students will apply methods
for organizing large amounts of information; solve problems involving probability and statistics; and carry out a culminating
project that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes
necessary for success in senior mathematics. Students planning to enter university programs in business, the social
sciences, and the humanities will find this course of particular interest.
Mathematics for College Technology, Grade 12, College Preparation MCT4C1
PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation
This course enables students to extend their knowledge of functions. Students will investigate and apply properties of
polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and
algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address
applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their
thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs.
Foundations for College Mathematics, Grade 12, College Preparation MAP4C1
PREREQUISITE: Foundations for College Mathematics, Grade 11, College Preparation
This course enables students to broaden their understanding of real-world applications of mathematics. Students will
analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; simplify
expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve
multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and
human services, and for certain skilled trades.
Mathematics for Work and Everyday Life, Grade 12, Workplace Preparation MEL4E1
PREREQUISITE: Mathematics for Work and Everyday Life, Grade 11, Workplace Preparation
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily
life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems
involving familiar situations; investigate accommodation costs and create household budgets; use proportional reasoning;
estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical
skills as they solve problems and communicate their thinking
| 677.169 | 1 |
a mathematical modeling course in a civil/environmental engineering program
This book has a dual objective: first, to introduce the reader to some of the most important and widespread environmental issues of the day; and second, to illustrate the vital role played by mathematical models in investigating these issues. The environmental issues addressed include: ground-water contamination, air pollution, and hazardous material emergencies. These issues are presented in their full real-world context, not as scientific or mathematical abstractions; and for background readers are invited to investigate their presence in their own communities.
The first part of the book leads the reader through relatively elementary modeling of these phenomena, including simple algebraic equations for ground water, slightly more complex algebraic equations (preferably implemented on a spreadsheet or other computerized framework) for air pollution, and a fully computerized modeling package for hazardous materials incident analysis. The interplay between physical intuition and mathematical analysis is emphasized.
The second part of the book returns to the same three subjects but with a higher level of mathematical sophistication (adjustable to the preparation of the reader by selection of subsections.) Many important classical mathematical themes are developed through this context, examples coming from single and multivariable calculus, differential equations, numerical analysis, linear algebra, and probability. The material is presented in such a way as to minimize the required background and to encourage the subsequent study of some of these fields.
An elementary course for a general audience could be based entirely on Part I, and a higher level mathematics, science, or engineering course could move quickly to Part 2. The exercises in both parts tend to be quite thought-provoking and considerable course time might be well devoted to discussing their solutions, perhaps even in a seminar format. The emphasis throughout is on fundamental principles and concepts, not on achieving technical mastery of state-of-the-art-models.
Excerpt: 2.4 Darcy's Law (p. 19)
In developing any kind of mathematical model, you need to figure out what the key physical variables are that control the situation of interest. We are interested here in the flow of ground water through some kind of porous geologic medium. In about 1850 a French engineer named Henri Darcy was interested in essentially the same question because he was trying to set up a system for filtering water in the city of Dijon, France, by passing it through beds of clean sand (such sand filters are still commonly used today.) The question he faced was really how much water could move at what rate through what size sand filter. To answer this question, he set up some simple experiements.
About the Author
Charles Hadlock received his Ph.D. from the University of Illinois in 1970, specializing in applied mathematics. He taught at Amherst and Bowdoin Colleges before joining the firm of Arthur D. Little in Cambridge, Massachusetts in 1977, where he developed and led an international consulting practice in environmental management and risk analysis. His central focus was the investigation and follow-up to the unfolding environmental calamities of the day, including Love Canal, Bhopal, Three Mile Island, and other well known cases, and the use of mathematical models to enhance the understanding of and response to these situations. In 1990 he moved to Bentley College as Chair of Mathematical Sciences, and is currently Dean of the Undergraduate College and Associate Dean of Faculty. Dr. Hadlock has written an award-winning book on Galois theory, as well as numerous research reports and publications, and he has chaired several major government panels reviewing environmental policies.
MAA Review
The author of this book is particularly well suited to writing about the subject. Starting off as a mathematics professor, he spent 13 years as an environmental consultant before returning to the classroom. Thus, many of the examples, experiences, and insights in the book are realistic and convincing. Continued....
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NCERT MATHEMATICS SOLUTION BOOK 12MATH
This book is sold subject to the condition that it shall not, by way of trade, be lent, re- ...solutions. We see this as crucial for liberating school mathematics from the .....Mathematics anxiety and 'math phobia' are terms that are used in popular ... even at an early age in a small number of children12. ...
Personal Reflections on Mathematics. Book Review and Resources. F. In the Classroom. C. 8 12... emotions that surface at the very mention of Math: ..... this is the only holistic solution to the problems discussed so ....Mathematics Curriculum in the National Curriculum Framework 2005, NCERT New Delhi
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Must you learn mathematics as in the 1800s
? Teach
yourself algebra and calculus -- and learn to use MATLAB®at the same time!
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the table of contents:
MATLAB as a Calculator
Systems of Linear Equation
Zeros and Extreme Points
Symbolic Algebra
Integrals
Random Events and Statistics
Complex Numbers and Functions
Differential Equations of First and Second Order
Fourier Series
Fourier Transforms
Magnetostatics
in (x,y)
Space Heat Conduction in (x,y)
Space
Viscous Flow past an Obstacle
Viscous Flow in Three Dimensions
Electromagnetic Waves in (x,y)
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Harmonic Oscillators in 1D and 2D
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This course, presented by MIT and taught by Daniel Kleitman, provided instruction on combinatorics, graph theory and discrete mathematics. The main content provided online is a sample final paper project assignment....
This lesson from Illuminations introduces students to to basic graph theory and Euler circuits. Students will gain hands on experience using graphs. The lesson involves sketching graphs that have Euler paths and...
This lesson from illuminations helps to illustrate quadratic equations. Students will determine the maximum value of a quadratic equation and compare different equations. The lesson also asks students to move between...
Graph theory is widely used in computer science, engineering and of course, mathematics. Here, visitors will find links to information about the applications and components of graph theory, as well as its pioneers.
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s a free textbook offered by BookBoon.'This book is a guide through a playlist of Calculus instructional videos. The...
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This sThe author states, "'A=B' is about identities in general, and hypergeometric identities in particular, with emphasis on...
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The author states, "'A=B' is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks, and we intend to maintain the latest versions of the programs that carry out these algorithms on this page. So be sure to consult this page from time to time, and help yourself to the latest versions of the programs.״The entire book is available for purchase, but can also be downloaded for free at this site. This website also included some reviews of the book.
According to the author, "We study fundamental algebraic structures, namely groups, rings, fields and modules, and maps...
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According to the author, "We study fundamental algebraic structures, namely groups, rings, fields and modules, and maps between these structures. The techniques are used in many areas of mathematics, and there are applications to physics, engineering and computer science as well. In addition, I have attempted to communicate the intrinsic beauty of the subject. Ideally, the reasoning underlying each step of a proof should be completely clear, but the overall argument should be as brief as possible, allowing a sharp overview of the result.״Each chapter of the book is downloadable as a separate pdf file.
״Abstract Algebra: Theory and Applications is an open-source textbook written by Tom Judson that is designed to teach the...
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״Abstract Algebra: Theory and Applications is an open-source textbook written by Tom Judson that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.״
'Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in...
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'Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in order to present the standard concepts and computational techniques of calculus. The student activities provide most of the material to be assigned as homework, but since the book does not contain the usual routine exercises, instructors wanting such exercises will need to supply their own or use a homework system such as WebWork. With this approach Active Calculusmakes it possible to teach an inquiry based learning course without severely restricting the material covered. Although this book is new, it has been class tested by the author and his colleagues both at their university and elsewhere.From the preface:Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer a plausibility argument for such results, rarely do we include formal proofs.'
This is a free textbook offered by InTech.'Adaptive filtering can be used to characterize unknown systems in time-variant...
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This is a free textbook offered by InTech.'Adaptive filtering can be used to characterize unknown systems in time-variant environments. The main objective of this approach is to meet a difficult comprise: maximum convergence speed with maximum accuracy. Each application requires a certain approach which determines the filter structure, the cost function to minimize the estimation error, the adaptive algorithm, and other parameters; and each selection involves certain cost in computational terms, that in any case should consume less time than the time required by the application working in real-time. Theory and application are not, therefore, isolated entities but an imbricated whole that requires a holistic vision. This book collects some theoretical approaches and practical applications in different areas that support expanding of adaptive systems.'
| 677.169 | 1 |
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom
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Introductory Mathematics 2
This course aims to consolidate and extend the topics covered in Introductory Mathematics 1. The course includes basic skills and their application to problem solving in the topics of linear function, graphing, probability and statistics.
Available in 2014
* Students will be proficient in their understanding of appropriate mathematical techniques when commencing undergraduate study. * Students will display competency, working individually and in groups. * Students will have acquired critical reasoning and problem solving skills in order to solve mathematical problems.
| 677.169 | 1 |
How is that you can walk into a classroom and gain an overall sense of thequality of math instruction taking place there? What contributes to gettingthat sense? In Math Sense, Chris Moynihan explores some of the componentsthat comprise the look, sound, and feel of effective teaching and learning.Does the landscape of the classroom feature such items... more...
How can we solve the national debt crisis? Should you or your child take on a student loan? Is it safe to talk on a cell phone while driving? Are there viable energy alternatives to fossil fuels? What could you do with a billion dollars? Could simple policy changes reduce political polarization? These questions may all seem very different, but theyWhile computational technologies are transforming the professional practice of mathematics, as yet they have had little impact on school mathematics. This pioneering text develops a theorized analysis of why this is and what can be done to address it. It examines the particular case of symbolic calculators (equipped with computer algebra systems) in... more...
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books.google.com - From... notions of algebra
Basic notions of algebra
From of sureness of foot and lightness of touch in the exposition... which transports the reader effortlessly across the whole spectrum of algebra...Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers; certainly beginning postgraduate students would gain a most valuable perspective from it but... both the adventurous undergraduate and the established professional mathematician will find a lot to enjoy..." Math. Gazette
From inside the book
Review: Basic Notions of Algebra
User Review - Joecolelife - Goodreads
The author explains not just the definitions but also the 'philosophy' of algebra with highly non- trivial examples from geometry,analysis & topology not to mention algebra itself. Examples motivate ...Read full review
Review: Basic Notions Of Algebra
User Review - Joecolelife - Goodreads
An off-hand account of algebra by one of the best authorities of the subject. Recommended as a "serious" pass-time.Read full review
| 677.169 | 1 |
I am selling my calculus book used for calculus 1-4. I will also include the solution manual for the $125 price. Both books are in like new condition. The Calculus book will include a binder. My email is: regnierz@msoe.edu
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A group Finnish mathematics students, teachers and researchers have made history during the last weekend of September, producing an open-license High School Mathematics book in a three-day booksprint, for the first time in the world.
"Usually writing a school book is a solitary process requiring at least a year of time, for which the author will receive a small financial compensation. Now, the same was achieved with inspired creative force over one weekend and everyone will get to benefit from the fruit of our labour," says project leader Vesa Linja-aho.
As far as as is known, this was the first one-weekend schoolbook sprint in the world. A similar approach has previously been used to produce manuals for open-source computer programs.
The new mathematics book consists of just over hundred pages and three sections: reading areas, applications, functions and equations. An electronic version of the book, as well as its LaTeX source code, is available for download at . A printed version will be available this year. Before printing, the book will be proofread by the community.
All 30 000 Finnish High school students can benefit from this book. The price for a similar mathematics book is around 15 euros, hence the possible value of the book project can be be up to half a million euros.
"The most important aspect of this project is openness and transparency. All development and evolution require copying and revising. This does not occur in current textbooks, which cannot be altered due to copyright reasons," says project member Tommi Sottinen, professor of business mathematics at the University of Vaasa.
The book will be published under open Creative Commons license, so anyone can copy and edit the book freely.
Over 30 math teachers, researchers and students took part in the project, but representatives of the end users were also present. High School seniors Tiina Salola and Anni Saarelainen tested the book as it was written. "We like the book very much as it presents complicated things clearly. The book starts from basics and does not make assumptions on the knowledge level of the student," said Salola and Saarelainen.
The project team hope that this will the beginning of a new way of producing learning materials.
"High-quality free material decreases the cost of studying. Currently even in Finland, where education is free, an individual student will pay over a thousand euros for books during their study years. Reduction in these costs will promote educational equality", says Linja-aho.
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MATH 96
Preparation for Elementary Statistics
This single one-semester course can be used to replace the traditional pathway to statistics (Math 88, Math 90, and Math 103 or Math 110).
Math 96 offers a streamlined approach to preparing you for transfer-level statistics at Cuyamaca College (Math 160), but it's nothing like your typical high school algebra course. We will study only the core concepts from arithmetic, pre-algebra, algebra, and introductory statistics that are needed to understand the basics of college-level statistics. We'll do a lot of writing in this course to answer questions such as, "Are adult's breakfast cereals healthier than children's breakfast cereals?" and "Do banks practice discriminatory lending practices?"
This is a new pathway to statistics designed for students who do NOT plan to major in math, science, engineering or business. Furthermore upon successful completion of Math 96, it is assumed that you will enroll in Math 160 Elementary Statistics at Cuyamaca College. Successful completion of Math 96 qualifies you to take transfer-level Math 160 at Cuyamaca College only and does not qualify you to take any other math course. At this time Math 96 does not transfer to other colleges. However, Math 160 meets the degree requirements at Cuyamaca College and transfers to the four-year institutions. So once you successfully complete Math 96 and Math 160, you could be done with the required math for your two-year and/or four-year degrees.
For financial aid purposes, Math 96 will count towards your financial aid if you are receiving financial aid at Cuyamaca College. It will NOT count towards your financial aid if you are receiving financial aid at Grossmont College. If you plan to take this course and have applied for financial aid, please contact an advisor at the financial aid office of either college to help you understand your financial aid options.
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including algebra 1, algebra 2 and calculus
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Product Description
Students will develop foundational math skills needed for higher education and practical life skills with ACE's Math curriculum. PACE 1088 covers identifying four types of prisms, and learning formulas to determine the surface area and volume of a prism, cylinder, and sphere
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Suitable for the GCSE Modular Mathematics, this book covers different concepts through artwork and diagrams.
Synopsis:
This book is revised in-line with the 2007 GCSE Modular Mathematics specification. This Student Book is delivered in colour giving clarity to different concepts through artwork and diagrams. Worked examples, practice exercises and examiners tips ensure students are fully prepared for their exams. It is written by an experienced author team, including Senior Examiners, which means you can trust that the 2007 specification is covered to ensure exam success
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academics
Mathematics
Pitzer's mathematics courses are designed to serve three purposes: general education; service to courses in social, behavioral and natural sciences; and the basis for the mathematics major.
Pitzer Advisers: D. Bachman, J. Grabiner, J. Hoste.
General Education in Mathematics
What is mathematics? What are its major methods and conclusions? How is it related to other subjects? What do modern mathematicians do? Several Pitzer courses specifically address these questions. These courses (described below) are: MATH001 PZ, Mathematics, Philosophy and the "Real World"; MATH 010 PZ The Mathematical Mystery Tour; MATH 015 PZ Mathematics for Teachers I: Number and Operation; MATH 016 PZ Mathematics for Teachers II: Geometry and Data. These courses cover mathematical material that is exciting and sophisticated and yet accessible to students with a standard high school education in mathematics. As such they offer students an excellent opportunity to break fresh ground in kinds of mathematics they are not likely to have seen before. All of these courses meet Pitzer's Educational Objective in Formal Reasoning.
The Precalculus and Calculus Sequences
MATH 025 PZ, Precalculus, is designed to prepare students for Calculus I. The course reviews linear, quadratic and polynomial functions, before introducing the exponential, logarithmic and trigonometric functions. These are the functions most widely used in the quantitative social sciences and natural sciences. MATH 025 PZ does not fulfill the Quantitative Reasoning Requirement.
MATH 030 PZ, MATH 031 PZ and MATH 032 PZ comprise the calculus sequence. The calculus, since it studies motion and change, is the key mathematical tool in understanding growth, decay and motion in the physical, biological, and social sciences. Pitzer offers MATH 030 PZ, MATH 031 PZ and MATH 032 PZ each year. Calculus is also offered at the other Claremont Colleges.
We also offer more advanced courses as part of The Claremont Colleges' Intercollegiate Mathematics program.
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Genre: Traditional story Learning Objectives: Language Comprehension Strand 7: Explore how particular words are used, including words and expressions with similar meanings. Writing Opportunities Strand 9: Sustain form in narrative, including use of person and time (e. g. writing about story characters).
Stewart's SINGLE VARIABLE CALCULUS WITH VECTOR FUNCTIONS has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that characterized all of James Stewart's texts. In this new text, Stewart focuses on problem solving, using the pedagogical system that has worked so well for students in a wide variety of academic settings
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Basic Math - Number Patterns Studying number patterns is important for two reasons. First, they help one better understand the concepts of arithmetic and provide a basis for understanding the concepts of more complex mathematics (algebra, trigonometry, calculus). Second, pattern recognition is a useful problem-solving skill, both in mathematics and in real-world situations. Patterns involving odd and even numbers are investigated. Patterns in multiples of certain numbers lead to an understanding of divisibility rules. Seque Author(s): No creator set
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Bioservers This site contains user-friendly tools to launch DNA database searches, statistical analyses, and population modeling from a centralized workspace. Educational databases support investigations of an Alu insertion polymorphism on human chromosome 16 and single nucleotide polymorphisms (SNPs) in the human mitochondrial control region. Author(s): No creator set
Best of the web - November 2010 Read more:
Watch our pick of the top science videos on the web this month Author(s): No creator set
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CSET Science Subtest II: Heat Transfer and Thermodynamics
This module includes the following chemistry topics:
History of Thermodynamics
Conservation of Energy
Heat Tra
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Statistical Reasoning II Statistical Reasoning in Public Health II provides an introduction to selected important topics in biostatistical concepts and reasoning through lectures, exercises, and bulletin board discussions. Author(s): John McGreadyMethods in Biostatistics II Presents fundamental concepts in applied probability, exploratory data analysis, and statistical inference, focusing on probability and analysis of one and two samples. Author(s): Brian Caffo
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Content within individual OCW courses is (c) by the Johns Hopkins University and individual authors unless otherwise noted. JHSPH OpenCourseWare materials are licensed under a Creative Commons License
Analyzing Statistics S.S. Europe and Russia Students will gather statistical information on countries in Europe and Russia from almanacs. The information will be recorded in a chart. Students will then take the information and make line or bar graphs. Students will analyze the information by answering higher level thinking questions. Author(s): No creator set
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Statistics Online Computational Resource for Education and Research The goals of the Statistics Online Computational Resource ( are to design, validate and freely disseminate knowledge. Specifically, SOCR provides portable online aids for probability and statistics education, technology based instruction and statistical computing. SOCR tools and resources include a repository of interactive applets, computational and graphing tools, instructional and course materials.
The core SOCR educational and computational components include: Distribution Author(s): No creator set
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Supporting Teachers Intervention in Collaborative Knowledge Building In the context of distributed collaborative learning, the teacher's role is different from traditional teacher-centered environments, they are coordinators/facilitators, guides, and co-learners. They monitor the collaboration activities within a group, detect problems and intervene in the collaboration to give advice and learn alongside students at the same time. We have designed an Assistant to support teachers intervention in collaborative knowledge building. The Assistant monitors the collabo Author(s): Chen Weiqin
Artificial Intelligence: Natural Language Processing This course is designed to introduce students to the fundamental concepts and ideas in natural language processing (NLP), and to get them up to speed with current research in the area. It develops an in-depth understanding of both the algorithms available for the processing of linguistic information and the underlying computational properties of natural languages. Wordlevel, syntactic, and semantic processing from both a linguistic and an algorithmic perspective are considered. The focus is on m Author(s): No creator set
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Examining the Burdens of Gendered Racism: Implications for Pregnancy Outcomes Among College-Educated Objectives: As investigators increasingly identify racism as a risk factor for poor health outcomes (with implications for adverse birth outcomes), research efforts must explore individual experiences with and responses to racism. In this study, our aim was to determine how African American college-educated women experience racism that is linked to their identities and roles as African American women (gendered racism).
Methods: Four hundred seventy-four (474) African American women collaborate Author(s): Jackson, Fleda Mask,Phillips, Mona Taylor,Hogue, C
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Formulas for functions of two variables This website features a chart of functions with two variables and the equations for their standard deviation. It is from the Engineering Statistics handbook whose goal is to help scientists and engineers incorporate statistical methods in their work as efficiently as possible. A link to tools and aids for using the handbook is provided. Author(s): No creator set
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Atmospheric Vertical Structure and the First Law of Thermodynamics This sequential set of in-class and homework problems concerns applications of the First Law of Thermodynamics. In the homework, students are first asked to compute and plot potential temperatures of specified adiabats. In a second assignment, the potential temperature from an observed sounding is computed and plotted to develop a framework for understanding the stratification of the atmosphere. These activities are intended to help students discover the importance and utility of conservation pr Author(s): No creator set
US History II Upon completion of this course you will: Demonstrate comprehension of a broad body of historical knowledge; Express ideas clearly in writing; Work with classmates to research an historical issue; Interpret and apply data from original documents; Identify underrepresented historical viewpoints; Write to persuade with evidence; Compare and contrast alternate interpretations of an historical figure, event, or trend; Explain how an historical event connects to or causes a larger trend or theme; Deve Author(s): No creator set
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Is this career the right one for you?
Expand knowledge in mathematical areas, such as algebra or geometry, by developing new rules, theories, and concepts
Use mathematical formulas and models to prove or disprove theories
Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, or other fields
Develop mathematical or statistical models to analyze data
Interpret data and report conclusions from their analyses
Use data analysis to support and improve business decisions
Read professional journals, talk with other mathematicians, and attend professional conferences to maintain knowledge of current trends
Career Overview
Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, and business problems. The work of mathematicians falls into two broad classes: theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined and often overlap.
Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although these workers seek to increase basic knowledge without necessarily considering its practical use, such pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements. Many theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research. (See the Professor or College Instructor career profile.)
Applied mathematicians use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the most efficient way to schedule airline routes between cities, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the cost-effectiveness of alternative manufacturing processes.
Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when solving a difficult problem. Some mathematicians, called cryptanalysts, analyze and decipher encryption systems—codes—designed to transmit military, political, financial, or law-enforcement-related information.
Applied mathematicians start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables. They often use computers to analyze relationships among the variables, and they solve complex problems by developing models with alternative solutions.
Individuals with titles other than mathematician also do work in applied mathematics. In fact, because mathematics is the foundation on which so many other academic disciplines are built, the number of workers using mathematical techniques is much greater than the number formally called mathematicians. For example, engineers, computer scientists, physicists, and economists are among those who use mathematics extensively. Some professionals, including statisticians, actuaries, and operations research analysts, are actually specialists in a particular branch of mathematics. (For more information, see the career profiles on actuaries, operations research analysts, and statisticians.) Applied mathematicians frequently are required to collaborate with other workers in their organizations to find common solutions to problems.
Work environment. Mathematicians usually work in comfortable offices. They often are part of interdisciplinary teams that may include economists, engineers, computer scientists, physicists, technicians, and others. Deadlines, overtime work, special requests for information or analysis, and prolonged travel to attend seminars or conferences may be part of their jobs.
Mathematicians who work in academia usually have a mix of teaching and research responsibilities. These mathematicians may conduct research by themselves or in close collaboration with other mathematicians. Collaborators may work together at the same institution or from different locations, using technology such as e-mail to communicate. Mathematicians in academia also may be aided by graduate students.
Training, Qualifications, and Advancement
A Ph.D. degree in mathematics usually is the minimum educational requirement for prospective mathematicians, except in the Federal Government.
Education and training. In private industry, candidates for mathematician jobs typically need a Ph.D., although there may be opportunities for those with a master's degree. Most of the positions designated for mathematicians are in research-and-development laboratories, as part of technical teams.
In the Federal Government, entry-level job candidates usually must have at least a bachelor's degree with a major in mathematics or 24 semester hours of mathematics courses. Outside the Federal Government, bachelor's degree holders in mathematics usually are not qualified for most jobs, and many seek advanced degrees in mathematics or a related discipline. However, bachelor's degree holders who meet State certification requirements may become primary or secondary school mathematics teachers. (For additional information, see the career profiles on teachers—elementary, middle, and high school.)
Most colleges and universities offer a bachelor's degree in mathematics, and many universities offer master's and doctoral degrees in pure or applied mathematics. Courses usually required for these programs include calculus, differential equations, and linear and abstract algebra. Additional courses might include probability theory and statistics, mathematical analysis, numerical analysis, topology, discrete mathematics, and mathematical logic. In graduate programs, students also conduct research and take advanced courses, usually specializing in a subfield of mathematics.
Many colleges and universities advise or require students majoring in mathematics to take courses in a closely related field, such as computer science, engineering, life science, physical science, or economics. A double major in mathematics and another related discipline is particularly desirable to many employers. High school students who are prospective college mathematics majors should take as many mathematics courses as possible while in high school.
Other qualifications. For jobs in applied mathematics, training in the field in which mathematics will be used is very important. Mathematics is used extensively in physics, actuarial science, statistics, engineering, and operations research. Computer science, business and industrial management, economics, finance, chemistry, geology, life sciences, and behavioral sciences are likewise dependent on applied mathematics. Mathematicians also should have substantial knowledge of computer programming, because most complex mathematical computation and much mathematical modeling are done on a computer.
Mathematicians need to have good reasoning to identify, analyze, and apply basic principles to technical problems. Communication skills also are important, because mathematicians must be able to interact and discuss proposed solutions with people who may not have extensive knowledge of mathematics.
Advancement. The majority of those with a master's degree in mathematics who work in private industry do so not as mathematicians but in related fields, such as computer science, where they have titles such as computer programmer, systems analyst, or systems engineer. In these occupations, workers can advance to management positions.
Employment
Mathematicians held about 2,900 jobs in 2008. Many people with mathematical backgrounds also worked in other occupations. For example, there were about 54,800 jobs for postsecondary mathematical science teachers in 2008.
Many mathematicians work for the Federal Government, primarily in the U.S. Department of Defense which accounts for about 81 percent of the mathematicians employed by the Federal Government. Many of the other mathematicians employed by the Federal Government work for the National Institute of Standards and Technology (NIST) or the National Aeronautics and Space Administration (NASA).
In the private sector, major employers include scientific research and development services and management, scientific, and technical consulting services. Some mathematicians also work for insurance carriers.
Job Outlook
Employment of mathematicians is expected to grow much faster than average. However, keen competition for jobs is expected.
Employment change. Employment of mathematicians is expected to increase by 22 percent during the 2008–18 decade, which is much faster than average for all occupations. Advancements in technology usually lead to expanding applications of mathematics, and more workers with knowledge of mathematics will be required in the future. However, jobs in industry and government often require advanced knowledge of related scientific disciplines in addition to mathematics. The most common fields in which mathematicians study and find work are computer science and software development, physics, engineering, and operations research. Many mathematicians also are involved in financial analysis and in life sciences research.
Job prospects. Job competition will remain keen because employment in this occupation is relatively small and few new jobs are expected. Ph.D. holders with a strong background in mathematics and a related discipline, such as engineering or computer science, and who apply mathematical theory to real-world problems will have the best job prospects in related occupations. In addition, mathematicians with experience in computer programming will better their job prospects in many occupations.
Holders of a master's degree in mathematics will face very strong competition for jobs in theoretical research. Because the number of Ph.D. degrees awarded in mathematics continues to exceed the number of available university positions—especially tenure-track positions—many graduates will need to find employment in industry and government.
Employment in theoretical mathematical research is sensitive to general economic fluctuations and to changes in government spending. Job prospects will be greatly influenced by changes in public and private funding for research and development.
Earnings
Median annual wages of mathematicians were $95,150 in May 2008. The middle 50 percent earned between $71,430 and $119,480. The lowest 10 percent had earnings of less than $53,570, while the highest 10 percent earned more than $140,500.
In March 2009, the average annual salary in the Federal Government was $107,051 for mathematicians; $107,015 for mathematical statisticians; and $101,645 for cryptanalysts.
For More Information
For more information about careers and training in mathematics, especially for doctoral-level employment, contact:
Information on obtaining positions as mathematicians with the Federal Government is available from the Office of Personnel Management through USAJOBS, the Federal Government's official employment information system. This resource for locating and applying for job opportunities can be accessed through the Internet at or through an interactive voice response telephone system at (703) 724-1850 or TDD (978) 461-8404. These numbers are not toll free, and charges may result.
For advice on how to find and apply for Federal jobs, see the Occupational Outlook Quarterly article "How to get a job in the Federal Government," online at
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Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.
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0471476021Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way.
Online applications help improve your mathematical reasoning.
Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at
Improve your grade with the Student Solutions Manual.
A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.
Related Subjects
Meet the Author
Doug Ensley is a full professor at Shippenshburg University with a Ph.D. from Carnegie Mellon. He is an active participant in national and regional committees determining the future of the discrete math curriculum, and he regularly speaks at Joint Math and MathFest.
Winston Crawley is a full professor and chair of the math department at Shippensburg University. He has a Ph.D. from University of Tennessee-Knoxville. Crawley developed the undergraduate computer science curriculum at Shippens
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GED Math Problem Solver - 2nd edition
Summary: The GED Math Problem Solverintegrates problem-solving and reasoning strategies with mathematical skills using problems encountered in everyday life. This text builds understanding of mathematical relationships by focusing on problem-solving skills, developing estimation and mental math strategies, and integrating algebra, geometry, and data analysis with arithmetic.FEATURES 25 lessons combining instruction, practice, and review Complete answer key, including solutions Cumulative...show more review and GED practice at the end of each lesson Test-taking lessons and practice Exercises using data and graphs collected in the appendix Calulator exploration using the Casiofx-260 Full-length GED Mathematics practice test ...show less
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People in the Department
Program Offerings
Mathematics Advising Guide
The Mathematics and Computer Science Department offers majors in
mathematics, mathematics education, and computer science. This
document is designed as a resource for students in navigating through
the requirements of the math or math education major. (There is a
companion guide for computer science.) It should also be valuable to
freshman advisors outside the department as well as advisors within
the department. The first section gives a brief overview of the
discipline; the remaining sections describe the major, the honors
program, and the minor.
As an additional resource, you can also use the Mathematics Major Form, which is
intended for students majoring (or considering majoring) in
Mathematics, and their advisors. This form will help you plan out
your mathematics courses.
Mathematics
Mathematics is a field that is rich in both theoretical analysis and practical
application. It is also quite broad in scope, encompassing subfields such
as statistics, applied mathematics, and the classical subjects of analysis,
algebra, and geometry. This diversity within mathematics makes most definitions
of mathematics either too narrow or too general. However, one can say that
mathematicians deal with objects (e.g. numbers, triangles, function), and
their patterns and relationships (e.g. prime numbers, isosceles triangles,
calculus of functions). The search for patterns and relationships involves
the process of abstraction, that is forming a generalization from a set
of examples that reflects shared properties of these examples. Mathematicians
use the skills of creative and analytical thinking to hypothesize the existence
of patterns and use logical argument to show the validity of these postulates.
Mathematics is also a science, a science of patterns and relationships.
Mathematicians experiment in various laboratories -- the mind, the computer,
and the natural world.
Mathematicians are always in demand in industry, business, government,
and academia. The breadth of subject matter and the logical, analytical
training required provide math majors with flexibility in their choice
of career.
Mathematicians are involved in activities such as:
mathematical modeling of semiconductors for a research laboratory
studying cryptology schemes for secure communication networks
teaching in the public schools
teaching at a college or university
researching the role that chaotic systems play in the regulation of the
heart
devising new fractal algorithms for the display of realistic natural objects
economic forecasting and model building for the government and industry
devising better ways to solve the differential equations arising in the
flow of turbulent fluids
working as an actuary for a large insurance firm
carrying out foundational mathematical research at a research university
or research laboratory
working as a statistician for a governmental agency
This is only the tip of the iceberg as far as career opportunities in the
mathematical sciences. For more information talk to someone in the Math/Computer
Science department or see the departmental secretary for brochures describing
careers in math.
Mathematics majors who are interested in research opportunities or in
teaching at the college level should choose a set of courses, in consultation
with a department member, that will prepare them for graduate study in
mathematics or a related field (such as economics, mathematical physics,
statistics, etc.)
The Major
This section lists the requirements of the math major and describes the
senior oral which is an optional component of the major. Qualified majors
may additionally participate in the honors program, which is described
in the next section.
A grade of C- or higher is necessary in all courses used to satisfy
the requirements of the major, which are as follows:
MCS-121, MCS-122 or MCS-132, MCS-220, MCS-221, and MCS-222, with a grade point
average of at least 2.333 in these five courses.
These five courses form the core of the major and should usually be taken
during the freshman and sophomore years.
MCS-142 and MCS-177. These two courses in cognate
fields to mathematics serve to give breadth to the math major.
Completion of at least one course from the classical core of mathematics:
MCS-321 (Complex),
MCS-313 (Algebra), and
MCS-331 (Real Analysis).
This course can count toward 3a.
Completion of at least one course from the applied areas of mathematics:
MCS-242, MCS-253, MCS-256, MCS-342, MCS-357, MCS-355, and
MCS-358.
This course can count toward 3a.
Either complete one of the capstone courses MCS-314, MCS-332, MCS-342,
MCS-344, MCS-357, MCS-358
(beyond any used for requirements 3) or alternatively pass a successful senior
oral examination covering the student's knowledge of mathematics. Successful
completion of an honors thesis also will
fulfill this requirement.
Senior oral
As described above, every math major must either take an additional upper
level math course from a specified list or alternatively submit to oral
examination during the Spring semester of their final year.
A student who chooses to take the oral examination selects, in consultation
with a faculty member, a topic to research. They then present a 20-minute
talk on that topic to an examining committee of three faculty members.
At the conclusion of the talk, the faculty question the student about the
talk, and also about fundamental topics from the student's full four years'
of courses. The goal is not to require recollection of details, but rather
to make sure that the student is leaving with the essentials intact.
The examination committee confers privately immediately after the examination
and delivers the results to the student at the conclusion of their deliberations.
The outcome is either that the student is deemed to have satisfied the
requirement or alternatively that the student is requested to retry the
examination at a later date. In the latter case, specific suggestions for
areas of improvement are provided by the faculty committee.
More information about the oral examination procedures and schedule
are provided routinely to those fourth-year majors who will likely choose
to take the examination.
Mathematics Education major
The requirements for the mathematics education major are met by the completion
of the mathematics major as listed above, with the additional requirement
that MCS-303(Geometry) and MCS-313 (Modern Algebra), must be completed. Math
education majors may substitute the sequence MCS-313-MCS-303
for the sequence requirement in part 3 of the math major.
Minnesota State
Standards for the Mathematics Education Major may be found here.
Concentrations
Within the math major there are two concentrations or tracks available
to students with specific interests.
Applied Mathematics
This concentration is for those students interested in the scientific applications
of mathematics, and who are planning on entering fields that require training
in mathematical modeling and the analysis of physical problems. MCS-253(Diff
Eqns) and MCS-357(Discrete Dynamical Systems) form the core of this track. Other highly
recommended courses would be MCS-321(Complex), MCS-358(Math Model Building),
and MCS-355(Numerical Analysis).
Statistics
This concentration is intended for students who wish to pursue a career
in actuarial science, or who will do graduate studying statistics, biostatistics,
or a related field. MCS-242(Appd Stats), MCS-341(Prob Math Stat I), and MCS-342(Prob
Math Stat II) form the core of this track. For those interested in actuarial
science, MCS-355 (Numerical Analysis) is recommended. Also,
a minor in economics or management is recommended. For those interested
in graduate study in biostatistics, epidemiology, or public health, a minor
in biology is recommended. For those interested in pursuing a PhD in statistics,
MCS-331(Real Analysis) and MCS-332(Topology) are strongly recommended.
Sample student plans
All students should ideally lay out a schedules of their own showing what
courses they plan to take when. This schedule may not accurately forecast
the future, but it is helpful none the less. The sample plans below are
a useful starting point in developing such an individual plan. You can
select the sample plan that comes closest to fitting your own situation
and then tailor it as necessary. Note that these sample plans show only
courses within the Math and Computer Science Department, but in some cases
exceed the requirements of the major. Also note that certain courses are
offered on an every-other year basis; for example MCS-314 (Algebra II) is
offered in the spring of odd years and MCS-332 (Topology) is offered in the
spring of even years. Courses offered every other year include MCS 242,
313, 314, 331, 332, 341, 342, 344, 358, 385, and 394. Please keep these
course alterations in mind when planning out your major. Check the college
catalog for when the courses you are interested in will be scheduled.
Traditional (MCS 313-314 (Algebra) sequence)
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
3rd year
222
321
4th year
313
357
314
Traditional (MCS 331-332 (Real Analysis) sequence)
Fall
Spring
1st year
121
177
122
2nd year
220
221
222
3rd year
142
313
256
4th year
331
332
Traditional (MCS 341-342 (Prob Math Stat) sequence)
Fall
Spring
1st year
121
122
142
2nd year
220
177
221
3rd year
222
331
256
4th year
341
342
Statistics concentration
Fall
Spring
1st year
121
122
142
2nd year
220
177
221
3rd year
222
331
242
4th year
341
342
Applied concentration
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
3rd year
222
331
253
4th year
357
355
321
Math Education (Even Year Graduation; Student Teach in Spring)
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
242
3rd year
222
313
253
4th year
303
358 J-term
student
teaching
Math Education
(Odd Year Graduation; Student Teach in
Spring)
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
256
3rd year
222
358 J-term
242
313
4th year
303
student
teaching
Math Education
(Even Year Graduation; Student Teach in
Fall)
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
242
3rd year
222
303
253
4th year
student
teaching
358 J-term
313
Math Education (Odd Year Graduation; Student Teach in Fall)
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
3rd year
222
303
358 J-term
242
313
4th year
student
teaching
253
Traditional, grad. school bound
Fall
Spring
1st year
121
177
122
2nd year
220
142
221
222
3rd year
331
332
321
4th year
313
314
Statistics grad. school bound
Fall
Spring
1st year
121
142
122
2nd year
220
177
221
222
3rd year
331
242
332
4th year
341
342
Applied, grad. school bound
Fall
Spring
1st year
121
177
122
2nd year
220
142
221
222
3rd year
331
321
253
4th year
357
313
355
Start with pre-calc
Fall
Spring
1st year
120
121
177
2nd year
122
220
221
3rd year
222
142
321
4th year
331
256
313
Fall junior year abroad
Fall
Spring
1st year
121
122
177
2nd year
220
142
221
3rd year
abroad
222
256
4th year
321
331
313
Spring (Stats) junior year abroad
Fall
Spring
1st year
121
122
142
2nd year
220
177
221
256
3rd year
331
222
abroad
4th year
341
342
Junior year abroad
Fall
Spring
1st year
121
177
122
2nd year
220
142
221
222
3rd year
abroad
abroad
4th year
313
331
321
256
Honors Program
In order to graduate with honors in mathematics, a student must complete
an application for admission to the honors program, showing that the student
satisfies the admission requirements, and then must satisfy the requirements
of the program.
Requirements for
graduation with honors
The requirements of the honors program, after admission to the program,
are as follows:
Attainment of a quality point average greater than pi in courses used to
satisfy the requirements of the major. If a student has taken more courses
than the major requires, that student may designate for consideration any
collection of courses satisfying the requirements of the major.
Approval by the Mathematics Honors Committee of an honors thesis. The thesis
should conform in general outline to the approved proposal (or an approved
substitute proposal), should include approximately 160 hours of work, and
should result in an approved written document. Students completing this
requirement will receive credit for the course MC96 (Honors Thesis), whether
or not they graduate with honors. (See the Mathematics Honors Thesis Guidelines,
below.)
Oral presentation of the thesis in a public forum, such as the departmental
seminar. This presentation will not be evaluated as a criterion for thesis
approval, but is required.
Honors thesis guidelines
Mathematics honors thesis proposals should be written in consultation with
the faculty member who will be supervising the work. The proposal and thesis
must each be approved by the Mathematics Honors Committee. These guidelines
are intended to help students, faculty supervisors, and the committee judge
what merits approval.
The thesis should include creative work, and should not reproduce well-known
results; however, it need not be entirely novel. It is unreasonable for
an undergraduate with limited time and library resources to do a thorough
search of the literature, such as would be necessary to ensure complete
novelty. Moreover, it would be rare for any topic to be simultaneously
novel, easy enough to think of, and easy enough to do.
The thesis should include use of primary-source reference material.
As stated above, an exhaustive search of the research literature is impractical.
None the less, the resources of inter-library loan, the faculty supervisor's
private holdings, etc. must be tapped if the thesis work is to go beyond
standard classroom/textbook work.
The written thesis should sufficiently explain the project undertaken
and results achieved that someone generally knowledgeable about mathematics,
but not about the specific topic, can understand it. The quality of writing
and care in citing sources should be adequate for external distribution
without embarrassment.
The thesis must contain a substantial mathematical component, though
it can include other disciplines as well. If a single thesis simultaneously
satisfies the requirements of this program and some other discipline's
honors program, it can be used for both (subject to the other program's
restrictions). However, course credit will not be awarded for work which
is otherwise receiving course credit.
The Mathematics Honors Committee will maintain a file of past proposals
and theses, which may be valuable in further clarifying what constitutes
a suitable thesis. In order to provide some guidance of the sort before
the program gets under way, here are some possible topics that appear on
the surface to be suitable:
A student could study the history surrounding Fermat's last theorem, and
discuss and explain past failed attempts and the recent successful attempt
to prove this theorem.
A student could research the topic of knot theory and discuss the implications
of this theory to the study of DNA and other biological materials.
A student could study the use of wavelets in signal analysis, and the general
usefulness of orthonormal families of functions in signal analysis.
The Mathematics minor
As with the major in mathematics, a minimum grade of C- must be attained
in all courses used to satisfy the minor. The necessary courses are
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Cambridge 3 Unit Mathematics Year 11
Cambridge 3 Unit Mathematics Year 11 by William Pender
Book Description
Cambridge 3 Unit Mathematics spans the full range of 3 Unit Mathematics students' abilities. The gradual changes of emphasis in the HSC examinations in NSW over the past ten years are entirely and expertly addressed by the authors. The book provides a large number and variety of questions in each exercise that are clearly graded according to ability. The authors go beyond and above the normative textbook by presenting mathematics in its pure, elegant form. They intend, in Cambridge 3 Unit Mathematics to inspire in students a passion for mathematics through clear and careful exposition, interesting questions, and particularly through demonstrating the relationships between the various topics.As well, the book: * provides links to other topics and requirements for explanation in the style of recent HSC papers * is designed to expand and develop the wide range of student abilities through extensive and aptly graded exercises * provides a large number of fully worked examples * provides theory that is logically developed and clearly explained * summarises main results and algorithms in numbered boxes for easy reference and revision * divides chapters systematically into manageable sections which consist of a substantial exercise preceded by theory and worked examples * includes exercises divided into three groups: foundation (basic algorithms), development (algorithms applied to appropriate problems and put in context with material from other sections), and extension (to inspire further thought and development amongst those students who wish to master the 4 unit course)
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Summer Link Math Plus Reading is designed to be a fun way to help a child prepare for the grade ahead during the summer. Each 320-page book includes fun learning activities covering a range of topics in math and readingSummer Link Math Plus Reading is designed to be a fun way to help a child prepare for the grade ahead during the summer. Each 320-page book includes fun learning activities covering a range of topics in math and reading.
The 100+ Series, Math Practice, offers in-depth practice and review for challenging middle school math topics including ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability.
Books By Author William Pender
A large number of fully worked examples demonstrate mathematical processes and encourage independent learning. Exercises are carefully graded to suit the range of students undertaking each mathematics course
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Contents for each week
Combinatorial matrix
theory, encompassing connections between linear algebra, graph
theory, and
combinatorics, has emerged as a vital area of research over the
last few
decades, having applications to fields as diverse as biology,
chemistry,
economics, and computer engineering.
The eigenvalues of a
matrix of
data play a vital role in many applications. Sometimes the
entries of
a data matrix are not known exactly. This has led to several
areas of
qualitative matrix theory, including the study of sign pattern
matrices
(matrices having entries in {+,- or 0}, used to describe the
family
of matrices where only the signs of the entries are known).
Early work
on sign pattern matrices arose from questions in economics and
answered
the question of what sign patterns require stability, and there
has been
substantial work on the question of which patterns permit
stability,
and on sign nonsingularity and sign solvability.
Linear algebra
is also
an important tool in algebraic combinatorics. For example,
spectral graph
theory uses the eigenvalues of the adjacency matrix and
Laplacian matrix
of a graph to provide information about the graph.
The
ability to carry out matrix computations numerically, with
accuracy and
efficiency, is essential for applications.
This week will
survey the most
important techniques for solving linear algebra problems
numerically,
with emphasis on computing eigenvalues and eigenvectors.
Methods for
solving small to medium-sized problems will be discussed and
contrasted
with methods for solving large to very large problems.
Sensitivity issues
and the effects of roundoff and other errors will be discussed.
Linear algebra is a key tool in the study of
ordinary
differential equations, including the explicit form of
solutions to linear
equations, linearization theory, and results on invariant
manifolds
and the Grobman-Hartman theorem.
The connection actually goes
much
deeper, as classes of matrices can be characterized by concepts
from
dynamical systems, such as Ck conjugacies and equivalences of
flows
in Rn associated with linear ODEs. Probing this connection
further, for a linear ODE one
can analyze its radial component (eigenvalues,
Floquet
exponents, Lyapunov exponents) and its angular component on the
sphere,
leading to an interesting introduction to attractor-repeller
pairs and
Morse decompositions. These topics will motivate the contents
of Week 4.
With this background it is now possible to use ideas from linear
algebra
for a variety of dynamic problems in the sciences and
engineering. We
will concentrate on control theory, specifically on questions
of robust
stability and stabilizability in engineering systems, including
(linear
and nonlinear) stability radii, characterization of
stabilizability
for uncertain systems, and - if time permits - on the global
behavior
of randomly perturbed systems.
Engineering systems to be
considered
include tank reactors, electric power systems, and nonlinear
oscillators.
Review material in week 1:
Topics from graduate linear algebra and basic
graph theory
that will be needed will be reviewed without proof but with
examples and
illustrations of use.
This includes Jordan and real Jordan
canonical form,
spectral theory of normal matrices, properties of unitary and
Hermitian
matrices, nonnegative and stochastic matrices, basic
terminology of
graphs and digraphs and connections with matrices.
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Course Description
This course will provide the learner with a better understanding of the underlying concepts of geometry. Through readings, lessons, quizzes and independent explorations, the learner will leave the course with more complete understanding of geometry and begin to be able to think in a geometrical fashion. Websites are also provided to help the learner further explore the topics on his/her own. At the end of this unit, the learner will be able to describe some of the basic premises behind geometric thinking, reasoning and study. They will also be able to demonstrate the following learning objectives:
Objectives (based on the Van Hiele levels of geometric thought):
Students will be able to demonstrate the ability identify the ways geometry is used by people in their daily lives (i.e. professions, synthetic universe, natural universe, in the home, etc...)
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Student Testimonials
"The instructor was very helpful and reachable in doing this class over the period of time it took for me to complete it." -- Greg K.
"The instructor was very helpful." -- Abigail N.
"I thought the most helpful was the part that explained about the faces, edges, and different shapes." -- Amanda F.
"All of it the course was great. The instructor is great." -- Barry S.
"I found the whole program to be helpful. It gave me a better understanding of geometry and the world of geometry." -- Alexis B.
"All of it was very helpful, it was very well explained." -- Betty G.
"As an introductory course I think the course was above excellent and a very high quality teacher. I liked the methodology used to teach geometry because it clarified a lot of areas for me. The course was structured so that I could learn the concepts and not worry too much about performance. I have to admit that this is the first math/science class that I have thoroughly enjoyed." -- Francisco M.
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Performs useful calculations such as finding the Area, Common Factors of a set of numbers, Distance between two points, Quadratic Roots, Midpoint, Perimeter, Find all the primes up to and including a number, the slope of a line, and the volume of a cube, cone, cylinder, and sphere.Finds the area of a Rectangle, Circle, Triangle, Oval, Cylinder, Cone, and Pyramid.Formula for each function is displayed at the top of the screen for easy reference. Easy to use, convenient and powerful math program. Great for math class and home work!An easy and convenient handwriting recognition system allows numbers to be entered by just writing on the screen with your finger
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Elementary Statistics: A Brief Version
Book Description: "Elementary Statistics: A Brief Version", is a shorter version of the popular text "Elementary Statistics: A Step by Step Approach". This softcover edition includes all the features of the longer book, but it is designed for a course in which the time available limits the number of topics covered. It is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses
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Summary: Contemporary's GED Satellite: Mathematics has been created to provide students with detailed study and practice for the 2002 GED Mathematics exam. This book begins with basic operations and moves through more complex mathematical study that contains activities for both the fx-260 calculator and longhand problems. Real-life examples are included to assist students in the application process. Alternate format responses play a role in GED-style question and in chapter r...show moreeview format. ...show less
Instructor's Edition. Shows some signs of wear, and may have some markings on the inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy!
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Magazine
mission of Plus magazine is elegant and wonderful: "to introduce readers to the beauty and the practical applications of mathematics." The magazine offers up a hearty dose of articles and podcasts on a diverse set of topics including algebra, geometry, mathematics in sports, and so on. The website has a number of fun features, including Dark Energy Say Cheese! and a fun sudoku-esque puzzle, Pandemonion! The sections here include Articles, Packages, Podcasts, and Reviews among others. The Podcasts are a delight and a short list of recent offerings includes "Do infinities exist in nature?" and "How many dimensions are there?" The Articles area is similarly rich and visitors can search through their archive, which includes several hundred items.Thu, 10 Oct 2013 11:00:40 -0500West Texas A&M University Virtual Math Lab
page from West Texas A&M University provides help for students in college algebra, intermediate algebra, beginning algebra, math for the sciences, and GRE mathematics preparation. Each area contains a number of individual tutorials that increase in difficulty. The GRE prep section includes two practice tests. This would be a wonderful resource for people looking to brush up on their math skills or students returning to college after some time away from math classes.Wed, 5 Jun 2013 13:13:34 -0500New Opportunities for Learning
ATETV project delivers web-based videos to connect students to careers in advanced technology. This episode of ATETV looks at non-traditional students returning to college for career training. These students have many useful skills already; returning to school makes them more marketable and ready to re-join the workforce once they complete their schooling.Running time for the episode is 3:00.Wed, 10 Oct 2012 13:26:08 -0500Adult Learning in Focus: National and State-by-state Data
document from the Council for Adult and Experiential learning discusses the status of adult learning in the United States. State policymakers care now, perhaps more than ever before, about the educational attainment of their states' working populations. They also care about the responsiveness of educational systems in their states to the needs of adult learners. But relatively few have the data they need to understand how their states are doing in developing and educating its citizens. In Adult Learning in Focus: National and State-by-State Data, CAEL has teamed with the National Center for Higher Education Management Systems (NCHEMS) to provide states with the information needed to assess state performance on adult learning and identify where to direct future strategies. This comprehensive report contains national and state-by-state data on adult learning. Included are data and comparative charts on adult educational attainment, adult learning participation, affordability, accessibility and aspiration. Also discussed are data gaps that need to be addressed and next steps for state education leaders.Thu, 15 Sep 2011 03:00:04 -0500Division of Career Education
Career Education prepares Missourians for the 21st century to better serve the needs of students, parents, educators, and employers through challenging, relevant, and accountable programs. Career Clusters provide a way for schools to organize instruction and student experiences around 16 broad categories that encompass virtually all occupations from entry through professional levels. These groupings of occupations are used as an organizing tool for curriculum design, a model for guidance and instruction, and a mechanism for seamless transition from secondary education to postsecondary education and/or careers.Thu, 1 Jul 2010 03:00:01 -0500Re-Inventing Classroom And Campus
university may need to reorganize itself quite differently, stressing forms of pedagogy and extracurricular experiences to nurture and teach the art and skill of creativity and innovation. This would probably imply a shift away from highly specialized disciplines and degree programs to programs placing more emphasis on integrating knowledge. To this end, perhaps it is time to integrate the educational mission of the university with the research and service activities of the faculty by ripping instruction out of the classroom- or at least the lecture hall- and placing it instead in the discovery environment of the laboratory or studio or the experiential environment of professional practice.Fri, 11 Jun 2010 03:00:01 -0500States Career Clusters
advances and global competition have transformed the nature of work. Tomorrow's jobs will require more knowledge, better skills, and more flexible workers than ever before. Tomorrow's workers must be prepared to change jobs and careers several times, continually updating their knowledge and skills. To prepare today's students for tomorrow, schools are working to help students achieve in challenging subjects. One key approach to this goal is to provide students with relevant contexts for learning. Career clusters link what students learn in school with the knowledge and skills they need for success in college and careers. Career clusters identify pathways from secondary school to two- and four-year colleges, graduate school, and the workplace, so students can learn in school and what they can do in the future. This connection to future goals motivates students to work harder and enroll in more rigorous courses.Fri, 11 Jun 2010 03:00:01 -0500Top Ten Challenges for the Academic Technology Community
is a PowerPoint presentation from the EDUCAUSE website. The Advisory Committee for Teaching and Learning (ACTL) identified the key technology-related teaching and learning issues in higher education for 2007. They include: establishing and supporting a culture of evidence; demonstrating improvement of learning; translating learning research into practice; selecting appropriate models and strategies for e-learning; providing tools to meet growing student expectations; providing professional development and support to new audiences; sharing content, applications, and application development; protecting institutional data; addressing emerging ethical challenges; understanding our evolving role.Wed, 1 Jul 2009 03:00:03 -0500Podcasts from the University of Oxford
University of Oxford offers free podcasts of lectures by Oxford professors on this very fine website. Nine different divisions of the University are represented, including the Humanities, Medical Sciences, Continuing Education, and Life Sciences. By clicking on "show media items" under the description of each lecture, you can see all the titles in the lecture series, and choose from there. In "Philosophy" under the Humanities division are the distinguished John Locke Lectures, which include twelve different talks. In the Social Sciences Division, you will find topics such as the "Environmental Change Institute Podcasts from Oxford University" that consist of lectures, seminars, and interviews. "Forced Migration Online Discussions" include exchanges between experts, interviews with refugees, and lectures at the Refugee Studies Centre. Overall, the site is a great educational resource and one that could be used in any number of classroom settings.Wed, 10 Jun 2009 03:00:01 -0500
| 677.169 | 1 |
MyStatLab ispart of the MyMathLab and MathXL product family is a text-specific, online course-management tool that integrates interactive multimedia instruction with textbook content. MyStatLab provides students with a personalized interactive learning environment, where they can learn at their own pace and measure their progress.Interactive Tutorial Exercises: A comprehensive set of exercises correlated to your textbook at the objective level are algorithmically generated for unlimited practice and mastery. Most exercises are free-response and provide guided solutions, sample problems, and learning aids for extra help at point-of-use. Personalized Study Plan: When students complete a test or quiz in MyStatLab, the program generates a personalized study plan for each student, indicating which topics have been mastered and/or links to areas that need remediation. Multimedia Learning Aids: Students can use online learning aids, such as video lectures, animations, and a complete multimedia textbook, to help them independently improve their understanding and performance. Statistics Tools: MyStatLab includes built-in tools for Statistics, including statistical software called StatCrunch. Students also have access to statistics animations and applets that illustrate key ideas for the course. For those who use technology in their course, technology manual PDFs are included. StatCrunch: A powerful online tool that provides an interactive environment for doing statistics, StatCrunch can be used for both numerical and graphical data analysis. This software can help students take advantage of interactive graphics so they can easily see the connection between objects selected in a graph and the underlying data. In MyStatLab, the data sets from your textbook are preloaded into StatCrunch. PearsonTutor Center ( Access is automatically included with MyStatLab. The Tutor Center is staffed by qualified mathematics instructors who provide textbook-specific tutoring for students via toll-free phone, fax, email, and interactive Web sessions.Visit for more information.6A4
Book Description:Prentice Hall, 2008. Misc. Supplies. Book Condition: New. This has not been opened, you will not be able to return it if you do open it . Photos: We now have a scanner in-shop and can provide you with a picture of this item if you do not currently see one. Bookseller Inventory # mon00001647
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More About
This Textbook
Overview
Success in your calculus course starts here!
Editorial Reviews
Booknews
A textbook for a course introducing students both to the practical applications and to the beauty of the field. Stewert (McMaster U.) focuses on the basic concepts, and presents the topics geometrically, numerically, and algebraically. No dates are noted for the early editions, but the fourth contains new exercises, updated data, projects for individual or group work, and other pedagogical features. The CD-ROM offers a demonstration version of the Journey Through Calculus program, which is referred to at appropriate places in the text. A full array of auxiliary material, including instructors guide and laboratory manuals, are also available. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
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Home
Welcome to Algebra Support!
This class is designed to help you through the Algebra I course. Like Algebra, you will earn credit through mastering the competencies listed throughout the course. The Algebra Support competencies work on basic Mathematic Principles that everyone should practice. During the year you will have extra time to work on Algebra assessments, review Algebraic concepts, and get personalized attention for the areas you need the most help with.
Use this site for homework and assignment updates, get copies of notes, preview and review lesson units, and get project details and rubrics.
If you should need assistance, at any time, feel free to email me at abanks@pittsfieldnhschools.org
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Credit only applies in mathematics education. A historical development of mathematics from primitive origins to the Twentieth Century concentrating on numeration systems, arithmetic methods. Euclidean and non-Euclidean geometries, number theory, theory of equations, and the origins of Calculus.
| 677.169 | 1 |
Graphs: An Introductory Approach - A First Course in Discrete Mathematics
An introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. ...Show synopsisAn introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. It introduces the concepts of logic, proof and mathematical problem-solving and places an emphasis on algorithms in every chapter.Hide synopsis
Description:Fair. Book is in good to acceptable condition with minor...Fair. Book is in good to acceptable condition with minor blemishes on the cover. Pages have highlighting and minor writing
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First Course in Mathematical Modeling
9780495011590
ISBN:
0495011592
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides m...yriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.
Giordano is the author of First Course in Mathematical Modeling, published 2008 under ISBN 9780495011590 and 0495011592. Four hundred fourteen First Course in Mathematical Modeling textbooks are available for sale on ValoreBooks.com, one hundred fifty three used from the cheapest price of $35.85, or buy new starting at $226 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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Brian Wynne = (awesome)^n
A calculus syllabus is a calculus syllabus is a calculus syllabus. No matter where it's taught, in the end the material is the same. Because of that, math classes tend to be defined by the professor.
Enter Brian Wynne—a young, nearly fresh-out-of-graduate-school doctor of mathematics who sports a kind of nerdy approachableness. He is the type of instructor who says things like, "The good times are rolling!" when a student shares her understanding of differential equations out loud; or: "This isn't rocket science! Well, actually, it is rocket science, but it's not that hard."
Wynne is the kind of professor who has fun teaching and talking math. And it's contagious. A group of former students, for instance, decided to pay homage to him by publishing a Facebook fan page titled "Brian Wynne=(awesome)^n." If you don't get the joke, you haven't taken a math class with him yet.
His humor and general playfulness is part fun and part strategy. Math can be heavy, which is why Wynne keeps the atmosphere light, informal--joyful, even. If the mood is strategically playful, the instruction itself is intentionally methodic.
Wynne first introduces a new idea and technique. Today, it's differential equations. "A differential equation is an equation involving the derivatives of a function. They are of great importance in the sciences, where they are used to describe how physical systems change over time," he explains. "Today we'll see how the calculus we've learned this semester can be used to analyze differential equations."
Next, he talks about real world applications. Some examples: It can be a good model for population growth, or predicting bacteria growth in a lab.
Then, he works on problems. He tries to keep the tasks manageable, even when the math sprawls in a way that can intimidate some of the most gifted math students in class. Knee deep into differentiating, Wynne stops before he tackles the second part of the equation with the class. "OK, now what you have to do here is steel yourself." A student asks what that means. "It means you need to prepare, to become strong."
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Textbooks
A survey of the use of mathematics in the modern world. Topics include: theory of elections, apportionment, and fair division; use of graphs to solve the postman problem, the traveling salesman problem, minimum cost networks problems, and scheduling problems; and introduction to statistics
Each student will need to have a calculator available for some of the material of the course.A four-function calculator with a square root (/) key will suffice.
Each student must purchase an access key to MyLab/Mastering, a course presentation system provided by Pearson Publishing Company. The key may be purchased through the campus bookstore, or directly at pearsonmylabandmastering.com. The homework assignments will be done online, although quizzes and unit tests will be done in class.
The access key provides access to an electronic version of the text. Students may wish to purchase a hard copy too.
To enroll in the on-line course use the course code tucker22384 and the zip code 76308
The course is broken up into three units, each consisting of four chapters from the text. They are:
Unit 1 Social Choice Chapters 1 through 4
Unit 2 Management Science Chapters 5 through 8
Unit 3 Statistics Chapters 14 through 17
Graded work in each unit consists of homework sets and a quiz for each chapter of the unit, followed by a unit test over the entire unit (all four chapters). Homework assignments should be completed before taking the chapter quiz. However, students may redo homework problems after taking quizzes or tests to improve homework grades. All homework assignments must be completed no later than the day of the final exam.
Grading Standards
Each unit will be weighted equally in the final grade
There are three graded components to the course:
Component Weight
Homework 10%
Quizzes 15%
Unit tests 75%
All chapter homework assignments will be used to determine the homework score, but only the highest three quizzes out of the four in each unit will be used to determine the over-all quiz score.
The following grade scale will be used to determine the final grade for the course
Percentage Grade
90 - 100% A
80 - 89% B
70 - 79% C
60 - 69% D
0 - 59% F
Final Exam
5/7/2014 10:30 am to 12:30 pm
Submission Format Policy
All homework is done on MyLab/Mastering on the web.
Quizzes will be answered on the paper provided by the instructor.
Unit tests will be multiple choice and each student must provide a long Scantron form for each test, and use a pencil to fill out the form. Any changes must be made by erasing the incorrect answer neatly and completelyStudents should finish each homework assignment by the homework due date listed on the syllabus given below.
Homework
Homework
Day
Date
Chapter
Due Date
Day
Date
Chapter
Due Date
Mon
13-Jan
1
Mon
10-Mar
7
Wed
15-Jan
1
Wed
12-Mar
8
Chapter 7
Fri
17-Jan
1
Fri
14-Mar
8
Mon
20-Jan
MLK Day No Class
Mon
24-Mar
8
Wed
22-Jan
1
Wed
26-Mar
14
Chapter 8
Fri
24-Jan
2
Chapter 1
Fri
28-Mar
Unit Test 2
Mon
27-Jan
2
Mon
31-Mar
14
Wed
29-Jan
2
Wed
2-Apr
14
Fri
31-Jan
3
Chapter 2
Fri
4-Apr
14
Mon
3-Feb
3
Mon
7-Apr
15
Chapter 14
Wed
5-Feb
3
Wed
9-Apr
15
Fri
7-Feb
4
Chapter 3
Fri
11-Apr
15
Mon
10-Feb
4
Mon
14-Apr
15
Wed
12-Feb
4
Wed
16-Apr
16
Chapter 15
Fri
14-Feb
5
Chapter 4
Fri
18-Apr
16
Mon
17-Feb
Unit 1 Test
Mon
21-Apr
16
Wed
19-Feb
5
Wed
23-Apr
16
Fri
21-Feb
5
Fri
25-Apr
17
Chapter 16
Mon
24-Feb
5
Mon
28-Apr
17
Wed
26-Feb
6
Chapter 5
Wed
30-Apr
17
Fri
28-Feb
6
Fri
2-May
17
Chapter 17
Mon
3-Mar
6
Wed
5-Mar
7
Chapter 6
Wed
7-May
Final Exam
Fri
7-Mar
7
10:30 - 12:30 Unit 3 Test2012-2014 Midwestern State University Undergraduate Catalog (page 71)
Class Attendance. "Students are expected to attend all meetings of the classes in which they are enrolled... A student with excessive absences may be dropped from the course by the instructor." (Read the intervening part in the MSU Undergraduate Catalog, Volume LXXIX, Number 1, 2012-2014).
Note: If a justifiable or authorized absence should occur, it is the responsibility of the student to make up all work missed. If a student misses a scheduled exam, he/she must be prepared to take the test immediately upon returning to class, or else no makeup will be given and the grade on the exam will be a zero. If a student knows in advance that he/she will miss an exam, every effort should be made to notify the instructor of this situation prior to the exam. An "absence" is defined as not being physically present in the classroom for the entire period. A student who comes in late or leaves early may be counted absent for the class period.
"EXCESSIVE ABSENCES" will be defined as FOUR (4) OR MORE UNJUSTIFIABLE ABSENCES.
Other Policies
Electronic Communication During Class: Students may not use cell phones, computers, ipads, tablets or other electronic devices to communicate with other individuals inside or outside of the classroom.
Any student found using any device other than a calculator during a test will be considered to be cheating, and will be subject to receiving a zero on the assignment. Cell phones are not acceptable for calculators on exams.
Students may use cell phones or cameras to copy material on the board, but electronic communication during class is not permitted.
Students may use personal computers to take notes during class, but again, communication with other people, surfing the web, playing games, or working on assignments for other classes is not permitted during this class. At the teacher's sole discretion, a device capable of electronic communication may be confiscated for the remainder of the class period.
Entering the class late or leaving the class early is a disturbance to the other students and to the teacher. Each student is expected to treat the other students and the teacher with respect. Any student who is being disruptive to the class may be asked to leave the classroom and will be counted absent for that day
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Math 101: Beginning Algebra
Applications of linear functions, quadratic functions and linear systems to problems. Emphasis on the development of models of real world applications and interpretation of their characteristics. Use of technology will be an important aspect of this course.
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This review is from: Basic Math and Pre-Algebra For Dummies Education Bundle (Paperback)
A pair of books which complement each other well. The chapters in each book mesh into each other well and its easy to plot a path whereby you tackle the chapter in the main book and then complete the relevant exercises in the workbook. I also found on a number of occasions that the explanation given in the workbook helped to further illustrate a point made in the main book i.e. reading an explanation of a concept for the second time in a slightly different set of words helped.
I think the approach taken is better suited for self-learning adults rather than children below 16 years.
As a bundle together this would qualify as a 5 star but for one problem which is the small print used to represent symbols such as the equals and division symbols or fractions. It is very small. My eyes are OK but I often found myself misinterpreting an equals symbol for a division symbol and vice-versa.
I did wonder if the two books could have just as easily been merged into one but at the available price its very good value.
This review is from: Basic Math and Pre-Algebra For Dummies Education Bundle (Paperback)
Just bought these two books as a combined sale. Had a quick look thru them today and they both look totally superb. And the authour has done an excellent job in making something which can seem formidable to many people be easily within their grasp.
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This package consists of the textbook plus an access kit for MyMathLab/MyStatLab.
Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in scenes from popular movies and television. By incorporating John Hornsby's "Math Goes to Hollywood" approach into chapter openers, margin notes, examples, exercises, and resources, this text makes it easy to weave this engaging theme into your course.
The Twelfth Edition continues to deliver the superlative writing style, carefully developed examples, and extensive exercise sets that instructors have come to expect. MyMathLab continues to evolve with each new edition, offering expanded online exercise sets, improved instructor resources, and new section-level videos.
MyMathLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online.
Editorial Reviews
Booknews
A textbook designed with a variety of students in mind and suited for several types of courses, including mathematics for liberal arts students, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle-school teachers. Some 80% of the exercises are new to this edition, which also sports extensive use of color and changes in format to create a fresh look. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
Charles Miller has taught at America River College for many years.
Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.
John Hornsby: When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentationswantmyboook
Posted June 12, 2010
I wish I had my book. I am still waiting for a response, a reply a book something from someone to let me know what is going on.
ordered book May 19,order# 134009217,from frtextbooks. still have not received the book sent email on 5/28 to frtextbooks, still havent received a reply. Reported it to b&n on 3 seperate occassions and still no reply or book. Extreme unprofessional service the book is ok, looked at a classmates, too bad I cant look at the one I paid for almost a month ago. I was told the book would be considered late on June 14. Per the invoice it was shipped on May 19. Guidelines state it should be shipped within 2 business days, well we are certainly past that. I have spoken with great reps at b&n, but that does not provide me with a book. Can someone email me and let me know WHERE IS MY BOOK? My class ends on July 26, so I guess I will get it on July 27 with a fake apology/lie it was lost in the mail. I deplore unprofessional business & service and that is what I am receiving. Barnes and Nobles this seller dropped the ball and by their ratings I am the 3rd customer to experience this. Please do something about sellers that disregard customers without dignifying them with a basic response "we mailed it on_______ date"
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Anonymous
Posted June 6, 2008
A reviewer
If this book is purchased with all its accompanying material it is sure to prepare students for employment in the data analyst field.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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MA 0060 - Basic Mathematics I
Course Description
This course is an individualized program of study which covers a review of reading, writing and rounding of whole numbers, if required, as well as whole number multiplication and division. Problem-solving is emphasized throughout, and squares, square roots, and the order of operations are introduced.
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Short version
I think mathematica is a good first programming language, and Stephen Wolfram has dropped some hints in a few places that it should get even better at being a beginner programming language soon:
It'll probably be related to my goal in the next year or two of making Mathematica definitively the world's easiest to learn language...
More ...
Mathematica is the best tutorial. It is a discovery tool - just start from something that he knows a bit already and you both take one little step at a time. Just try things.
1st Thing - Try this Link => Hands-on Start to Mathematica
I personally would recommend engaging with him in a project of making an application and submitting it to the Wolfram ...
I own a copy of Modelling Financial Derivatives with Mathematica by William Shaw. I think it was a ground-breaking book for its time. However, here are some issues you should be aware of:
It was published in 1998 and is based on Mathematica version 3. We are now at 8, anticipating 9. Much of the graphics code he uses is now obsolete (eg Graphics`Graphics).
...
The course material I used to learn Mathematica myself is directed at beginners. You should have no problem following it even if you have next to zero prior programming experience. It is a bit outdated (it was written for an old version of Mathematica), but I think that it is still a very useful learning resource today. Most importantly, it includes ...
Affirming Vitaliy's suggestions I'll say something beyond his comprehensive answer and to a certain extent more specific.
A great mathematician S.Banach used to say (maybe as a joke) that children shouldn't be taught mathematics early because that would be a too sharp tool for them. There is an obvious analogy and this is why children shoudn't be taught ...
Vitaliy's suggestion is indeed very good.
What I want to add is that the Documentation is a good place to start. Say he's interested in drawing some graphs to illustrate something, then the Guide page for Graphs is a great place to start and the reference pages have tons of examples to build from.
Once one has solved a problem or two with Mathematica ...
Update: I described an alternative approach based on built in plotting functions in this answer. That approach is not very practical here though because I need to be able to handle points at arbitrary positions while built in functions work with a rectangle-based mesh. I am still looking for improvements.
I came up with this very naive approach and ...
I'm a bit late to this party, but I can assure you that it is possible to learn Mathematica as your first and only programming language. I know because I did it. It is also most certainly possible to use Mathematica as your calculation "Swiss Army knife" if you are an economist. I know because I am an economist, too, and I have been successfully using it as ...
One unconventional but possibly very useful approach it to introduce him to Project Euler. While many of the newer questions are completely beyond me (mind you that is not saying much), many of the earlier ones are quite approachable. If your friend has the desire to learn and an interest in puzzles/challenges, this site will grow as he grows.
Most of the ...
The methods NDSolve uses are documented in detail here:
Advanced Numerical Differential Equation Solving in Mathematica
This section says that PDEs are solved using the "method of lines", and explains which kinds of problems this method can deal with. There's also a detailed example of how the method works.
The numerical method of lines is a ...
I just wrote a book on financial engineering that uses Mathematica heavily. The publisher (World Scientific) says it should be available for purchase within a week or two. I have taught risk management and asset pricing and derivatives with these materials for the past few years at NYU-Poly. The point of the book is precisely to do lots of projects, the ...
I started learning Mathematica a couple of months ago, and all these suggestions are good. I'd also say that, although it's possible to surround yourself with books and tutorials, it's even more important to have some focus or goal to give shape to your learning efforts. You can find yourself bouncing from one interesting corner to the next (particularly ...
In a comment you asked about learning algorithm development and functional programming basics. Take a look at the courses at . Wolfram offers many of them as free videos that you can watch any time.
Check out the "General Mathematica" section for some introductory courses. There is also a free Functional Programming: Quick ...
I know this is an old thread now, but this might prove useful to someone. I have been teaching Mathematica to high school students for almost a year now. I have had to make my own resources, as I couldn't find any that were fit to purpose. I am happy to share them, and here is the Dropbox link:
Mathematica Exercises
All mistakes are my own! I am also happy ...
This page could be quite interesting in your case
The animations here explain some common Mathematica functions in a quite funny way.
There's a huge list of other resources here where you could pick what you think suits you.
Where can I find examples of good Mathematica ...
Here are some links I collected in my answer to the post Where can I find examples of good Mathematica programming practice?. The first link exposes quite well the new functionalities of Mathematica in this field.
Finance (some CUDA examples also)
High-Performance Computing in ...
As far as I know there's no reference book available yet that is using the new reliability functionality in Mathematica.
Two other resources are:
Reliability calculations for complex systems, academic thesis
Reliability Mathematics, Wolfram Blog
Those two focus on RBDs, Fault trees and system structures.
I've had an interest (as one can see in my other posts) in a wide range of distributed processing and parallel computing approaches and while not seen in any of my posts machine learning approaches as well. I looked at neural networks some years ago, and while they didn't suit the problems I worked on at the time I remembered the article Duncan and Tweney ...
Mathematica's documentation is also available online in the pdf format, as a tutorial collection. The place to look for it is here. Also, some books on Mathematica are now available as kindle editions, from Amazon. Finally, for those books which have Mathematica notebook versions, you can probably make a pdf from those notebooks for a personal use, if that ...
Introduction to Probability Models by Ross gives good description of stochastic processes.
Applied Intertemporal Optimization by Walde also has easy to follow structure on stochastic models in both discrete and continuous time and it is free to download pdf.
There's a second year mathematics and a computation physics course taught by Paul Abbott at the University of Western Australia that uses Mathematica for all of the lectures, workshops and assessments.
The maths course uses a customised stylesheet and the assessment notebooks have automated FTP uploading to the assignment dropbox. However, most of the ...
Although exporting x3d format maintains the light sources and exports the mesh, it isn't perfect when used with Blender (the only 3D editor I tried). However, since it's the best solution I have, I wrote some brief instructions for that procedure. It's important to note that I used Blender version 2.60 and Mathematica 9.
Since the instructions are almost ...
The GraphUtilities documentation has a whole section that should answer your question: "Algorithms for Finding Community Structure". The reference for the algorithm it uses is: A. Clauset, "Finding Local Community Structure in Networks," Physical Review E, 72, 026132, 2005 (arXiv mirror).
The references mentioned in the other answer do not really pertain too much to the problem of minimax approximation; they are more concerned with the other functions in FunctionApproximations` that deal with numerical differential equation solving; that is, the content that was once in the old NumericalMath`packages Butcher` and OrderStar`.
Indeed, a look ...
To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, ...
Here you can find some software to convert Mathematica graphics for input into POVray (untested and rather old, though)
Edit
Maeder's book and files aren't available for online downloading (you've to purchase the book)
Edit Or perhaps you can find them at the link provided in the comments
With regards to 'Learning Finance with Mathematica', one of the best sites I've seen is
It has two focuses; real estate and the financial market. The financial market end is very instructional and contains demo mathematica code as well as free downloadable code. It focuses on a number of market concepts, namely: risk, trends, ...
Mathematica is a registered trademark of Wolfram Research, Inc. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith.
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Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 3rd Edition Algebra 2 textbook and tests/worksheets book & answer key, as well as the DIVE Algebra 2 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Algebra 2 covers geometric functions like angles, perimeters, and proportional segments; negative exponents; quadratic equations; metric conversions; logarithms; and advanced factoring.
The DIVE software teaches Saxon lesson concepts step-by-step on a digital whiteboard, each lesson averaging about 10-15 minutes in length. Because
System Requirements:
Windows & Mac 98 or higher (including Vista)
Speakers
CD-ROM Drive
This Kit Includes:
Saxon Algebra 2 Math Textbook, 558 pages, hardcover, 3rd Edition
Saxon Algebra 2 Test Book, 3rd Edition
Saxon Algebra 2 Answer Key, 3rd Edition
DIVE Algebra 2 CD-ROM, for the 3rd & 2nd Edition Saxon Algebra 2 Kit & DIVE CD-Rom, Third Edition
Review 1 for Saxon Algebra 2 Kit & DIVE CD-Rom, Third Edition
Overall Rating:
5out of5
Saxon Algebra 2 w/ DIVE CD
Date:October 30, 2010
Chea
Location:Sacramento
Quality:
5out of5
Value:
5out of5
Meets Expectations:
4out of5
I've used ALL the Saxon Math books along with the DIVE CD starting in the 78 series. I've been completely satisfied with the Saxon and DIVE lessons. After finishing the Algebra II lessons, I was surprised to discover the Saxon books did not cover ALL the Algebra concepts (85%). Luckily, with the help of the DIVE CD series for Algebra II, my son was able to complete the needed Algebra to qualify to pass his CLEP exams.
I'm not familiar with the Saxon CD series, but we did review a sample Saxon CD and my son found he liked the DIVE better, which I enjoyed because it's cheaper then the Saxon, plus my son seemed to relate better DIVE.
I gave a four star rating for "Meets Expectation" due to the number of errors and typo's I found in this book. But luckily you can find them on the Saxon Home page. I just didn't like having to track them down. I have enough to do as a home-school mom. But I love Saxon Math and will never sell or give away my library of them. They can always be used for future grandkids too.
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Starting at $20Math Study Skills Workbook
Math Study Skills Workbook, 4th Edition
Summary
This workbook helps learners identify their strengths, weaknesses, and personal learning styles--and then presents an easy-to-follow system to increase their success in mathematics. With helpful study tips and test-taking strategies, this workbook can help reduce "math anxiety" and help readers become more effective at studying and learning mathematics.
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Course Description: An in-depth study of algebraic equations and inequalities. Comprehension of the underlying algebraic structure will be stressed as well as appropriate algebraic skills. The study will include polynomials, rational, exponential, and logarithmic equations as well as systems of equations/inequalities.
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Students define the product rule and use it to solve problems. In this calculus lesson, students review rules they learned and memorize the new rules as it relates to derivatives. They solve problems through differentiation by proving the product ruleTwelfth graders explore the concept of limits. In this calculus lesson, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
Students investigate derivatives using the product rule. In this derivatives using the product rule lesson, students use the Ti-89 to find the derivatives of functions such as x^2 and sin(x) using the product rule. Students visualize the process of finding the derivatives using the product rule on the Ti-89.
In this calculus worksheet, students solve 10 different problems that include determining the first derivative in each. First, they apply properties of logarithmic functions to expand the right side of each equation. Then, students differentiate both sides with respect to x,using the chain rule on the left side and the product rule on the right. In addition, they multiply both sides by y and substitute.
Pupils solve problems using integration by parts in this calculus instructional activity. Learners apply the product rule and integration by parts. They graph the equation and use the TI to observe the integration process.
This lesson plan provides an introduction to integration by parts. It helps learners first recognize derivatives produced by the product rule and then continues with step-by-step instructions on computing these integrals. It also shows integrating special forms with e and trigonometric functions. This resource includes handouts and a practice worksheet.
In this calculus learning exercise, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .In this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Twelfth graders assess their knowledge of trig functions and their properties. For this calculus lesson, 12th graders take a test on derivatives, trig functions, and the quotient rule. There are 2 different versions of the same test available.
Students review integrals and how they apply to solving equations. In this calculus lesson plan, students assess their knowledge of derivatives, rate of change, and lines tangent to a curve. This assignment contains two version of the same test concept.
Students review derivatives and equations for their test. For this calculus lesson, students review average rate, parametric equations, tangent line to a curve and value of a derivative to prepare and show mastery on a chapter test. They show proficiency on rig derivatives and differential equations.
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Friendly Introduction to Number Theory, A courses in Elementary Number Theory for non-math majors, for mathematics education students, and for Computer Science students. This is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results.
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Concepts of Modern Mathematics (Dover Books on Mathematics)
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself
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practical guide to modern financial risk management for both practitioners and academics The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates. Covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing Introduces risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing Explains time series analysis, including interest rate, GARCH, and jump-diffusion models Explores bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further.
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Prerequisites to follow this textbook are pre-calculus algebra and one year of calculus. The first six chapters are accessible to an average (European) high-schooler. The author says that the ultimate goal is to reach a substantial result in abstract algebra, namely, the classification of finite fields; this reviewer thinks that the crowning jewel of the book is the section on quadratic reciprocity law. The starting point is very elementary and passage to more complicated topics is fairly smooth. Every section is accompanied by a set of exercises, mostly easy, but some challenging. Motivating illustrations are often given by way of modern applications (within 50 years), notably almost all in computer domain (cryptography, etc). Alas the credit number check (Luhn's algorithm) does not seem to work on any of this reviewer's credit cards, perhaps indicating that the algorithm is no longer used for that purpose; Luhn's patent application was in 1954 granted in 1960). An attempt is made to revisit same topics from different points of view, as the new material is developed. The author rightly teaches the reader that many deep theorems that are used today, and in applications at that, go back to the old Greece. The author made a wise choice to include actual formulas for roots of polynomial equations of 3rd and 4th degrees; so was also the choice of not-so-frequent-to-be-found estimates of polynomial roots in terms of their coefficients (but see more general estimates in: [R. Dimitrić, Math. Balk., New Ser. 11, No. 3–4, 203–206 (1997; Zbl 1032.12002)].
Reviewer's remark: A spot-check revealed a few misprints. There are some problems common with (calculus) textbooks that have to cover a large stretch of the mathematical cultural territory within the short spectrum of abilities of an average (American) student. Thus the notions of range and codomain of functions are confused, as typically found in such textbooks.
"Determinants" go only to size 3 by 3. A pedagogical assumption is made throughout the book that more special is clearer, than more general. On p.172 a nonsensical claim is made that order of an element in a finite cyclic group and least common multiple of two numbers are "similar" notions...
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This text, which grew out of a NSF grant, takes a fresh approach with a focus on the underlying concepts of precalculus, rather than sheer algebraic manipulation. It effectively prepares students for a new generation of calculus courses and allows instructors to become actively involved in the teaching process. The authors make extensive use of real world applications, showing students how mathematics relates to their field of study, as well as including a thorough integration of technology. Additionally, the authors have incorporated a number of learning features designed to ready students for a more positive calculus experience.
Whether making a presentation or dealing one on one, interacting at a meeting or just answering questions, do others listen when you talk? This book explains how to communicate successfully so people listen, understand, and are persuaded. It is a comprehensive guide to every aspect of communicating in the workplace and beyondReal World Windows 8 Development is a developer's handbook - an essential guide to building complete, end-user ready Windows 8 applications on the XAML and C# programming stack from start to finish. Starting with Windows 8 basics and walking through practical aspects of building your Windows 8 application, you'll find step-by-step instructions and practical advice that will leave you with a modern, elegant app written to the highest of standards.
| 677.169 | 1 |
How to Teach Mathematics - 2nd edition
Summary: This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues.
Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. ...show moreHe also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner.
The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications5.646.0951 +$3.99 s/h
Good
Campus_Bookstore Fayetteville, AR
Used - Good TEXTBOOK ONLY! 2nd75 +$3.99 s/h
New
Dream Books Company, LLC Englewood, CO
1999 Paperback New Book may contain minor shelf wear.
$24.97 +$3.99 s/h
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One Stop Text Books Store Sherman Oaks, CA
1999
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Student Solutions Manual for Faires/Burden's Numerical Methods, 4th
Book Description: 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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Start Learning Algebra 2
Special Note: As a special benefit to homeschooling families I organized the videos on this site in a course format. I encourage you to use the material on this blog as a "basic" course. A great way to supplement these basic courses is to invest in the workbook. However if you really like my video lessons than you want to take my full TabletClass Math courses.
Don't Forget To Sign Up For My Email List To Get Up To 50% OFF My Full TabletClass Courses!
Ch. 1 – Ch. 14:
Ch. 15:
Ch. 16:
Ch. 17:
Ch. 18:
This course is designed as a high school second or third year college prep math course. A strong foundation in concepts and skills of Algebra 1 is required.The first part of the course is an extensive series of sections on basic algebra topics that students should have mastered in Algebra 1. Part 2 of the course focuses on quadratic equations/complex numbers, linear systems and matrices/determinants.The next part of the course covers functions and relations and powers and radicals at a more advance level.
The course finishes by introducing many advance level topics to include exponential/logarithmic functions and solving polynomials of n-degree. Also a chapter on rational functions is explored to include a section on graphing rational functions.
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handyCalc is a powerful calculator with automatic suggestion and solving which makes it easier to learn and use.With almost all the features you can imagine on a calculator, waiting for you to explore.* currency convert, unit convert, graph, solve equations
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College MathematicsCollege Mathematics Catalog #: 10804107
Credits: 3.00
This course is designed to review and develop fundamental concepts of mathematics pertinent to the areas of: 1) arithmetic and algebra; 2) geometry and trigonometry; and 3) probability and statistics. Special emphasis is placed on problem solving, critical thinking and logical reasoning, making connections, and using calculators. Topics include performing arithmetic operations and simplifying algebraic expressions, solving linear equations and inequalities in one variable, solving proportions and incorporating percent applications, manipulating formulas, solving and graphing systems of linear equations and inequalities in two variables, finding areas and volumes of geometric figures, applying similar and congruent triangles, converting measurements within and between U.S. and metric systems, applying Pythagorean Theorem, solving right and oblique triangles, calculating probabilities, organizing data and interpreting charts, calculating central and spread measures, and summarizing and analyzing data.
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A is for Algebra-and that's the grade you'll pull when you use Bob Miller's simple guide to the math course every college-bound kid must take
With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student's best friend. He breaks down the complexities of every problem into easy-to-understand... more...
Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts.... more...
Everything you need to know to ace the math sections of the NEW SAT!
He's back! And this time Bob Miller is helping you tackle the math sections of the new and scarier SAT! Backed by his bestselling "Clueless" approach and appeal, Bob Miller's second edition of SAT Math for the Clueless once again features his renowned tips, techniques, and... more...
STUDENT TESTED AND APPROVED!
If you suffer from math anxiety, then sign up for private tutoring with Bob Miller!
Do mathematics and algebraic formulas leave your head spinning?
If so, you are like hundreds of thousands of other students who face math-especially, algebra-with fear. Luckily, there is a cure: Bob Miller's Clueless series!... more...
With Bob Miller at your side, you never have to be clueless about math again!
Algebra and calculus are tough on high school students like you. Professor Bob Miller, with more than 30 years' teaching experience, is a master at making the complex simple, and his now-classic series of Clueless study aids has helped tens of thousands understand... more...
In Tales from the Los Angeles Kings Locker Room , Bob Miller shares 40 years of Hollywood hockey with fans, reminding them of the highs and lows of Los Angeles hockey, while entertaining them with behind-the-scenes looks into the history of the 2012 Stanley Cup championship team. As the ?Voice of the Kings,? Miller has been part of the Kings experience... more...
Exploring the theories of Tacit Knowledge, this book unites discussions of the philosophical and scientific basis of Tacit Knowledge and reviews its different applications in economics and business. more...
A memoir of growing up in mob-run Sin City from a casino heir-turned-governor who?s seen two sides of every coin When Bob Miller arrived in Las Vegas as a boy, it was a small, dusty city, a far cry from the glamorous, exciting place it is today. Driving the family car was his father Ross Miller, a tough guy?though a good family man?who had operated... more...
Introduction to Adaptive Arrays, 2nd Edition is organized as a tutorial, taking the reader by the hand and leading them through the maze of jargon that often surrounds this highly technical subject. It is easy to read and easy to follow as fundamental concepts are introduced with examples before more current developments and techniques are introduced
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Math - Mrs. Macalena
Welcome to 8th Grade Math!
Course Description for Algebra 8
Algebra One is taught from the book published by McDougall Littell. The chapters covered in this course include Expressions, Equations, and Functions, Properties of Real Numbers, Solving and Graphing Linear Equations and Functions, Writing Linear Equations, Solving and Graphing Linear Inequalities, Systems of Equations and Inequalities, and Exponents and Exponential Functions.
Accelerated Algebra One will cover Polynomials and Factoring, Quadratic Equations and Functions, Radicals and Geometry Connections, Rational Equations and Functions, and Probability and Data Analysis in addition to the above concepts.
Learning Goals
Use basic math and problem-solving skills to solve real life problems.
Explain how and why we solve math problems.
Recognize patterns and trends is math relationships
Supplies
Students must bring these supplies with them to class everyday. If you run out of supplies you need to bring more from home.
3 subject notebook
folder
pencils
scientific calculator (graphing calculators are provided as needed)
CLASSROOM EXPECTATIONS
BE READY
BE PREPARED
BE CONSIDERATE
BE KIND
BE COOPERATIVE
BE RESPONSIBLE
Grading
Homework and Class Work: 35% Assignments must be turned in on their due date for full credit. After the due date they are worth ½ credit until the chapter test.
Tests and Quizzes: 60% Quizzes are given after every few lessons during a chapter. They are used to check our knowledge of the concepts we are learning. Tests are given at the end of each chapter. Students are given opportunities to study for quizzes and tests in class are well as through review assignments. All tests will be announced.
Participation and Responsibility: 5% Each quarter there are 100 points given to each student. The goal is to not lose any of those points! You can keep these points if you complete and hand in the warm up for each day, come prepared and do not need to borrow a book, calculator, or pencil, and participate in class discussions.
Extra Credit opportunities are available! Ask the Teacher for more information.
Math Links
*** These are just a few sites to help you with your homework, refresh your basic math skills, or practice skills through games and activities. If you know of another site not listed, please feel free to share those with me. I would love to add more.***
Classzone.com - The website for the Math/Algebra 8 Textbook. You can find an electronic textbook, extra examples, practice problems and more. Ask Dr. Math - Homework help site. You can ask DR. Math about different math concepts, and receive step by step examples. A+ Math - This site is great practice for our basic math skills. Fun Brain - This site has a variety of games in all subject areas. Check it out.
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All Around
* Problem-solving principles and strategies are introduced in chapter one and are used consistently throughout the text. * Of Further Interest ...Show synopsis* Problem-solving principles and strategies are introduced in chapter one and are used consistently throughout the text. * Of Further Interest sections appear at the end the chapter, and cover current topics that are exciting for students but are not typically part of the standard curriculum. * Statement Headings provide the students with a clear idea of the concept being discussed and are useful when reviewing for exams. * Applications motivate the discussion of the mathematics and increase student interest in the material. * Quiz Yourself questions are found throughout each section, and allow students to gauge their level of understanding before moving on to the next concept. * Some Good Advice is a feature that provides students with timely hints, tips, cautions and warnings about the material being covered. * Highlights are boxed features that consist of historical notes or biographical vignettes, uses of technology, and interesting applications.Hide synopsis
Description:Good. Looseleaf. May include moderately worn cover, writing,...Good. Looseleaf. May include moderately worn cover, writing, markings or slight discoloration. SKU: 978032183738737387.
Description:Good. Book only-sorry, no online code. 5th Edition. Used-Good....Good. Book only-sorry, no online code. 5th Edition. Used-Good. Used books do not include online codes or other supplements unless noted. mReviews of Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing stuff
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Peer Review
Ratings
Overall Rating:
This site contains reference material in Matrix Algebra. Topics covered include matrix operations, linear equations, determinants, eigenvectors and eigenvalues. S.O.S. Mathematics--Matrix Algebra is a part of an independent, commercial site that offers straightforward technical assistance primarily to high school and college students.
Learning Goals:
To serve as reference in the algebra of matrices or as a supplement for a standard course in Linear Algebra.
Target Student Population:
Students studying linear algebra and matrices.
Prerequisite Knowledge or Skills:
College Algebra.
Type of Material:
Reference and tutorial.
Recommended Uses:
Referrence guide.
Technical Requirements:
None.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This is a straightforward introduction to the matrix-related topics found in typical Linear Algebra courses. This learning resource does a good job of motivating some concepts that other texts often leave as mere definitions, like matrix multiplication (an application precedes the definition) and determinants of order higher than two (a set of defining properties is determined from the 2 X 2 case).
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This site could be of significant benefit to students who would like a supplement to their text in a Linear Algebra course. The presentation is brief, and the writing is clear and concise. Concepts are often motivated better than in many mainstream texts. A number of examples scattered throughout will aid student understanding.
Concerns:
Exercises with solutions would significantly improve the effectiveness of this site.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This learning resource is easily navigable. The topics are well-organized and all the key concepts are properly emphasized. Commercial advertising is somewhat distracting in places, but the layout is otherwise clean and simple, with good displays of mathematical formulas that load acceptably fast.
Concerns
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Data and Probability Connections - 07 edition
Summary: Part of a project funded by the National Science Foundation to improve the quality of mathematics and science teaching in grades K-12, this new text helps future teachers connect their college-level statistics to topics in standards-based middle school mathematics curricula. Designed to promote active learning, Data Analysis and Probability Connections models the student-centered approach recommended by the National Council of Teachers of Mathematics. Feat...show moreures
Connections to standards-based middle school curricula - Provides future middle grade mathematics teachers with a strong mathematical foundation, connecting the mathematics they are learning with the mathematics they will be teaching.
Visual or geometric approach to formulas and procedures - Gives enhanced meaning to formulas often presented as simply definitions to be memorized.
Numerous illustrations and problems drawn from middle school mathematics curricula - Assist students in making explicit connections between a typical college elementary statistics course and the statistical concepts taught by middle school teachers.
Exploration problems at the start of each chapter - Lay the foundation for developing key concepts and ideas throughout the chapter and provide a more active way to engage students.
''Focus on Understanding'' activities - Provide opportunities for students, working either in groups or individually, to apply and extend chapter concepts under discussion.
Integrated technology throughout - In keeping with the NCTM principles, explicit directions for using the TI-83 Plus calculator is integrated throughout the text, as well as additional computer software projects in the appendices37.64 +$3.99 s/h
Good
newrecycleabook centerville, OH
013144922252
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definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high school students. The first eight chapters are mostly accessible to any educated reader; the last two chapters and the two appendices contain more advanced material, such as the classification of motions, hyperbolic trigonometry, hyperbolic constructions, classification of Hilbert planes and an introduction to Riemannian geometry.
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Single Variable Calculus : Concepts and ContextStewart's clear, direct writing style in SINGLE VARIABLE CALCULUS guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.
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In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems.... more...
With the spread of the powerhouse MATLAB software into nearly every area of math, science, and engineering, it is important to have a strong introduction to using the software. Updated for version 7.0, MATLAB Primer, Seventh Edition offers such an introduction as well as a "pocketbook" reference for everyday users of the software. It offers an intuitive... more...
Contains lecture notes on four topics at the forefront of research in computational mathematics. This book presents a self-contained guide to a research area, an extensive bibliography, and proofs of the key results. It is suitable for professional mathematicians who require an accurate account of research in areas parallel to their own. more...
Features topics that include theoretical aspects of numerical techniques and algorithms as well as of applications in engineering and science. This book presents an overview of the modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications. more...
This text, based on the author's teaching at --Eacute--;cole Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Including numerous exercises and examples, this is an ideal text for advanced students in Applied Mathematics, Engineering, Physical Science and Computer Science. - ;This text, based... more...
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing... more...
Written for graduate students in applied mathematics, engineering and science courses, the purpose of this book is to present topics in "Numerical Analysis" and "Numerical Methods." It will combine the material of both these areas as well as special topics in modern applications. Included at the end of each chapter are a variety of theoretical and... more...
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More About
This Textbook
Overview
A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of most readers. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Chapter topics include Functions and Their Graphs; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Exponential and Logarithmic Functions; and more. For anyone interested in trigonometry.
Editorial Reviews
From The Critics
The textbook seeks to account for students with little mathematics background and a fear of mathematics who will end their mathematics education with a trigonometry course, and those with a strong mathematics foundation who are preparing for more advanced courses at the upper level undergraduate and graduate levels. Earlier editions were published between 1987 and 1999. The sixth includes many visits to the Motorola company. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Booknews
Covers functions and their graphs, applications of trigonometric functions, analytic geometry, and exponential and logarithmic functions. This edition features a new four-color design and real- world problems that can be analyzed using the material found in the chapter and information found on the Web. Appends sections on algebra topics and graphing utilities. Annotation c. by Book News, Inc., Portland, Or.
Related Subjects
Meet the Author
Mike Sullivan Professor of Mathematics at Chicago State University received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 35 years. He has been writing textbooks in mathematics for over 30 years. Mike has authored or co-authored over ten books. He is a native of Chicago's South Side and currently resides in Oaklawn. He has four children: Kathleen, who teaches college mathematics, Mike III, who co-authors many titles as well as teaches college mathematics, Dan, who is a Prentice Hall sales representative, and Colleen, who teaches middle-school mathematics. Nine grandchildren round out the family.
Why I Wrote This Book:
As a professor of mathematics at an urban public university for over 35 years, I understand the varied needs of precalculus math and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four, I also understand the realities of college life. I have taken great pains to insure that this text contains solid, student-friendly examples and problems, as well as a clear writing style. I encourage you to share with me your experiences teaching from this text.
The eighth edition of this series builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of the previous edition the previous edition. I am sincerely grateful for this feedback and have tried to make changes that improve the flow and usability of this text.
Preface changes chapterIntroduction changes chapter
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23.74,"ASIN":"0195061373","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":20.25,"ASIN":"0195061365","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":22.36,"ASIN":"0195061357","isPreorder":0}],"shippingId":"0195061373::0dKpVwQI7S8Of%2B9fy94Pktt8CpltXVyfjpP9wp1Mmqz6Cc%2FM9RmtZ9qkwQrKMUvUTnvqTRtuBldO2RORpfNZbuMzmrlH%2BZtvinqJk%2B03xkE%3D,0195061365::IUhYsWRpnZNJ1jwaA7mmUiO6JvupOoz9fOYs%2BPavdGIfwFyqdq4wXoJ9LVNJjgvSQauYb9uWRfs6bkdKoW7yZFqavtdRzjdtpgAhyDzae68%3D,0195061357::debHDu3xgvJUibW1pLqKM6wfDlDNGyO0Vl6ExcX3fpZKTQdvQlG%2Fs7GqYkHr1jVKKrqw2FAliiaQfa%2FUwlWk9zJftMk2CX7BKGU2ufcw2EU thorough exposition of the history of mathematics for mathematicians. For non-mathematicians, I recommend Mathematics for the Nonmathematician by the same author. This will be more accessible to the layperson like this one, just put Morris Kline in the search bar at the top of any Amazon page!
This book starts with "modern" topics like projective geometry after leaving off with calculus in the second volume. Like his intuitive calculus book, it alsoThe cool thing is that, unlike his books written in the 60's, this volume was 1990, just at the "reincarnation" of projective geometry and other "historical" math phenomena like quaternions, in new trends like video games and 3D computer animation. Still very relevant, and one of the best ways to learn more advanced math, due to Kline's wonderful teaching style, intuitive explanations, and comparisons with "everyday" physical happenings that FINALLY (at least in my case) helps you get what that equation really "means!"
If you see reviews trashing this or any other math book due to Kindle, don't fault the book!Read more ›
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for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.
This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra.
Features
Extensive applications of linear algebra concepts to a variety of real world situations. These applications introduce new material and show relevance of the material covered. Students learn how theories and concepts of linear algebra can help solve modern day problems.
Interesting and current examples include the application of linear transformations to an airplane, eigenvectors determining the orientation of a space shuttle, and how Google Inc. makes use of linear algebra to rank and order search results.
Abundant computer exercises, more extensive than any other linear algebra book on the market, help students to visualize and discover linear algebra and allow them to explore more realistic applications that are too computationally intensive to work out by hand.
These exercises also provide students with experience in performing matrix computations.
Worked out examples illustrate new concepts, making the material less abstract and helping students quickly build their understanding.
Two chapter testsfor every chapter help students study for exams and get the practice they need to master the material.
A comprehensive MATLAB® appendix gives users all the information they need to use the latest version of MATLAB. A series of MATLAB and Maple™ guides are also available at no additional charge with this text.
New To This Edition
1. New Section on Matrix Arithmetic
One of the longer sections in the previous edition was the section on matrix algebra in Chapter 1. The material in that section has been expanded further for the current edition. Rather than include an overly long revised section, we have divided the material into sections titled Matrix Arithmetic and Matrix Algebra.
2. New Exercises
After seven editions it was quite a challenge to come up with additional original exercises. This eighth edition has more than 130 new exercises. The new exercises are not evenly distributed throughout the book. Some sections have many new exercises and others have few or none.
3. New Subsections and Applications
A new subsection on cross products has been included in Section 3 of Chapter 2. A new application to Newtonian Mechanics has also been added to that section. In Section 4 of Chapter 6 (Hermitian Matrices), a new subsection on the Real Schur Decomposition has been added.
4. New and Improved Notation
The standard notation for the jth column vector of a matrix A is aj , however, there seems to be no universally accepted notation for row vectors. In the MATLAB package, the ith row of A is denoted by A(i, :). In previous editions of this book we used a similar notation a(i, :), however, this notation seems somewhat artificial. For this edition we use the same notations as for a column vector except we put a horizontal arrow above the letter to indicate that the vector is a row vector (an horizontal array) rather than a column vector (a vertical array).
We have also introduced improved notation for the standard Euclidean vector spaces and their complex counterparts.
5. Other Revisions
Various other revisions have been made throughout the text. Many of these revisions were suggested by reviewers.
6. Special Web Site and Supplemental Web Materials
Pearson has developed a special Web site to accompany the 8th edition. This site includes a host of materials for both students and instructors.
Table of Contents
Preface
What's New in the Eighth Edition?
Computer Exercises
Overview of Text
Suggested Course Outlines
Supplementary Materials
Acknowledgments
1. Matrices and Systems of Equations
1.1 Systems of Linear Equations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 Elementary Matrices
1.6 Partitioned Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
2. Determinants
2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 Additional Topics and Applications
Matlab Exercises
Chapter Test A
Chapter Test B
3. Vector Spaces
3.1 Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
Matlab Exercises
Chapter Test A
Chapter Test B
4. Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
Matlab Exercises
Chapter Test A
Chapter Test B
5. Orthogonality
5.1 The Scalar Product in Rn
5.2 Orthogonal Subspaces
5.3 Least Squares Problems
5.4 Inner Product Spaces
5.5 Orthonormal Sets
5.6 The Gram—Schmidt Orthogonalization Process
5.7 Orthogonal Polynomials
Matlab Exercises
Chapter Test A
Chapter Test B
6. Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Systems of Linear Differential Equations
6.3 Diagonalization
6.4 Hermitian Matrices
6.5 The Singular Value Decomposition
6.6 Quadratic Forms
6.7 Positive Definite Matrices
6.8 Nonnegative Matrices
Matlab Exercises
Chapter Test A
Chapter Test B
7. Numerical Linear Algebra
7.1 Floating-Point Numbers
7.2 Gaussian Elimination
7.3 Pivoting Strategies
7.4 Matrix Norms and Condition Numbers
7.5 Orthogonal Transformations
7.6 The Eigenvalue Problem
7.7 Least Squares Problems
Matlab Exercises
Chapter Test A
Chapter Test B
Appendix: MATLAB
The MATLAB Desktop Display
Basic Data Elements
Submatrices
Generating Matrices
Matrix Arithmetic
MATLAB Functions
Programming Features
M-files
Relational and Logical Operators
Columnwise Array Operators
Graphics
Symbolic Toolbox
Help Facility
Conclusions
Bibliography
A. Linear Algebra and Matrix Theory
B. Applied and Numerical Linear Algebra
C. Books of Related Interest
Answers to Selected Exercises
About the Author(s)
Steven J. Leon is a Chancellor Professor of Mathematics at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis.
Leon is currently serving as Chair of the Education Committee of the International Linear Algebra Society and as Contributing Editor to Image, the Bulletin of the International Linear Algebra Society. He had previously served as Editor-in-Chief of Image from 1989 to 1997. In the 1990's he also served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 1992–1997.
PearsonChoices
Give your students choices! PearsonChoices products are designed to give your
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Books
Geometry & Topology
From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem....
This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well-motivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and well-motivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.
The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.
Complex Analysis with Mathematica offers a new way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos, and advanced conformal mapping. A CD is included which contains a live version of the book, and the Mathematica code enables the user to run computer experiments.
This book develops methods which explore some new interconnections and interrelations between analysis and topology and their applications. Emphasis is given to several recent results which have been obtained mainly during the last years and which cannot be found in other books in nonlinear analysis. Interest in this subject area has rapidly increased over the last decade, yet the presentation of research has been confined mainly to journal articles.
A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.
This advanced textbook on topology has three unusual features. First, the introduction is from the locale viewpoint, motivated by the logic of finite observations: this provides a more direct approach than the traditional one based on abstracting properties of open sets in the real line. Second, the author freely exploits the methods of locale theory. Third, there is substantial discussion of some computer science applications. As computer scientists become more aware of the mathematical foundations of their discipline, it is appropriate that such topics are presented in a form of direct relevance and applicability. This book goes some way towards bridging the gap for computer scientists.
The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.
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College Algebra : Concepts and Models - Text Only - 4th edition
Summary: College Algebra: Concepts and Models was the first college algebra text to be developed specifically for students who may not be proceeding on to calculus or upper level math courses, but who need a solid understanding of algebra for their social sciences and liberal arts majors. It encourages student understanding of algebra through the use of modeling techniques and real-data applications. Optional use of technology is carefully integrated throughout the text. ...show more ...show less
Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about the use of computer technology as a teaching tool and motivational aid. His Interactive Calculus(a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level. It is currently the first mainstream college textbook to be offered on the Internet.
Hostetler, Robert P. : The Pennsylvania State University, The Behrend College
Bob Hostetler received his Ph.D. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include Remedial Algebra, Calculus, Math Education and his research interests include mathematics education and textbooks.
Hodgkins, Ann V. : Phoenix College
View Table of Contents
Note: Each chapter includes a Mid-Chapter Quiz and concludes with a Summary, Review Exercises, and a Test.
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Math Center
The Math Center is a non-credit, Community Education class which provides assistance
in mathematics as a completely free service. Current Allan Hancock College students
as well as other individuals who are 18 years or older may fill out a simple registration
form and attend as frequently as they want. Registration forms may be found in the
Math Center or at Community Education in Building S.
The goal of the Math Center (sometimes called the Math Lab) is to assist students
in the successful completion of any Allan Hancock College mathematics class by providing
additional instructional resources. The Math Center offers many resources, including
one-on-one, drop-in tutoring by our staff of instructors and student tutors. Please
see the full list of resources below:
Free, drop-in tutoring
A place to study individually or in small groups
In-house loan of current textbooks and solutions manuals
A library of supplemental books, DVDs, and video tapes for check-out
Computers for mathematical purposes
Calculators
Handouts on math topics, including content from various math courses as well as information
on overcoming math anxiety and preparing for and taking math tests
Two private study rooms
Make-up testing
Workshops
Joining the math center group
Current students may access more detailed information by entering their myHancock
portal and joining the Math Center Group. Details may include information such as
the current schedule of instructors and student tutors who work in the Math Center,
a schedule of instructors and tutors who specialize in statistics, upcoming workshops
on selected topics, etc. To join the Math Center Group:
Enter myHancock
Look at the center of the Home page in the box titled "My Groups." Click on "View
All Groups" at the bottom of the box.
STAFF
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History of Mathematics - 3rd edition
Summary: The updated new edition of the classic and comprehensive guide to the history of mathematicsFor more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincar_ Conjecture, in addition to recent advances in areas such as finite group theory and...show more computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.Whether you ? re interested in the age of Plato and Aristotle or Poincar_ and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it. ...show less
0470525487 Brand New. Exact book as advertised. Delivery in 4-14 business days (not calendar days). We are not able to expedite delivery71.50 +$3.99 s/h
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PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI
0470525487
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El Cerrito Statistics, it is intended for math majors. I got "A" in that course. My instructor was a visiting scholar and taught more theorems than other Linear Algebra sections
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Elementary Statistics: A Brief Version, is a shorter version of the popular text Elementary Statistics: A Step by Step Approach. This softcover edition includes all the features of the longer book, but it is designed for a course in which the time available limits the number of topics covered. It is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and teaching problem solving through worked examples and step-by-step instructions. This edition places more emphasis on conceptual understanding and understanding results. This edition also features increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI-84 Plus graphing calculators; computing technologies commonly used in such courses.
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MSM701 and acceptance into the Master of Arts in Teaching Middle School Mathematics program or permission of the Program Coordinator. Not available for degree credit towards the MAT or MS mathematics programs
Description
This course is intended to bridge the gap between algebra and calculus. It will develop a firm understanding of the concept of function, how to graphically represent various functions, analyze their behavior and create new functions from old. The course will look closely at various function classes including polynomials, exponential, logarithmic and trigonometric. Functions will be used to model real-life situations.
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Mathematical Methods for Physicists : A Comprehensive * Updates the leading graduate-level text in mathematical physics * Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering * Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relations New in the Sixth Edition: * Updated content throughout, based on users' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell's equations * A new chapter on probability and statistics * More elementary sections have been deleted
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Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C), and MAT 080 (min grade C), or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
30201
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MAT115 Principles of Modern Math
Prerequisite: MAT 076 (min grade C) or 1 year high school geometry (min grade C), and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement score or ACT score of 21-22
IAI#: M1904
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08:00-09:15
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JL. Horn
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MAT121 College Algebra
Prerequisite: MAT 076 (min grade C) or 1 year of high school geometry (min grade C) and MAT 080 (min grade C) or 2 years of high school algebra (min grade C) or appropriate Placement or ACT score of 21-22
30139
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$10
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$10
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$10
MAT122 Trigonometry
Prerequisite: MAT 121 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and apprpriate placement score or ACT score of 23-25
30142
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MAT203 Calculus & Analytic Geometry I
Prerequisite: MAT 122 (min grade C) or appropriate Placement score or 4 years of college preparatory high school mathematics (min grade C) and appropriate Placement score or ACT score of 23-25
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Purpose of the unit: This unit is designed to develop students' understanding of basic geometry and math concepts that are needed in order to continue in this class of algebra.
Rationale of the unit: The unit topic is important for building a foundation of knowledge for the following units in algebra. A clear understanding of the objectives will increase their chance of success for the rest of the year in the class of algebra. The integration of the concepts with the other core subjects will not only help the students understand the concepts but also see the significance of math concepts in many areas of study.
Goals of the unit: The goals of this unit are for the students to : 1. To develop an understanding of basic and introductory geometry and math concepts. 2. To look forward to continuing in the study of algebraic concepts. 3. To understand how geometry and algebra relate to many other areas of study such as science, social studies, and language arts. 4. To understand how the concepts of geometry and algebra are relevant to their daily lives. 5. To look forward to living a life of discovery.
Instructional objectives (discoveries) of the unit: 1. To be able to do geometric formulas. 2. To understand tree diagrams. 3. To understand the coordinate plane. 4. To be able to round and estimate. 5. To be able to add and subtract decimals. 6. To be able to multiply and divide decimals. 7. To use divisibility rules to find all factors of a given number and to identify numbers as prime or composite. 8. To write the prime factorization of a number. 9. To find the GCF of two or more numbers and to find the LCM of two or more numbers. 10. To write equivalent fractions and write fractions in simplest form.
Unit Overview: Throughout this unit students will developing an understanding of basic geometry and algebraic concepts through lectures, class discussions, games such as Sudoku, and story problems that incorporate the them e of discovery and integrate the core subjects as well.
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Cognition and Learning Background: Absolute Value
Methods of Teaching
The typical method of teaching absolute value involves memorization of the formal definition and application of the case-by-case method and the properties of inequalities in order to solve problems (McLauren, 1985, p. 91).
Typical instruction with absolute value begins with the definition used in conjunction with algebraic representation in simple equality equations (such as or ). While more textbooks are emphasizing conception of absolute value as distance and using number lines as a tool to understanding, the more common approach is procedural solution using algebra and representation of the answers algebraically and on a number line. The prolonged connection of absolute value with distance or number line representation tends to fall by the wayside in favor of procedural fluency as a goal.
California State Standards Involving Absolute Value
Grade Seven
2.5 - Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
California State Standards Glossary Definition of Absolute Value
A number's distance from zero on the number line. The absolute value of -4 is 4; the absolute value of 4 is 4.
Cognitive Obstacles and Common Misconceptions
Basic misconceptions
Absolute value is "always positive" meaning that the solution of an absolute value problem can never be negative
Absolute value is "always positive" and so any solutions must be made positive
Absolute value problems only have one solution
Absolute value problems have two solutions which are always mirrors (i.e. 4 and -4)
Note that these misconceptions are related but distinct. There is a difference between a negative solution being impossible (i.e. not to be considered) and having only positive solutions, which may involve considering a negative solution but subsequently making it positive.
Cognitive Obstacles with the Definition of Absolute Value
The definition of absolute value is:
Sink (1979) found that students ignore the conditions (the if statements above). Students have been trained since elementary grades to treat the absolute value of a quantity as a nonnegative value. Students will often say that absolute value means "the answer is always positive". However, as they tend to ignore the condition statements and , students become confused with the second sentence of the definition. The idea that contradicts their previous understanding that the absolute value would be nonnegative.
Cognitive Obstacles with Inequalities
Absolute value is often found in conjunction with inequalities, leading to all of the cognitive obstacles that are associated with linear equality and inequality equations. Because absolute value in conjunction with inequalities typically leads to compound inequalities, the number of intertwining cognitive obstacles can quickly increase.
This section can be removed and expanded upon when the Inequalities page is developed.
Students have difficulty reading inequalities correctly
As with equalities, students are confused by variables on the right side of the inequality
is more cognitively demanding than
Compound inequalities necessitate the ability to use variables on the right sight of the inequality sign
Students do not understand that inequalities can not be read left to right and right to left in the same way
Students are used to equality equations, which can be read in any order
Students read as "6 is equal to x" and "x is equal to 6"
Students likewise read as "6 is greater than x" and "x is greater than 6" even though this is incorrect
Conjunction and disjunction of compound inequalities are not well understood
Compound inequalities can be written as one statement or as two statements joined by a keyword
The singular statement guarantees that one part of the inequality must be correctly read right to left (see above)
The joined statements require selection of the correct keyword ("and" or "or")
The keyword may or may not be present in the presentation of the problem
Sometimes it is given in the problem or implied by the section of the book being studied (see below)
Sometimes it must be inferred from the behavior or the graph
Students are encouraged to think of problems as "and" or "or" inequalities
Students do not often understand which is the correct keyword and why
Textbooks often divide these problems artificially into two sections
Students are led to believe they are separate kinds of problems
The cases of overlapping inequalities or all real number solutions are not always presented as possibilities
Students are trained to classify the problems but do not understand the underlying meaning or purpose of the classification
Compound inequalities can be represented with a number line
Early problems often require usage of the number line
Textbooks typically drop the requirement for the solution to be represented as a number line with the more complicated problems
Students are taught to observe the basic characteristics without understanding what they truly mean
Students have difficulty with the various kinds of notation
Inequality notation ()
Used to formulate problems and solutions
Compound inequalities can be represented with inequality notation, but have their own cognitive obstacles (see above)
Inequality notation requires the use of a variable
Interval notation ()is typically introduced earlier in the school year
Interval notation is used only for representing solutions to problems written in other notations
Interval notation does not make use of variables
Compound inequalities can be represented with interval notation, but require special symbols
The union and intersection symbols ( and ) are typically taught during set theory and hastily reviewed (and then forgotten) when teaching interval notation
The union and intersection symbols are another way of representing "and" and "or"
Set notation (
Used to formulate problems and solutions
Less frequently used to describe inequalities before Algebra II
Number Line Graph notation
Can be used as ways to understand and conceptualize problems
Used mainly to describe solutions; usage of the number line as a tool for solving the problem diminishes after early examples
Have two styles that relate to interval notation
Cognitive Obstacles with Absolute Value Inequalities
Students are instructed to solve problems using the case-by-case method
There is a "positive" case and a "negative" case
The "shortcut" for the negative case is to reverse the inequality sign and the sign of the constant on the side opposite the variable
The reason for this "shortcut" is often poorly explained
The quantity inside the absolute value sign can be positive or negative
If this quantity is negative, the resultant equation can be multiplied or divided on both sides by -1
Even if this process is explained, it is often not related back to distance or another way of making sense of the operation
Since students do not understand the procedure, they will often forget to reverse one or both signs
This illustrates a typical example of the case-by-case solution method. The procedure skips right to the "shortcut", where the inequality and the right hand side constant have their signs reversed without explanation. Since the coefficient of the variable is negative, the solution obtained by dividing both sides by -2 requires the inequality to be reversed again. Students will mistakenly think this has already been taken care of since they have already flipped the inequality sign once.
Textbooks sometimes instruct that answers to absolute value inequalities will be "or" if the original problem is > or and "and" if the original problem is < or
This is an additional procedural step to memorize or forget
Sometimes the mnemonics "greatOR than" or "less thAND" are used
This is only true for absolute value inequalities -- it does not transfer to compound inequalities as a whole
Students are often only given this procedural step and mnemonic and do not understand the underlying concepts
Furthermore, students will neglect to check that their answer makes sense and will default to the what the mnemonic or shortcut indicates
Dean (1985) pointed out that students will assume that the solution set always contains only alternating intervals. Multiplicity and the sign of factors can change the solution intervals even when the critical points remain the same.
Pedagogical Tools and Strategies
Ahuja - absolute value as distance
Ahuja (1976) suggests considering absolute value in terms of distance, making the definition of absolute value:
For real numbers and , consider as the distance between and , where and are the representations of the numbers and , respectively, on the real line.
Example: Solve
Since the distance of from 5 is 2, can be either 7 or 3.
Example: Solve
. This equation says that the distance of from -7 is 3. The answer would be either -4 or -10.
Arcidiacono (1983) recommends using piecewise functions to reinforce the algebraic and graphical representations of the absolute value function together from the beginning of instruction. His three stage approach to absolute value is:
Ballowe - use square roots to rewrite absolute value problems
Ballowe (1998) suggests using the definition to rewrite the problem without absolute value signs.
Example:
rewrite using the definition
square both sides
Brumfiel - teach all five definitions of absolute value
Brumfiel (1980) recommends teaching five definitions of absolute value and the investigation of one problem with all five definitions. The definitions are:
Let be any real number. On a coordinate line let be the point whose coordinate is . Then is the undirected distance between and the origin.
Let be any real number. Choose any numbers and so that . Let and be the points whose coordinates are and . Then is the undirected distance between the points and .
is the "larger" of the numbers , . We write this briefly as = Max {, }, that is, is the maximum element of the set that consists of and . Of course we agree that Max {,} = . This takes care of the case .
Note that Definition 2 is essentially the same as Ahuja's(1976) recommendation.
Note that Ballowe (1998) expanded upon the ideas in Definition 4
Note that in Definition 5, Brumfiel (1980) has ordered the definition such that the condition comes first in each statement, addressing Sink's (1979) concern that the condition would be ignored by the student.
McLauren - evaluate the critical points
McLauren (1985) recommends solving absolute value inequalities as equalities, plotting the results on a number line, listing the intervals defined by the critical points, and testing each interval to see if it is a solution. This technique can be extended to quadratic and rational inequalities.
Sink - rooting out definition misconceptions
The teacher must show with examples how substituting values according to the conditions causes the result to be nonnegative.
Example
Example
Stallings-Roberts - the Absolute Value Scale (AVS)
The Absolute Value Scale (AVS) (Stallings-Roberts, 1991) is a manipulative tool that students can create themselves that helps to visually associate absolute value problems with number lines and the concept of absolute value as distance.
Students can make the AVS from a sheet of ruled notebook paper, creased lengthwise, creating two one-inch by eleven-inch strips that are placed next to one another. The bottom strip represents the number line. The top strip represents the distance scale that corresponds to the number line.
AVS can be used to model algebraic problems
AVS can be used to understand how to rewrite some equalities and inequalities in terms of absolute value.
Wagster - solve by intervals
Wagster (1986) recommends a way similar to McLauren's (1985). First, the zeros of each expression in an absolute value inequality are marked on a number line. Then, in each interval on the number line, the equations are solved for that interval only. If the solution is within the interval, it is a solution of the inequality.
Curricula and Technological Resources
Technological Activities
Students can use graphing calculators to plot absolute value equations with two expressions. Students can examine equations with one, two, or no solutions and use the graphing calculator to find precise intersections.
The following links are tools to help visualize absolute value graphs, both on the number line and in the coordinate plane. A indicates the best tools for learning. Many of these are simple tools that allow users to see how a graph of
an absolute value equation behaves. The better tools show different aspects of absolute value or show how intersecting graphs
produce solutions to the equations being graphed.
Websites - Games
The following links are to games that utilize absolute value in some way. None of the games are involved or teach the concepts. They could, however, be used to reinforce lessons or provide extra practice with the basic concepts of absolute value. These are all drill-and-practice
type activities and don't explore the conceptual side of absolute value like the tools above.
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Modify Your ResultsPrentice Hall Mathematics is designed to enable students tap into the power of mathematics.
The text will help them be successful on the tests they take in class and on high-stakes tests required by your state. The practice in each lesson will prepare them for the format as well as for the content of these tests.
The authors and consulting authors on Prentice Hall Math: Tools for Success team worked with Prentice Hall to develop an instructional approach that addresses the needs of middle grades students with a variety of ability levels and learning styles. Authors also prepared manuscripts for strands across three levels of Middle Grades Math. Consulting authors worked alongside authors throughout program planning and all stages of manuscript development offering advice and suggestions for improving
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High School Mathematics - Algebraic Modeling Workshop NY
Wayne State University of Detroit, Mi is proud to offer a workshop for high school mathematics teachers. The course builds on algebraic modeling concepts developed in Algebra II, and all of the material presented is developed around real-world contexts that answers the question - When will I ever use this? It is designed for a wide range of student mathematical abilities. The Program Outline Day 1: Morning - Multi-Criterion Decisions e.g. select cellphone plan, college to attend Day 1: Afternoon… Show more - Systems of Linear Inequalities - Max profit of skateboards - Implemented in Excel Day 2: Morning - Sensitivity Anlysis - What if? Interpret output of Excel Day 2: Afternoon - Optimize diet, minimize cost of controlling water pollution Day 3: Morning - Integer Variables - Schedule workers, plan shipments Day 3: Afternoon - Binary (0 or 1) Decision Variables - Select optimal set of projects, create teams Day 4: Morning - Select location for retail outlets, tornado emeregency response center Day 4: Afternoon - Project Management - Develop plans to manage complex projects
There is no cost for participation in the workshop. Participants will gain access to materials including a full textbook, curriculum, and online support which can be implemented in any school as a fourth year mathematics course. With more than 50 schools across Michigan, North Carolina, California, Georgia, and New York participating in the curriculum, the analytics course has proven to be popular amongst teachers, administrators, and students alike. As the only curriculum which seeks to answer the question of, "When will I ever use this?", partners have said the following about this opportunity: Parents: 1). I don't know what you are doing but for the first time my child enjoys and finds success doing mathematics. 2). I hated math when I was in school. I wish I had had this course when I was in high school. Students: 1). I like this course because it's the first time I have ever been asked my opinion in a math class. Some of the problems were really cool because it was my choice of what was most important, and I could see how different choices played out. 2). I used some of the tools that I learned to make a decision about which boy I would take to prom. I got to understand how to weigh variables, and how to use math to make better decisions. Teachers: 1). I love this course. For the first time, I have not been scared to answer the question, How will I use this in my life. Thank You!!!! 2). This course has been a blessing. Even with an extreme range of student's abilities in my classroom, the content was interesting enough to keep the attention of the mathematic all stars, as well as some of my mathematically challenged students. The blend of application based learning with the real-world contexts made all of the students fascinated by the power of mathematic application to various industries and professions.
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More About
This Textbook
Overview
Math Study Skills outlines good study habits and provides students with study strategies and tips to improve in areas such as time management, organization, and test-taking skills. With a friendly and relatable voice, Alan Bass addresses the misgivings and challenges many students face in a math class, and offers techniques to improve their study skills, as well as opportunities to practice and assess these techniques. This math study skills workbook is short enough to be used as a supplement in a math course, but can also be used as a main text in a study skills class.
Related Subjects
Meet the Author
Alan Bass earned his Master of Science degree in Mathematics from the University of North Carolina at Wilmington. Presently, he lives, writes, runs, swims, bikes, hikes, and plays music with his wife Holly in sunny San Diego, CA. (He also enjoys fine wine and all things nerdy). He is an Associate Professor of Mathematics at San Diego Mesa College (just got tenure) and has been teaching developmental math for more than ten years. He is a big advocate for math study skills so, through a grant project called Pathways through Algebra, he got into networking with other schools to make study skills programs happen. He has worked on developing learning communities, establishing curriculum and pedagogy for study skills classes, and methods for incorporating study skills directly into the classroom. He has created and accumulated a ton of material, and wants to share it with you! For more information, check out
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Maple Quick Start Tutorial
Can't see the video? Update to the latest Adobe Flash Player, or use an HTML5 compatible browser.
Description
In this introductory course, you will become fluent in the Maple environment, without ever having to leave your desk. You will learn how to use context menus, task assistants, and palettes to perform powerful analyses and create high-impact graphics with only a minimal knowledge of commands. This course will give you the tools you need to get you started quickly, and a solid foundation upon which to build your future Maple explorations.
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Teaching experiments with pairs of children have generated several hypotheses about students' construction of fractions. For example, Steffe (2004) hypothesized that robust conceptions of improper fractions depends on the development of a splitting operation. Results from teaching experiments that rely on scheme theory and Steffe's hierarchy of fraction schemes imply additional hypotheses, such as the idea that the schemes do indeed form a hierarchy. Our study constitutes the first attempt to test these hypotheses and substantiate Steffe's claims using quantitative methods. We analyze data from 84 students' performances on written tests, in order to measure students' development of the splitting operation and construction of fraction schemes. Our findings align with many of the hypotheses implied by teaching experiments and, additionally, suggest that students' construction of a partitive fraction scheme facilitates the development of splitting.
In advanced mathematical thinking, proving and refuting are crucial abilities to demonstrate whether and why a proposition is true or false. Learning proofs and counterexamples within the domain of continuous functions is important because students encounter continuous functions in many mathematics courses. Recently, a growing number of studies have provided evidence that students have difficulty with mathematical proofs. Few of these research studies, however, have focused on undergraduates' abilities to produce proofs and counterexamples in the domain of continuous functions. The goal of this study is to contribute to research on student productions of proofs and counterexamples and to identify their abilities and mathematical understandings. The findings suggest more attention should be paid to teaching and learning proofs and counterexamples, as participants showed difficulty in writing these statements. More importantly, the analysis provides insight into the design of curriculum and instruction that may improve undergraduates' learning in advanced mathematics courses.
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A week's worth of teaching on the Binomial Theorem. Lesson examples and a plethora of worksheets included. Learners find coefficients of specific terms within binomial expansions using notation of factorials and then apply these skills in using the Binomial Theorem to find solutions to practical applications.
In this video on the Binomial Theorem, Sal tries to give an intuition behind why combinations are part of its definition. By looking at the expansion of (a + b)3 and carefully looking at where each value originates from, one can see how we are really asking a question about combinatorics.
A comprehensive lesson that explores and researches Pascal's triangle and relates its properties to the Binomial Theorem through a variety of lessons. Have the class practice expanding polynomials using the theorem. A few other formulas and functions related to this theorem will be explored.
In this Algebra II worksheet, 11th graders apply the binomial theorem to expand a binomial and determine a specific term of the expansion. The one page worksheet contains four problems. Answers are provided.
Sal shows two ways to quickly calculate the coefficients of a binomial expansion. With the first method, he shows the relationship between PascalÕs triangle and the coefficients, and in the second method, he shows an even faster way for one to write the coefficients without calculating previous rows of coefficients.
Continuing his discussion of the Poisson Distribution (or Process) from the previous video, Sal takes students through the derivation of the traffic problem he had begun. The math gets gritty in this video as Sal takes out the graphic calculator to solve the problem.
In this system of equations worksheet, 11th graders solve and complete 23 various types of problems. First, they graph each system of inequalities shown. Then, students write a polynomial function of least degree with integral coefficients that has the given zeros. They also determine the equation for each conic, name the conic and state the center.
In this difference of equations worksheet, students solve and complete 49 various types of problems. First, they obtain the solution of any linear homogeneous second order difference equation. Then, students apply the method of solution to contextual problems. In addition, they use generating functions to solve non-homogeneous equations.
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Customer Reviews for McGraw-Hill Key To Geometry, Book #7
Whether you're looking for preparation for geometry, a remedial course or a basic refresher, Key to Geometry is a non-threatening way to gain a working, practical knowledge of the subject. Students begin by drawing lines and bisecting angles, eventually working their way to sophisticated constructions involving over a dozen steps. When the course has been completed, students will have been introduced to 134 geometric terms and will be ready to geometric proofs. 55 pages, paperback.
Workbook 7 covers perpendiculars and parallels,Chords and Tangents and Circles.
Customer Reviews for Key To Geometry, Book #7
This product has not yet been reviewed. Click here to continue to the product details page.
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MATH TREK Algebra 1
04/01/04
For curriculum-based algebra instruction, teachers and students can use MATH TREK Algebra 1. The multimedia program includes tutorials, assessments and student tracking. Students can use the program's scientific calculator, glossary and journal to help them complete the various exercises and activities. The assessment and student-tracking features provide immediate feedback to students so that they can stay on top of their progress. This engaging program, complete with sound, animation and graphics, can be used on stand-alone computers or a network. NECTAR Foundation, (613) 224-3031
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...Feel free to reach out with any questions or comments.Like any language, we learn algebra for a purpose. In prealgebra we were introduced to the vocabulary and grammar of the algebraic language (e.g. we say "3x" and not "x3") so that we can use it as an efficient shorthand in recording our thou
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Prentice Hall Algebra 1, Geometry, Algebra 2 help students see math like never before. This blended print and digital curriculum provides an environment where teachers can engage students, teach for understanding, and promote mastery-for success today and throughout life. It's a whole new way to look at math.
With online sampling for Prentice Hall Mathematics you can review the program on your schedule and at your pace.
Program Facts
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Appendix E serves as a foundation for the identification and alignment of intervention resources, although instructional materials designed specifically for intervention will not be available until the 2007 mathematics instructional materials adoption. Until that time, schools and districts will need to conduct an alignment process using their existing state-adopted materials. This process involves matching key content standards to the intervention volumes, then determining which grade-level instructional materials would be most appropriate for intervention instruction. With this information, schools can construct an effective mathematics intervention program using their existing grade-level instructional materials.
Here is an example of how this alignment process might be undertaken by a school and/or district collaborative team designing intervention for fifth-grade students.
Volume 5 of the intervention guide deals with Functions and Equations, which correlates to the areas identified for intervention. It suggests that the following three content standards be considered in a fifth-grade intervention program addressing this topic area: Algebra and Functions 1.5; Statistics, Data Analysis, and Probability 1.4; and Statistics, Data Analysis, and Probability 1.5. One additional standard—Algebra and Functions 1.4—was identified as foundational for algebra readiness.
The chart below lists these standards and their references in the intervention guide. The number of CST questions indicates the relative importance of each standard. The team also looked at the standards in relationship to the California High School Exit Exam (CAHSEE) and found that three of the standards were key for that assessment as well.
Fifth Grade Intervention Alignment Example
California Standard
Intervention
reference
Algebra Readiness
reference
Number of CST questions
CAHSEE
Algebra and Functions 1.4: Identify and graph ordered pairs in the four quadrants of the coordinate plane
Topic 7
4
x
Algebra and Functions 1.5: Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid
Volume 5
5
x
Statistics 1.4: Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph
Step 2—Once the planning team determined the alignment of key grade-level standards to the intervention topic, the next step was to explore the released test items from the California Standards Tests related to those standards. This gave the planning team an opportunity to specifically identify what students are being asked to know and be able to do. In this case, the team identified seven Grade 5 released test items from CDE's 2005 Released Test Questions, < and matched each question to the standard or standards tested.
Step 3—Next, the planning team identified the academic vocabulary required for learning these four standards. Specifying the academic vocabulary required, and developing strategies for teaching that vocabulary, is a key part of successful mathematics intervention for English Learners.
Step 4—The planning team then located the targeted standards in their adopted instructional materials. Questions that the team considered when undertaking this materials review and planning for intervention instruction included:
How are the assessments in the instructional materials similar to or different from the CST released items?
What additional language or instructional strategies should be implemented to serve strategic and intensive students so that they can learn efficiently from basic grade-level instructional materials?
Below is a listing of which resources the team identified for addressing students' intervention needs using adopted mathematics textbooks for Grade 5.
Harcourt Math
Topics: Graph Relationships and Integers on the Coordinate Plane; Using an Equation to Graph
| 677.169 | 1 |
Who & What
Jack W. Crenshaw, Ph.D. (Physics)
wrote his first computer program in
1956 for an IBM 650. He has been working with real-time software for
embedded systems ever since -- contributing several years to NASA
during the Mercury, Gemini, and Apollo programs. In addition to other activities, he is currently a contributing editor for Embedded Systems Programming magazine and author of the
Programmer's Toolbox column.
In Math Toolkit for Real-Time Programming, his effort is
focused on describing the pitfalls of vendor-provided math libraries
and providing robust replacements. In section one he gives a thorough overview of constants and the various manners in which to declare them, naming conventions, and error handling. As the work progresses, in section two, he builds a library of proven algorithms ranging from
square roots to trigonometrical functions to logarithms. Did you suffer through calculus in college with a barely passing grade?
Section three will teach you more about numerical calculus in a half-hour than you may have learned in three semesters.
Kudos
Math Toolkit is written in an easy to understand
anecdotal manner. You might be tempted to think that the author was
animatedly relating the history of computing square roots while having
lunch with you. This method works very well and keeps what could be a
rather heavy subject from becoming too much of a burden. Most chapters
have historical tidbits liberally sprinkled throughout.
Even if college algebra left you with post-traumatic stress disorder, you will not have any trouble with section two. Indeed, you may find
yourself intently following the author on the trail of the perfect arctangent algorithm -- much as a sleuth on the trail of a villain.
The depth of knowledge shown, and its presentation, is exceptional. The author's years of experience are evident in his
self-confident writing style. You will rarely see a clearer overview of numerical calculus.
Quibbles
The cover of the book states: "Do big math on small machines." This, combined with the Real-Time
Programming phrase in the title, might lead one to believe that the book's primary audience is intended to be the embedded microcontroller crowd. Sadly, not so. There is very little here for
the die-hard assembler programmer other than some very handy integer square root and sine routines - and these examples are in C++. Based on the cover, I would have liked to see a greater emphasis on
processors lacking a floating point unit. Also, some code examples in pseudo-assembler would have been welcome, as the author chose C++ as
the language of choice for all examples.
Crimes
As is so often the case nowadays, there are various typographical
errors scattered throughout. This seems to be an epidemic in current
technical books. Fortunately, it didn't affect the readability of Math Toolkit.
Conclusions
I believe Math Toolkit for Real-Time Programming would be a great, perhaps mandatory, addition to the bookshelf of anyone that
is involved in writing code that has a heavy math component. Other
than the somewhat misleading cover, I cannot find anything truly negative to say about this work. Congratulations are in order to
Mr. Crenshaw on a job well done.
The book also includes a CD-ROM of all example source code. In reality, to get the best benefit from the book, you should mostly
ignore the CD-ROM and work through the examples. To quote the author: "Never trust a person who merely hands you an equation."
Table of Contents
Getting The Constants Right
A Few Easy Pieces
Dealing with Errors
Fundamental Functions
Getting the Sines Right
Arctangents: An Angle-Space Odyssey
Logging in the Answers
Numerical Calculus
Calculus by the Numbers
Putting Numerical Calculus to Work
The Runge-Kutta Method
Dynamic Simulation
Appendix A: A C++ Tools Library
Disclosure
I received a review copy of this book from the publisher. Thus, my loyalties and opinions may be completely skewed. Caveat Lector.
is Real Time programming still a Real Issue? (3, Interesting)
Back in the day, a book like this would have been a real life saver for those of us slugging it out with brain-damaged operating systems (e.g. MS-DOS). From things like MIDI sequencers to guidance systems, the need for real-time speed was a real issue.Though I admit, having to write my share of real-time apps back in the day has me curious enough to put the book on my wishlist.
Re:is Real Time programming still a Real Issue? (4, Interesting)
Someone marked this question redundant? Guess that shows you jerks are everywhere.
Hey, I understand completely what you're saying. I for one am glad I don't have to deal with such as latency and pre-emption. In fact, here is a link to a nifty article entitled "Real Time Issues in Linux [helsinki.fi] " that essentially sums up what you asked with a resounding yes.
Re:is Real Time programming still a Real Issue? (5, Informative)
This deserves some more explanation, since everyone here seems to have missed this point.
A Real Time system is one where the ouptut isn't correct unless it arrives on time. Real Time systems are deterministic - not necessarily fast. The key is to use bounded-time algorithims so that you can predict the worst case execution time at compile time. RTOS's aren't designed to be fast, they are designed to have deterministic schedulers and kernel services.
Of course, faster processors make it easier to meet real time deadlines, but as processors get faster I'm seeing engineers ignore the real time analysis and design because the code passed the last test they ran. Then they are surprised when it fails in the field...
Re:is Real Time programming still a Real Issue? (5, Insightful)The above generally doesn't apply to anyone doing serious embedded work with small and midrange microcontrollers. Often an operating system is thin to non-existent on these platforms. Some of the lower-range parts may have a 2-byte hardware stack, 28 bytes of RAM and maybe 512 bytes of program memory. Obviously, you won't be doing much sophisticated numerical work on these smallest of microcontrollers, but for more midrange parts, I've found this book to be a godsend.
Re:is Real Time programming still a Real Issue? (2, Informative)
Well... Realtime programming might now be an issue for you if you use an advanced OS coupled with a mighty cpu. But in many situations you might find yourself programming for, say, a small 1 MHz cpu in a timecritic controllsystem at a factory or chemicalplant or something like that. That's when you'll need your skills in realtime programming.
Re:is Real Time programming still a Real Issue? (4, Interesting)
I work with a group of eight other people updating 40 year old Assembler on an IBM Series 1. Something tells me that if this was included in our training programs, those that are
SUF
FER
ING
through the digit-crunching wouldn't have such a hard time. Most people consider this back-in-the-day, but there's an aaaawwwful lot out there that still reeks of old german engineering, and chunk-button ATMs.
Re:is Real Time programming still a Real Issue? (3, Informative)
I actually have this book. It does read fairly well with some good examples: although I should note that I haven't finished it yet. One thing it is especially usefull for is defining a math library that's accurate. Crenshaw talks about how a lot of compiler's built in function/methods don't hold up to rigorous math and he's right. But instead of just complaining about it he walks through solid alternatives. Overall it's pretty good and would provide some quality code for open projects. IMHO anyway.
Re:is Real Time programming still a Real Issue? (3, Interesting)
Not all computers are desktop PCs. Have you ever heard of Palm Pilots? These things are slow!
I searched some time to find a decent integer square root routine to calculate object distances in my elite for palmos game [harbaum.org] . I would have loved such a book...
Re:is Real Time programming still a Real Issue? (4, Insightful)
I am currently trying to get a data-acquisition computer to keep up with a five thousand frame-per-second video feed [redshirtimaging.com] while doing processing between the frames. Hard real-time is a real issue for me.
Re:is Real Time programming still a Real Issue? (2, Insightful)
Of course. Real time doesn't mean low latency. It means predictable (bounded) latency! It's a secondary issue if that latency is low or high. My Linux is reasonably fast, but it's still far from real time: each time I touch my xawtv window, the whole machine freezes for a second...
Wow, I'm old, I haven't seen Runge-Kutta in years (5, Insightful)
I remember when having a solid math background was de reguire for a programmer. Of course, I'm talking the mid 80's, engineering school and Fortran, so I'm kind of krufty.Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (2)Huh? What's the use of sine in an OS besides to draw glitzy GUI stuff?
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (3, Interesting)
Funny this topic should come up. I just did a 'Store Locator' for the company I work for (I'm the IT Manager, belive it or not). All I have is your basic HS diploma, and in creating the search, I realized I don't know a damn thing about sine and cosine. I don't know how they're used, or how they're applied. I have a feeling that they're somehow related to geometry (which makes sense, seeing I have to get a distance between two points on a curve - the earth), but I'm not sure.
Sure, it's probably taken me longer to write this post, than it took to find the php code I used as a basis for the search, but how much math is REALLY needed overall?
I slept through school, I did really bad, all because I felt it was worthless. I did feel that my business class, business law, and basic Algebra has been useful. But overall, it wasn't worth my time. Hell I had a physics teacher who'd pick on me because I was flunking (it's amazing what good test grades + 0 homework does to you), but I just found physics interesting - jeez, it was only HS. I was testing the waters, not padding my GPA. I believe that's what's HS is FOR.
And if you KNOW what you want to do (I knew I wanted to fix/program computers when I played on my Apple ][ in 6th grade), what the hell is college for?
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (3, InsightfulBut to get a job writing computer graphics software, or audio processing, or designing any sort of embedded hardware, knowledge of advanced math is required. The people who want to do this kind of work pursue higher educations, and if they enjoy what they're doing then that's great, too.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (1Well, that sounds a bit belittling. I think building networks (I'm beyond admin, I just do EVERYTHING - including PBX) can be just as difficult as programming, and you get the same rewards.
I don't really grind out anything. Hell, I put up a TV antenna last summer, and hooked up the security cameras to a linux box for motion detection around xmas. I'd much rather be doing 90 different things, than concentrate on programming in 'X'..
Maybe I should have left out the 'Manager' part:) (I'm just the only one here.)
Then again, maybe I AM that good, and you're all just jealous! muhuhuhahaha!:)
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (2)
It wasn't meant to sound belittling. I meant what I said: if you find it rewarding then that's great. Now it sounds like you've got a good mind and a good head start in the IT world so I wouldn't be too worried, but just know that your field isn't going to be getting any less competitive.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (1)
For what I've seen, I think they're mostly programmers and MCSE's. That's not too damaging to me. For practial, in-house purposes, I can pickup whatever I need programming-wise. I completely understand I won't be programming games, or advanced simulations any time soon (Hell, you can find my pitiful posts on wine-devel about trying to get FoxPro running.. rick@v a leoinc). But those positions always seemed like a small percentage of the market as a whole. Everybody needs a network, internet access, firewalls, phones - infrastructure. It just seems like a bigger target to me.
Fortunately for me, most people I run into are sorely lacking on what I would lump together as basic infrastructure.
(but at this moment, I have to put php aside,so I can figure out an EDI issue with FoxPro) I love having so many different things. How many EDI people know PC's? Networks? The consultant who interviewed me for this job didn't know many, so here I am!
Ok.. enough of the ego-boosting stuff for now:)
Personally, I think experience can replace college. You just have to be resourceful, and create a resume that shows it. I think I did a good job doing that.
Now, Social Skills OTOH....It would have been good for me to live in a dorm for a few years. I dormed weekends with my girlfriend - which got me to where I am today, family-wise:)
Score -1 ignorant (-1, Offtopic)
No, computers don't need math (3, Interesting)
I've been programming since 1968, and very little had anything to do with math. People give me the same line, wow, I'm no good with math, I couldn't program, and don't believe me when I say computers add and subtract, multiply once in a while (array subscripting usually), and hardly ever divide.
Scientific or engineering programming, they need the math because they are math programming. The rest, forget it, maybe you add some numbers for a shopping cart, multiply for sales tax, but programming has little use for math.
I learned long ago that when an 8 bitter needs trig functions, you use a look up table generated externally.
mathematical algorithms and nonmathematical algorithms. To a computer scientist, this makes no sense, because every algorithm is as mathematical as anything could be. An algorithm is an abstract concept unrelated to physical laws of the universe.
Nor is it possible to distinguish between "numerical" and "nonnumerical" algorithms, as if numbers were somehow different from other kinds of precise information. All data are numbers, and all numbers are data.
So maybe most of the math is trivial, but that's not the same as being useless...:-p
Follow-up (1)
How did you write the search function? Did you come up with an alorgithm on your own? Did you use a prewritten, off-the-shelf search routine?
Note that I'm not making judgements here, I'm just underscoring the point that there are some jobs that require certain knowledge, and others that don't.
And FYI (so you can impress your coworkers and/or significant other <g>): The sine of an angle refers to the y-coordinate of the point at which a line drawn from a starting point at that angle would intersect with a circle of radius=1 drawn around the starting point.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (5, Insightful)
I won't bash you like some of the other replies to your post, nor will I give you hope that you can advance past a limited set of jobs in the IT industry.
College (esp for computer engineering and CS) fundamentally teaches you:
1. How to solve problems
2. A toolset (ie math, algorithms) to go about solving those problems
True, you may not ever use calculus, but as a computer scientist you will use matrix theory because it is the best way to solve some problems.
This is not only for scientific/research either. If you try to write anything performance related, you'll have to use higher math. Computer science ain't easyRe:Wow, I'm old, I haven't seen Runge-Kutta in yea (1)
I won't bash you like some of the other replies to your post, nor will I give you hope that you can advance past a limited set of jobs in the IT industry.
Thanks for not bashing, and please don't think I'm attacking when I say this but:
If anything was learned from this post, it's that there are a lot of PROGRAMMERS who read Slashdot. IMHO, Programming in itself is a limited set of jobs in the IT industryYou post sounds depressing, but don't worry about me, I'm all set (maybe I'm even in that small percentage). Maybe I'll go back to college when my kids are teenagers. I'll still be less than 40. Yes, I did EVERYTHING early - against the grain, thankyouverymuch:)
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (3, Insightful)
Your code may do the job, but does it do the job efficiently? And if it didn't, how would you know?
I changed majors from CS to Mathematics halfway through because I realized that programming is easy; you can always learn a new language or a new technique by picking up the appropriate O'Reilly book on the subject. But writing good programs -- programs that are robust, that scale well, that do as much as possible as quickly as possible -- is really applied math. And math is hard.
You simply have no idea how much you don't know, and with the attitude you have, you probably never will.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (1)
Funny, I'm someone with a lot of mathematical training (Ph.D. in Applied Math) but only a few courses in computer science. Somehow, I've managed to pick up a humungous amount of CS along the way, things like algorithm design and analysis, designing and coding industrial-strength C/C++ libraries and applications (yes I get paid for this), high-performance computing, OpenGL coding to roll my own volume visualization apps, doing all of my own unix system administration, setting up all of my own hardware...I've always thought that the best way to become really good at coding and software engineering is to first get a degree in mathematics. If you can do that, the rest is easy.
(Okay, I am a bit biased; I'm a college math professor, and in addition I do a lot of research and consulting related to numerical computation).
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (4, Interesting)
When I went for my Comp Sci bachelor's I was amazed at how many math-phobics there were in my Comp Sci classes. As part of earning the degree you had to take 4 specified math classes (Calc 1 & 2, Linear Systems, Probability). You only had to take one more math class to get a minor in mathematics, Calculus 3.
Now I've always been big on math but I was kind of surprised at how few people were willing to take a single class to earn a full-fledged minor.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (2)
May I be the first to say, that is a sad Math minor. You should at least need to get to Number Theory or Algebra and Real Analysis to qualify for a Math minor. Those five classes are (or should be) requirements for any science course, including Comp Sci.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (0)
Interesting at my university you can't earn a minor by choosing courses that overlap in different programs... well this is in Finland.
For example my current major is theoretical computer science and one of my minors is pure maths. Many courses in discrete math are part of both programs, but I have to choose which program I want to include these courses in. So if I take all courses in discrete math and I include them in my major, I get no credits for them to my minor, so I still have to study a minimum of 20 credits of math...
Anyway I've noticed myself that most comp sci students study only the math they have to i.e. Single/Multi Variable Calculus, Complex Analysis, Linear Algebra, Algebra, Set Theory, Logic, Graph Theory, Combinatorics and Probability. Almost no one takes further courses about the theory of generating functions, stochastic processes, mathematical logic, set theory or basic analysis like topology , measure theory, functional analysis etc.
Also few people study the theory of real-time systems or the theory of parallell and distributed systems still most of them have to code multithreaded programs when they've got their M.Sc. and start working as programmers. Most just choose a few practical courses about these subjects and ignore the theory.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (0)
We would probably have rock solid operating systems without all the glitzy GUI stuf..
And we do have those today... if that's what you need. And we also have glitzy GUI-based OS's for the people that need them.
But you seem to be drawing a very bizarre conclusion in the first place. Are you saying that coders that don't know basic math tend to develop GUI-based operating systems?
And how deep do you want to go? Even if you think you know how the chip works, well... you're really just assuming that all those registers and address lines are working by magic. But if you really want to understand how those itty bitty chips work, then you have to know how transistors work, what their slew rates are, how flipflops work, and you have to be able to describe how charges move across a PN junction for all of the above to work. And to know that you'd need an understanding of how the doping compounds affect the behavior of your semiconductor crystals in the first place.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (2)
<rant>Oh, the majority of coders know basic math, all right, or at least the most important concepts that are needed to hold down a job in today's IT business. They know that time equals money, and that taking the time to get the thing done right in the first place costs too much. They know (or they think they know) that it isn't necessary to worry overmuch about program size and speed any longer, because they can always depend on the hardware engineers rescuing them with the next set of more powerful products. They know that they get a greater return on effort spent on making pretty presentation slides of all the wonderful new features that are to be put into the next release and then transcribing the slides into the product's gui than on analyzing whther the new features are being provided in a consistent and unconfusing way, or even if they are needed in the first place.</rant>
It's not that trading raw power against development costs is unreasonable where that choice exists - far from it - but rather that hand-waving away questions of efficiency on the assumption that God (or Moore's Law[1]) will provide is a sure recipe for the sort of bloated and near-unmaintainable messes that are so common today. A Mbyte here, a Mbyte there, an assumption that the compiler will find and optimize the invariant components of loops... if you're not careful these all start adding up to measurable numbers "why is this so s l o w . ..")
[1]And, of course, one can always paraphrase Parkinson's Law [google.com] for IT: programs and data expand to fill the processor power and storage available.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (2)
Most of us wouldn't be any better at all. My math is rather rusty, though I used to be good at it at school. The reason my maths is rusty is because in the 7 years I've been doing commercial software development I have almost never needed any maths.
When I have, I've never needed anything beyond what I could find in a textbook or online in less than 5 minutes.
Heck, I've practically never even had any reason to use floating point math over that period of time.
Sure, there are lots of areas where you do need maths beyond what you can pick up from a book in 5 minutes, but there are far more where maths is irellevant.
Beyond basic algebra, maths is just another set of domain knowledge that you'll need to aquire to do particular types of software development, not something that is an inherent requirement in order to be a good coder.
Engineer versus Programmer (2)
Embedded systems gurus are primarily ECE types. They are engineers that know programming. The math knowledge and emphasis will depend primarily on your background. There are a lot of so-called programmers out there that come from a variety of background and consequently have varying exposures to mathematics. You even tend to find programmers with MIS backgrounds who have never taken a calculus course.
It will depend really on what you call yourself. I am an engineer and I have been programming for almost 25 years however my background is definitly skewed towards scientific programming. You can even see it in the sequence of programming languages that I learned over my career:
BASIC->FORTRAN->ASSEMBLER->PASCAL->C->LISP->XLISP- >C++->JAVA
I don't call myself a programmer, but an engineer who programs. This is because you will notice there are some importand tools missing from the above list. Things such as PERL which we know that every real programmer would have in their toolbox.
Re:Wow, I'm old, I haven't seen Runge-Kutta in yea (1)
I don't know how most schools are...but the school I just got by BS from lumps math and comp sci right together. Though we had to take a lot of math as it was (especially higher math, discrete math), we also had some math professors teaching CS courses (algorithms, intro to computer systems, even operating systems).
I think this prepared us pretty well for what would be a more theoretical-type CS career (i.e. not just going to work as a programmer or web developer, but also continuing on to your masters or PhD).
Some of the ideas the department was real big on was proving correctness, for example, by induction. Instead of giving you a compiler and API and saying here, do this, they made you write it out and actually write a proof about why/how your program works (now imagine people actually doing that, for their OS's CreateProcessEx function!).
Re:flimsy review (3, Informative)
The subject matter of this book is slightly different, since it has an emphasis on real-time [techtarget.com] . If you're just interested in crunching a large problem as fast as possible, then latency [netacquire.com] is not an issue.
BTW, if anyone wants to take a gander at Numerical Recipes in C/Fortran they are available here [nr.com] .
Re:flimsy review (2)
It seems to me that the book itself is
pretty flimsy, content-wise. Yeah, if you
need a lot of hand-holding about the various
polynomial approximations and iterative approaches
to calculating special functions, you'll probably
learn something. But the end
of the book is Runge-Kutta; that's a technique that's covered pretty
early on in Numerical Recipes or even a freshman
class in numerical analysis.
Re:flimsy review (0)
I've not taken the opportunity to really sit down and crawl through "Math Toolkit" but when I've skimmed it, it seemed to me to be almost a prequil to NR. There is some over lap (i.e. RK methods) but NR generally assumes you have a working IEEE-754 compliant math lib and goes from there. NR talks a bit about precision, but they don't dwell on it, instead focusing on packing as many different twists on numerical algorithms as possible into the book -- ending up with something that's not far from usable in a production environment at the end of each chapter -- NR in C and C++ still bears some transliteration artifacts from Fortran which bug the bejeezus out of me.
Re:Numerical Recipes (3, Insightful)
Interesting read. Still, I would challenge all these numerical specialists to come up with a tome that is equally comprehensive and equally readable by scientists without extensive numerical analysis training. The book has been so successful because it hits the target audience perfectly.
An indispensible treasure (3, Troll)
In my field, it is absolute essential that one squeeze every last bit of math power out of the CPU. So this books occupies a place of honor on my shelf and I refer to it almost daily when I write my Perl scripts.
I'm surprised to see it posted on/., though, because he's pretty harsh towards the gaming community. In fact, he says near the beginning that game-related technology in CPUs (MMX and so forth) is taking away much-needed brainpower from research that should be reaching towards making chips do more math per unit time (not to mention driving up production costs for toy-obsessed, joyless loners). He calls for an immediate end to the pandering that Intel et al do to get into the pocketbooks of the socially-inept, technology pseudo-elite and wants real reform in the area of empowering science.
Dear Ubermuffin (-1, Offtopic)
I am writing to you as PhysicsGenius has chosen to ignore my previous letters. I write in the hope that you are of a more affable disposition.
You see, in the course of readjusting myself post-flatulance it appears that I may have caused some minor soilage. If this is the case then I may require a quick trip to the bathroom. As I am the cautious sort of chap, further investigation will be required before I take action.
I will be sure to write and let you know the outcome of my investigations.
Re:An indispensible treasure (1, Insightful)
You know, it's really easy to write complete bullshit on slashdot and get +5, so to add a little challenge, good trolls add a small self-contradition to signals to other trolls that their post is a troll. Kudos to PhysicsGenius for mastering the art of good trolling to such precision!
Re:An indispensible treasure (2)
I have to ask. If you're trying to squeeze all the math power you can out of your computer, why are you using an interpreted language? Use something compiled so your computer can spend its time doing the math, not parsing the code.
Re:An indispensible treasure (2)
If you're doing a lot of number crunching or data manipulation (in big sets, with hashes, etc) you're probably spending most of your time in the libraries which are written in C. In fact, being that they're written by programmers skilled in that specific area, you're probably getting better performance than if you wrote them yourself.
Perl isn't an interpretted language, in the traditional sense. In most BASICs, when the execution comes back to a given line it's parsed again, executed, and dumped. If anything, they usually only cache a line or two to help tight loops. Perl is interpretted/compiled all at once, when you start.
Runtime speed is a little slower than other languages, but it's mainly because you've got a lot of runtime checks and hidden memory allocation turned on. Use C++ with automatic array expanding and garbage collecting and you'll see the same kind of performance hits.
That said, the ease of perl causes a lot of features to be misused by programmers who don't know how long it'll take. If you have two pieces of data (a header name and value for instance) it's common to toss them into a hash to keep them related. This isn't really a good idea unless you need to look them up by the header name. If you're just going to dump them out in arbitrary order, you should probably use two arrays in sync. Pre-allocate them to avoid a little delay at every operation. This way you avoid the overhead of the hashing algorithm that you're never going to use, and the slightly-slower lookups compared to an array.
You can also do more complex things this way. I've seen people use hashes here and read the list out by sorting the keys to the hash and iterating through. They'll then do this a few times, sorting at every step. If you want these arrays sorted, but you still don't care about finding a specific header, use an array of two-element arrays, sort the master based on the first element, and not only do you avoid almost all the overhead of hashes, but you have a permanently sorted array, no need to sort at every use.
These programming "errors" are worse in Perl than most older languages because they're easier to implement. In C you'd have to find a library function to create hashes, or write your own. If you started to write your own you'd quickly realize how many cycles you were burning and probably find an easier way unless your application demanded it. In perl (and many little "scripting" languages) you can do so much in a single command that you may not realize.
This is why if I were hiring I'd only take programmers with a "traditional" background of C or other low-level language, before they got to the Perl, Java, Python, or whatever modern rapid-development language we were using. ASM experience is even a plus. Nobody understands the cost of a routine like someone who programmed in ASM. And it's worth thinking about. Usually you say that requiring 512MB of ram ($40 these days) is worth it to save an hour or two of programming, but hopefully at other times you realize a CGI on a busy site can't be that greedy.
So, in conclusion. Perl isn't traditionally interpretted. It's almost as fast, or faster, than C for anything that spends much time in libraries (most code). Most of what slows down Perl (or Python, or Java, or C++, etc) is programmers who don't know what routines they really need to use. The cause of this is usually not enough experience in less "helpful" languages.
Re:An indispensible treasure (1)
Agreed, much like using Matlab (which incidentally requires a rudimentary understanding of matrix algebra) - its very fast if used correctly and yet painfully slow when used incorrectly. loops = bad, vectorization = good
Re:An indispensible treasure (1)
Grrr. It's one thing to do a physics simulation with 64 bit doubles, and another thing to keep it stable with 32 bit floats. It's an art and not for the shallow thinker talk to real physicists (and gamers) at companies like Havok and MathEngine. As for intel pandering, he ought to read a book like "Platform Leadership" to learn just what Intel have done to get stuff into the hands of peasants like me, for whom Cray did diddly squat. Scientists? Hah!
Forth Algorithms (4, Interesting)
The Forth literature contains many examples of high-performance hardware-integer-math-only routines. A core feature of most Forth algos is rescaling to a power of two space at the start of the algo and from it at the end. This allows bit shift operators to do their stuff. It can take non-trivial fiddling to rescale algorithms - hence, it's nice to just look them up.
Unfortunately, it's tricky to find Forth books these days.
That's a shame, because along with Smalltalk, Lisp and APL, I think Forth is one of the "mind expanding" languages all programmers should at least experience, instead of just deciding C/Java/C++/VB is the one true language.
Re:Forth Algorithms (0)
"...That's a shame, because along with Smalltalk, Lisp and APL, I think Forth is one of the 'mind expanding' languages all programmers should at least experience..."
Absolutely. Forth has a few very simple ideas at its core that can be applied in many areas. Leo Brodie's "Thinking Forth" didn't just help my Forth code, but taught me a good deal about factoring problems --- a vital skill in any programming language. I also just finished a project that had some very Forthy code hidden within it: a custom rule compiler written in C# which used System.Reflection to spew out CIL code for the.NET runtime. Due to its stack-based nature, emitting CIL turns out to be very much like compiling Forth words into a dictionary.
Math in CS programs (2, Interesting)
I don't know of other programs, but I know at the University of Waterloo (where I am a computer science student), we must take quite a lot of math courses, ranging from linear algebra, calc, classical algebra, combinatorics & optimization and statistics. The math content for the CS program is very high, and in the end you get a BMath degree.
Maybe this is different at other schools (well, actually I know it is at most, most don't do nearly as much math), but I would hope not. I think to be a solid programmer a solid math background is a requirement.
oh, and btw, for anyone nitpicking, UW now offers a BCS program, as well as the typical BMath Honours CS. The BCS seems to offer a bit more flexibility, so BCS students may not choose to take 'as much' math.
Re:Math in CS programs (2, Interesting)
This is pretty much Waterloo's claim to uniqueness, is it not? Something about being the only Univeristy in Canada with a math _Faculty_?
I think this may provide some insight into whether or not it's a GoodThing for CS students to have more math in their degrees. Microsoft hires more programmers from Waterloo than anywhere else. And just look at the QUALITY of their code.:)
On a somewhat tangential note, I'm in Communications Engineering at Carleton, and we badly need a stochastics course in our program, so Digital Comm doesn't keep flying over our heads. Sometimes more math is good.
Re:Math in CS programs (1)
The schools in my area all have at least one or maybe two big employers. The curriculum is generally based on the needs of these few employers
See, that is where your problem is! The school is setting curriculum based on employers. It should not happen this way. Your school is shortchanging every student who goes there, by effectively (though obviously not completely) limiting their student's employment choices after school. Post-secondary education, especially at the university level, should educate its students in a way in which they can work almost anywhere, not just the 1 or 2 big companies in the area.
And oh, as a side note for another reply, yes, MS hires more grads from U.Waterloo then anywhere else, and when even the slightest controversy comes about over MS controlling curriculum [slashdot.org] , people get angry and fights start.
Neglected subject, good review, integer!=assembly (5, Interesting)
This is a subject that's rather neglected -
three years of college math didn't go very far in letting me understand
how math (fp and otherwise) is actually done in discrete systems.
A year (or so) ago I attended a lecture given by Guy Steele (of Lisp/Java/
Crunchly fame) on his proposal to alter how IEEE floating point numbers
are mapped to real numbers. It quickly flew over my head, but gave a great
insight into the whole field. Steele then had a fair old "discussion" with
the one person in the audience whose head hadn't been overflown (sic), as
there was plainly still much controversy left in this area. On trying to do
some "why didn't I get this stuff at college" reading, I found there wasn't
a great deal of literature.
The reviewer's concern that coprocessor-less systems should be covered is
valid, but I'm not sure going as far as assembly is necessary. For example,
I once had the privilige of reading through Hitachi's libm implementation for
their H8 series microprocessor/microcontroller (one would be generous to
call H8 a 16-bit system, and ungenerous to call it an 8-bit system). With one
small exception (I think the cos table lookup) the whole thing was in (quite
readable) C, and (at least for basic libm stuff) performance was perfectly
acceptable. For didactic purposes, a C (or sane C++) implementation would
be the thing one would want to find in a book - I get very annoyed at embedded
books where the examples are written in asm for the author's favourite (obscure)
microcontroller.
Re:Neglected subject, good review, integer!=assemb (3, Informative)
A year (or so) ago I attended a lecture given by Guy Steele (of Lisp/Java/ Crunchly fame) on his proposal to alter how IEEE floating point numbers are mapped to real numbers. It quickly flew over my head, but gave a great insight into the whole field.
Steele is God. He also invented Scheme, wrote the original Common Lisp manual, co-wrote with Harbison a classic reference manual for C, and wrote parallel languages for the Connection Machine.
On trying to do some "why didn't I get this stuff at college" reading, I found there wasn't a great deal of literature.
Same Crenshaw? (0)
Is this Crenshaw the same guy who wrote that compiler tutorial, the mini-epic that lasted a decade? His aim was to guide budding compiler writers in the direction of creating a native Pascal compiler. His style was lucid, informative yet friendly. I think timothy's words, "self-confident" aptly describes it. I'd recommend anyone to the works of Crenshaw and I agree, his knowledge of the subject areas is always superb.
Thats a good tutorial (0)
Lets write a compiler! is a good tutorial. I wouldn't have wanted to try and follow it as he was writting it (Some chapters are many years apart!), but these days you can easily read the whole thing (If you don't mind the fact that its writting in Pascal and targets the 68000 CPU).
As you say, the style of writing is warm and friendly, and he takes his time to properly explain the concepts. A very good writer.
Link & More (1, Interesting)
That's it. For those who want the quick link for the Let's Write a Compiler, right here [iecc.com] (
I really hope that Crenshaw might write again about compilers. I agree with the Pascal and 68k part -- they're old, and even some of the approach taken by the tutorial is probably not up to speed with modern practices. But hey, at least it gives a good historical account.
Under covered subject; average review... (4, Interesting)
To be honest, a lot of embedded coding is done with C or C++ these days. I've been following Crenshaw's articles in Embedded Developer magazine for years now. He explains a lot of what they try to teach in college Calc, etc. in simple, practical terms, and reduces it to usable algorithms.
College Math (3, Interesting)
I graduated as a Math/CS double major from Drake University, where almost all CS majors also got a Math degree because the CS prereqs covered all but 3 of the Math prereqs. It has actually helped me enormously as a programmer to know math: in the past month, I've needed transformation matrices, sine/cosine stuff, and a bunch of other things that, granted, could have been lifted verbatim from Google groups, but it's often faster (and the code is better) if I just do it myself.
Yes, it's an interesting book... (3, Interesting)
Not being exactly a math whizard myself, I found this book extremely entertaining. It's pretty easy to see that the author is a heavy follower of the KISS philosophy. He tries to keep it simple not just in his code, but also in his explanations. It is possible to understand most of his explanations, even if you don't know much about differential equations, fft's or anything else.
As for the title, I agree it's a bit misleading. The book has pretty little to do about real-time (in fact nothing, as far as I could see). What it really should be called is "Computer arithmetic and a little of numerical methods for dummies". This book will help you understand how to write your own libm, and give you some ideas for more advanced tasks, but that's about it.
For me, who didn't know much of this stuff, it was very interesting. It will probably not save you that course in numerical algorithms (which I for one haven't taken), but even then, it will probably contain some interesting tidbits you didn't know.
On the other hand, if you have years of experience in writing computer math routines, it will probably quickly become dull, but that's true about anything you already know.
Decimal libraries (3, Interesting)
As a biz-app programmer, I am bothered by too much attention given to floating point math and not enough to decimal math. A decimal-centric approach would give better results for monetary calculations, because any truncation and rounding are at decimal (base-10) boundaries instead of base-2 boundaries. It gives results more like one expects doing it by hand on paper, which shapes most peoples' perceptions of what they expect (and the customer is always right, even if they are boneheads).
The only library I know that supports it is the BC-library sometimes used with PHP. (Well, I guess you could say that COBOL has such also.) It actually uses strings to hold the results so that there is no machine-based limitation on precision size. Plus, that improves its cross-language use since almost everything supports dynamic strings these days.
(Not the fasted approach I suppose, but most biz apps are not math intensive anyhow. Most code is devoted to comparing strings, codes, and ID's and moving things around from place to place. IBM used to include decimal-friendly operations in its CPU's. Those days seem gone for some reason, yet biz apps are still a huge domain.)
Re:Decimal libraries (2)
The reason so little focus is given to what you call "decimal math", and most people would call "fixed point" is that there's a very simple way of doing it: You do everything with integers scaled sufficiently high up, and move the comma to the right the prerequisite number of steps to get the number of decimal points you want.
Oh, and there are lots of old fixed point code floating around. Looking for "fixed point" instead of "decimal math" might help you find what you want...
Re:Decimal libraries (1)
(* there's a very simple way of doing it: You do everything with integers scaled sufficiently high up, and move the comma [euro decimal?] to the right the prerequisite number of steps to get the number of decimal points you want.*)
Integers have a limited length in most built-in stuff. What if you want to store 0.666666666666666666666 in a variable?
Besides, one should still wrap such behind a library rather than manually manage the decimal position. You would then have an integer version of the BC library I mentioned.
Re:Decimal libraries (1)
If memory serves, the Mac's math libraries initially used decimal strings to
represent numbers - it's been a decade since I wrote a Mac program - perhaps
someone with more current knowledge can shed some light as to whether this is
still the case?
Also, Java's java.lang.math.BigDecimal class contains just the kind of
functionality you describe - its docs are
here [sun.com] .
In general, I think you'll find lots of fixed point math libraries around - they're
mostly intended for numerical computation and mathematical cryptography (e.g RSA),
but they should be quite applicable (if sometimes overkill) for your biz-app
uses.
Re:Decimal libraries (2)
I think you will find that floating point calculations have much more applications in realtime environments.
Why is that?
BTW, could you clarify what you mean by "real-time"? I have seen 2 different definitions before. One is that the response time has to be within a specified tolerance 100% of the time. The other is "interactive". I did not use that term IIRC.
Also wrote "Let's Build A Compiler" series... (2, Informative)
Mr. Crenshaw is also the author of the popular Let's Build a Compiler [iecc.com] series of articles a while back.
These articles don't go into a lot of the complicated stuff that's involved in modern compiler design-- Crenshaw keeps it simple, keeps it straightforward, and still produces a working (if not optimizing) compiler by the end of the second or third article.
No, it won't let you code a C compiler that will beat the pants off of gcc or Borland's latest offering, but the end result is pretty useful.
Amazon link, too (2, Interesting)
For those who don't support Slashdot's Amazon embargo, here's their link to the book [amazon.com] . Not only are they selling the book for $35, they have 25 sample pages, including the entire index and the first half of the first chapter. (And no, I'm not in Amazon's affiliates program and don't make a dime if you buy the book using the link that I provided, as a quick glance at the URL will prove.)
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Mathematics
Professors Goloubeva and Williams
Mathematics is an analytic tool used in all of the science and engineering courses. At the same time, by its very nature, mathematics is an abstract science. Mathematics at Webb is presented from the applied viewpoint, drawing upon the physical world for its motivation, developing the abstract concepts to refine the physical ideas, and finally applying those abstractions to a better understanding of the phenomena of nature. Many Webb students go on to graduate work involving higher mathematics, and it is a strong objective of the mathematics program to prepare them well for this work.
Freshman Year
MATHEMATICS I - CALCULUS I
This is an introductory course whose main purpose is to fill in the background of students who have already had an exposure to calculus in high school. The topics covered include limits, continuity, a review of trigonometry, derivatives of functions of one variable, the Riemann Integral and applications of derivatives and integrals to simple physical problems involving related rates, optimization, volume and center of mass. The mean value theorem is covered and extended to series approximations and applied to limits via L'Hopital's rule. The course also covers the elementary transcendental functions of exponentials, logarithms, inverse trigonometric functions, hyperbolic functions and their inverses and concludes with a quick review of the basic techniques of integration such as integration by parts and partial fraction decomposition. The pace is brisk.
The class meets four hours per week in the first semester.
MATHEMATICS II - CALCULUS II
This course contains most of the calculus of functions of several variables and includes partial derivatives, multiple integrals and gradients. Vectors are discussed along with the geometry of three-space. There is considerable emphasis of visualization and graphic representation of figures by the computer. The dot product is introduced in such a way as to facilitate its extension to higher dimensional space and ultimately this becomes the inner product in the function space of continuous functions over an interval. This function space approach is used to develop the generalized Fourier series. The trigonometric Fourier series is studied as a special case of the generalized Fourier series. The course also includes an introduction to linear algebra, which covers the rudiments of matrix algebra. Determinants are also introduced here. The course concludes with a unified discussion of real infinite series. The class meets four hours per week in the second semester.
Sophomore Year
MATHEMATICS III - DIFFERENTIAL EQUATIONS
This class is a basic course in differential equations. It covers the fundamental theorems that guarantee when differential equations and initial value problems, which involve first order linear and non-linear differential equations, have solutions. Linear first order ordinary differential equations with constant coefficients are first studied and general principles are developed which are applicable to all linear ordinary differential equations. This includes integrating factors, variation of parameter techniques and applications to RLC electrical circuits. This study of the linear ordinary differential equations also includes Taylor's series and series solution techniques and problems with singularities. Laplace transform techniques are studied for initial value problems. The course concludes with a review of Fourier series, which are then applied to the basic three forms of initial value problems involving partial differential equations. The class meets three hours per week in the first semester.
MATHEMATICS IV - ADVANCED ENGINEERING MATHEMATICS
There are essentially three separate components to the course. The first component involves vector calculus and lasts for about 7 weeks. This material can best be described as the mathematics that is needed to study fluids. The course covers vector functions, gradients and vector and scalar field. Multiple integrals are covered more extensively than in Mathematics II and emphasis is placed on transformation of space/coordinates and the role of the Jacobian. The curl and divergence are introduced from a very physical point of view and their meaning in fluids is covered. Finally the three major theorems of vector calculus, Green's theorem, Stoke's theorem and the Divergence (Gauss') theorem are covered. A strong emphasis is placed on physical interpretation. This material is highly visual and extensive use is made of Maple to illustrate the concepts.
The second component of this class involves complex variables and lasts for about 7 weeks. This component covers the basic arithmetic and geometry of the complex number system. Then the calculus of functions of complex numbers is studied including the Cauchy-Riemann equations and the implications for harmonic functions. Complex exponential, trigonometric and logarithmic functions are defined and studied and there is a brief treatment of conformal mapping. In addition the standard Cauchy integral theorems are treated and these are related to Taylor's and Laurent series.
The third component of this course lasts about 10 class sessions and covers the remaining essential parts of linear algebra to which the students have not previously been exposed. The main focus is on finding and understanding eigenvalues and eigenvectors and what these mean for reduction of matrices into simpler equivalent forms. The class covers the Cayley-Hamilton theorem on the use of the characteristic polynomial to find inverses of matrices. We also cover the reduction of matrices to Jordan canonical forms. Part of the class is devoted to the calculus of matrices, which involves finding functions of matrices and using these functions to solve large systems of differential equations.
The course meets four hours per week in the second semester.
Junior Year
PROBABILITY AND STATISTICS
This course begins with an introduction to probability theory, including set theoretic and combinatorial concepts. This is followed by treatments of discrete random variables and distributions and continuous random variables. Generating functions are discussed at some length. Particular emphasis is placed on the Rayleigh and Weibull distributions, which are applied subsequently in the Ship Dynamics course as models of wave spectra and are also encountered as models of the manufacturing process. The latter third of this course addresses the application of statistical methods to engineering experimentation, beginning with an introduction to estimation and hypothesis testing and culminating with an overview of experiment design. The course meets four hours per week in the first semester.
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Why is Maple Better than a Graphing Calculator?
Maple is easier to use than a graphing calculator, does a better job solving mathematical problems and creating plots, and provides more extensive mathematics, learning tools, and a technical documentation environment. Maple can help you with your courses today, next year, and even after graduation.
Maple is Easier to Use
Maple's Clickable Math™ techniques allow you to enter and solve problems with a click of a button. Maple provides palettes, context-sensitive menus for mathematical operations, interactive tutors and demonstrations for learning and doing precalculus, calculus, linear algebra, and other subjects, assistants for in-depth explorations, and task templates for multi-step problems. With these tools, you can solve your problems quickly, easily, and accurately.
And because you are in a word-processor-like environment, you have a large screen that holds lots of information at the same time. It is easy to scroll up and change your original problem; copying and pasting or dragging and dropping are all available; and, you can have multiple screens, including help pages, open simultaneously.
Maple Does it Better
Maple's mathematical abilities are superior to those of a graphing calculator.
Exact answers - Maple gives exact answers, not numeric approximations. If the answer is that is what Maple will give you. If you want Maple to approximate the answer for you, just tell Maple how many digits you want, and Maple will do that too.
Modify problems - With Maple, you can change your problem in place using the 2-D editor. Then you can ask Maple to recalculate all your steps with the new values. All intermediate steps are updated. All plots are updated. Just make your change, and click a button.
More graphs - Maple has over 150 plot types and options built into the product. Dozens of different 2-D and 3-D plots and animations can be created with a click of a button, and the rest can be created with a single command. Plot options such as changing colors, line thicknesses, and placement of tick marks can be set using menus. You can zoom, pan, and rotate 3-D plots interactively.
Self-documenting - Maple automatically generates a record of the steps performed using the context-sensitive menus. That way, your work is easier for you and others to follow.
Maple Does More
Maple provides much more functionality than a graphing calculator.
Symbolic math - Maple includes the ability to do symbolic math as well as numeric calculations. This means that you can ask Maple to:
More math - Maple includes support for basic and advanced algebra, calculus, differential equations, linear algebra, transforms, optimization, graph theory, differential geometry, and a whole lot more. Maple will stay with you throughout your complete academic career and beyond into the workplace, whether that workplace is an engineering design firm, a university research institute, a high school classroom, or any technical position.
Education tools - Maple comes with a series of student packages and interactive tutors specifically designed to help you learn mathematical concepts from precalculus, calculus, linear algebra, and more. Tutors provide easy visualization of difficult concepts (including 2-D and 3-D animations) and step-by-step problem solving complete with hints, including step-by-steps solvers for integration and differentiation. Maple also has a math dictionary, an Exploration Assistant for easy visual explorations of mathematical expressions, a Student Portal, and a Student Help Center.
Technical documents - Maple incorporates a complete technical document environment, completely integrated with its interactive calculation tools. You can add titles, explanations (written in text and in mathematical notation), diagrams, sections, and more. You can add legends, titles, arrows and free-hand drawings to plots and images. And of course, you can save your work, print it out, export it to other formats, and share it with your colleagues, or even turn it into a full-blown interactive application with buttons, sliders, plots, dials, and more.
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1/2004While using Elementary Algebra, Second Edition, you will find that the text focuses on building competence and confidence. The authors present the concepts, show how to do the math, and explain the reasoning behind it in a language you can understand. The text ties concepts together using the Algebra Pyramid, which will help you see the big picture of algebra. The skills Carson presents through both the Learning Strategy boxes and the Study System, introduced in the Preface and incorporated throughout the text, will not only enhance your elementary algebra experience but will also help you succeed in future college courses. Book jacket.
Table of Contents
Preface
p. vii
To the Student
p. xvii
Learning Styles Inventory
p. xxiii
Foundations of Algebra
p. 1
Number Sets and the Structure of Algebra
p. 2
Fractions
p. 11
Adding and Subtracting Real Numbers; Properties of Real Numbers
p. 24
Multiplying and Dividing Real Numbers; Properties of Real Numbers
p. 41
Exponents, Roots, and Order of Operations
p. 56
Translating Word Phrases to Expressions
p. 70
Evaluating and Rewriting Expressions
p. 78
Summary
p. 89
Review Exercises
p. 95
Practice Test
p. 99
Solving Linear Equations and Inequalities
p. 101
Equations, Formulas, and the Problem-Solving Process
p. 102
The Addition Principle
p. 118
The Multiplication Principle
p. 132
Applying the Principles to Formulas
p. 147
Translating Word Sentences to Equations
p. 153
Solving Linear Inequalities
p. 164
Summary
p. 177
Review Exercises
p. 182
Practice Test
p. 186
Problem Solving
p. 189
Ratios and Proportions
p. 190
Percents
p. 205
Problems with Two or More Unknowns
p. 221
Rates
p. 236
Investment and Mixture
p. 244
Summary
p. 252
Review Exercises
p. 257
Practice Test
p. 262
Chapters 1-3 Cumulative Review Exercises
p. 264
Graphing Linear Equations and Inequalities
p. 267
The Rectangular Coordinate System
p. 268
Graphing Linear Equations
p. 277
Graphing Using Intercepts
p. 289
Slope-Intercept Form
p. 299
Point-Slope Form
p. 313
Graphing Linear Inequalities
p. 327
Introduction to Functions and Function Notation
p. 337
Summary
p. 355
Review Exercises
p. 363
Practice Test
p. 370
Polynomials
p. 373
Exponents and Scientific Notation
p. 374
Introduction to Polynomials
p. 387
Adding and Subtracting Polynomials
p. 400
Exponent Rules and Multiplying Monomials
p. 411
Multiplying Polynomials; Special Products
p. 423
Exponent Rules and Dividing Polynomials
p. 435
Summary
p. 451
Review Exercises
p. 454
Practice Test
p. 458
Factoring
p. 459
Greatest Common Factor and Factoring by Grouping
p. 460
Factoring Trinomials of the Form x[superscript 2] + bx + c
p. 471
Factoring Trinomials of the Form ax[superscript 2] + bx + c, where a [not equal] 1
p. 478
Factoring Special Products
p. 487
Strategies for Factoring
p. 496
Solving Quadratic Equations by Factoring
p. 502
Graphs of Quadratic Equations and Functions
p. 515
Summary
p. 525
Review Exercises
p. 530
Practice Test
p. 533
Chapters 1-6 Cumulative Review Exercises
p. 534
Rational Expressions and Equations
p. 537
Simplifying Rational Expressions
p. 538
Multiplying and Dividing Rational Expressions
p. 552
Adding and Subtracting Rational Expressions with the Same Denominator
p. 563
Adding and Subtracting Rational Expressions with Different Denominators
| 677.169 | 1 |
More About
This Textbook
Overview
Mathematicians, students and researchers constantly refer to various sources for different formulas, equations, etc. "The Handbook of Mathematics and Computational Science" puts up-to-date equations, formulas, tables, illustrations, and explanations in one invaluable reference volume. Fully up-to-date, this handbook will quickly become the standard reference for mathematicians and students. 545 illus.
Mathematicians, students and researchers constantly refer to various sources for different formulas, equations, etc. The Handbook of Mathematical Formulas puts up-to-date equations, formulas, tables, illustrations, and explanations in one invaluable reference volume. Fully up to date, this handbook will quickly become the standard reference for every mathematician and student. 1025 pp. Pub: 10/96.
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From the Publisher
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"It is the best text of its type that I have come across to date - an excellent resource for anyone involved in mathematical practice up to and including degree standard (...) it is a pleasant experience to flick through it at leisure, dropping in here and there on some of the thousands of results the book holds. It is beautifully illustrated and set out (...) we have here a comprehensive volume whose worth will not readily fade with time (...) If you feel the need to own a mathematical reference to see you through school and university mathematics to graduation, you couldn't do much better than to buy this one" (MATHEMATICS TODAY
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