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Instructor Class Description
Learning Strategies in Mathematics
Explores applications of formulae, computational skills, and interpreting certain quantities. Reviews study techniques to enhance course comprehension, and the pros and cons of the use of calculators in a math class. Co-requisite: either B CUSP 122 or B CUSP 123. Credit/no-credit only. Offered: AWSp.
Class description
This course is supplemental to BCUSP 122 and prepares students for success in college-level Algebra classes. This course focuses on strengthening computational skills and exploring learning strategies for use in mathematics and other technical disciplines.
Student learning goals
Solve algebraic problems.
Present a solution to a mathematical problem in a logical and systematic way.
Apply mathematical ideas to new problems.
Identify and implement effective techniques for learning mathematics and other technical disciplines.
Class time will be spent working independently to improve computational skills, in groups on a project, and in interactive workshops.
Recommended preparation
Students must be registered in BCUSP 122 to take this support class.
Class assignments and grading
There will be online assignments,individual and group work. Grades will be based on student's performance on this work Milagros C Loreto
Date: 04/21/2014
Office of the Registrar
For problems and questions about this web page contact icd@u.washington.edu,
otherwise contact the instructor or department directly.
Modified:April 23, 2014
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Precalculus Functions And Graphs
9780495108375
ISBN:
0495108375
Edition: 11 Pub Date: 2007 Publisher: Thomson Learning
Summary: Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this text popular among students year after year. This latest edition of Swokowski and Cole's PRECALCULUS: FUNCTIONS AND GRAPHS retains these features. The problems have been consistently praised for being at just the right level for precalculus students like you. The book also p...rovides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics.
Swokowski, Earl W. is the author of Precalculus Functions And Graphs, published 2007 under ISBN 9780495108375 and 0495108375. One hundred forty Precalculus Functions And Graphs textbooks are available for sale on ValoreBooks.com, eighty eight used from the cheapest price of $20.33, or buy new starting at $83.36
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The goal of these DVD's is to give your student a firm foundation for Algebra 1. The DVD"s are part of a great series that has been created by Jason Gibson. I thought that the material was presented in a really thorough way and yet in a relatively short amount of time. This allowed us plenty of time to practice the concepts each section taught and not have to deal with students who are overwhelmed and frustrated. The concepts were explained clearly and prior knowledge was not "assumed".
In most cases, the teacher briefly reviewed information that had been given previously, as he was working a problem. I found that to be very helpful with my "somewhat-forgetful-after-a-Summer-break" kids! Mr. Gibson seems to have a good grasp of how young people learn (by doing!) We especially enjoyed his teaching style and calm "can do" attitude!
We also have invested in the $19.99 per month, Membership Plan at the Math Tutor Website, so I was able to use the worksheets at the website for practice. They compliment the DVD's very nicely, by the way.
We also were able to use and review the Calculator Tutor DVD for our TI-84 Plus Calculator. This was a fabulous tool that I recommend to you if you have one of these, or if you are planning to purchase one of these terrific calculators. The 8 hour/ 3 Disc set contains 37 Sections which cover all the functions and modes as well as how to use them for correct calculations. The video uses a screen shot of the actual calculator in order to show the many uses in a very specific and visual way. He includes information that will help students save time on tests! The DVD's will definitely help you to use your calculator wisely!
We just purchased the TI-84 this year to help my 10th Grader practice for the SAT/ ACT tests. Up until last year, my children were actually very calculator illiterate, since I never allowed them to use one. In our State, we are required to test every year and this year we used the same test, but did "group" testing with our Homeschool Support Group. My kids were very surprised to find out that they were allowed to use a calculator in some areas of the test, and that the testing company even recommended calculator use for the portions of the test where it was allowed. Not only that, they were quite upset to learn that the other kids has all been using calculators on their tests for years! Their shock reminded me of the day that they discovered from their friends that there were actually computer games that were NOT educational :)
The Math Tutor Pre-Algebra DVD Volume 1 is available at the Math Tutor Website for $26.99
Even if you are not sure you need one of these DVD's just yet, I would encourage you to check out the Math Tutor website. They have materials to teach Math from Pre-school through College! These DVD lessons are a great way to help supplement your regular Homeschool curriculum or your child's public school lessons. Mr. Gibson also provides free articles on teaching Math, free samples of his video lessons so that you can try before you buy and as I mentioned, the Monthly Membership which includes access to all the Math lessons as well as printable worksheets for practice, further examples and a discussion forum.
Right now, they are offering a deal on shipping so that you pay the same shipping costs on one or multiple DVD's. The Math Tutor products come with a money back guarantee so that you can be assured of their usefulness and quality.
If you would like to take a look at what some other Homeschoolers who have used these materials thought about them, then check out this link to the TOS Crew Blog and click the links for other crew members' opinions:
I learned about the Math Tutor DVD's last year, through the reviews I have been privileged to do for the Old Schoolhouse Review "Crew". I recently received the above two DVD's free of cost in order to use, review and blog about them so that you can have an honest opinion about the products from me. No other compensation has been received
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Mathematical Modeling in Industry-A Workshop for Graduate
Students Mathematics in GPS
Tutor: Craig Poling, Lockheed Martin
On day 1, 7/22/98, we will briefly survey the wide range of commercial,
defense and scientific applications where the Global Satellite Positioning
System GPS has had a major impact. Following the introduction we will
develop the mathematical notation, definitions and framework necessary to
describe: 1) conventional, 2) differential and 3) interferometric, or real
time kinematic, positioning and attitude determination. Following the
development of the mathematical framework necessary to understand GPS we
will pose selected challenging mathematical problems which arise from
attempts to determine ultra high precision interferometic position and
attitude. GPS workshop participants will then be given selected reading
material to aid in the mathematical modeling and solution of the problems
that are posed.
During the course of the workshop GPS antenna and receivers will be used to
collect pseudorange and integrated carrier phase data. This data can be
used by the workshop participants to evaluate their mathematics models and
approaches to achieving high precision position and attitude estimates.
Some exposure to classical mechanics, numerical analysis, and stochastic
processes would be helpful, although the workshop is designed to be
self-contained.
By the end of the GPS workshop, participants will have learned how to
resolve positions anywhere on the earth to subcentimeter accuracy and to
determine orientation in space with accuracy comparable to that achieved byVLBI methods using quasars (e.g. 1.4 x 10-8 degrees). In addition, workshop
participants will have been exposed to some of the principal research
questions which arise in high precision GPS position and attitude
applications.
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These popular and proven workbooks help students build confidence before attempting end-of-chapter problems. They provide short problems and exercises that focus on developing a particular skill, often requiring students to draw or interpret sketches and graphs, or reason with math relationships. New to the Second Edition are exercises that provide guided practice for the textbook's Problem-Solving Strategies, focusing in particular on working symbolically.
May have minimal notes/highlighting, minimal wear/tear. Please contact us if you have any Questions.
$3.00Everett Everett
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Shipping prices may be approximate. Please verify cost before checkout.
About the book:
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating to prime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics. Those who will later specialize in number theory, algebraic geometry and related subjects will benefit more directly, but all mathematics students can enjoy the book.
Softcover, ISBN 0387568441 Publisher: Springer-Verlag, 1993 Used - Good, Usually dispatched within 1-2 business days, A good reading copy. May contain markings or be a withdrawn library copy. Expect delivery in 20 days.
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Find a Miami LakesThe following are the topics most often found in Discrete Math Text Books: Set theory, Graph theory, Probability, Number theory, Algebra, Calculus of finite differences, discrete calculus or discrete analysis, Geometry, Topology, Game theory, decision theory, utility theory, and social choice the...
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A curve fitting program: Lorentzian, Sine, Exponential & Power series are available models to match your data. A Lorentzian series is recommended for real data especially for multiple peaked data. Another improved productivity example.
Math Science Quest is a fun way to learn the fundamental reasoning skills that are the essence of scientific method. It can be played as an individual puzzle or a multi-player game. Players explore a complex mathematical puzzles finding solutions.
VisualStat is a major integrated development environment for R. It incorporates all the descriptive statistics, parametric and nonparametric statistical methods, charts and data transforms you will need for analyzing and presenting data.
This software is intended for simulating and analyzing samplings from experimental data, using both infinite and finite populations; supports basic statistics, frequency and graphics for both the population and simulated samples data.Magic Box is a collection of applications. In it you will find some popular jokes and puzzles such as magic square, magic eye, latent image fading dollar and math transformation. Will the program learn the unknown number?
This software utility can plot regular or parametric functions, in Cartesian or polar coordinate systems, and is capable to evaluate the roots, minimum and maximum points as well as the first derivative and the integral value of regular functions.
PTC Mathcad Express is free-for-life engineering calculation software. You get unlimited use of the most popular capabilities in PTC Mathcad allowing you to solve, document, share and reuse vital calculations.
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Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories.
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Most Helpful Customer Reviews
It is a good book if you are studying the subject. It is also a good book for just refering to. Made easy to understand, I found that it was one of my favourite books to use to study anything that I needed to learn. It is also a good substitute for your lecturer!!!!!
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
3 reviews
2 of 2 people found the following review helpful
Good concise review of the basics3 Nov. 2006
By
A. T. Jones
- Published on Amazon.com
Format: Paperback
Verified Purchase
This text was short and sweet. It reviewed vectors and linear transformations at a level that suited me (since it had been a long time since I last used them). The book is heavily slated toward vector geometry, but does mix in some conventional analytic geometry as well.
I am not a proof oriented individual, so I appreciated the direct approach. The book contains a lot of useful examples and exercises with answers.
1 of 1 people found the following review helpful
Simple But Comprehensive Vector Operations Book24 Aug. 2008
By
Terrance R. Banach
- Published on Amazon.com
Format: Paperback
Verified Purchase
This book presents vector math with a view from the geometrical perspective. The material is easy to follow. I found the instruction simple but well written. The book would be great as either an intro to vector analysis or as a quick review text.
1 of 2 people found the following review helpful
Math in Plain English22 May 2007
By
Kat on Kindle
- Published on Amazon.com
Format: Paperback
Verified Purchase
This book is a simple introduction to vectors and is for high school students in calculus up through college students in their second year of mathematics. Get this book before the "real" math books get a hold of you and complicate the topic of vectors. Read this first and then when they try to make it obscure in your later course work, you can smile to yourself because you understand.
Read the first four chapters to assist with High School / Freshman calculus and physics use of vectors. The first 4 chapters are 48 pages of a book the size of a popular paperback. It wont overload you to read this in addition to your course work IF it CLEARS things up.
Read the remainder of the book in your sophmore year at college to simplify your study of vector (multivariable) calculus, and linear algebra.
I own a copy online and a hard copy of this book. I have loaned it out to students I have tutored in math.
Note that modular math also has a book out on multivariable or vector calculus. As a second year college math student, also consider that book to carry you further along..Vector Calculus (Modular Mathematics Ser)
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This is the first class that focuses on math with a variable (x). Basically you learn how to treat equations with x instead of just numbers. Algebra 2 focuses in depth what Algebra 1 presents. This is where you really start getting into core math topics needed in later math classes.
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Get the most out of Chegg Study
Math Guided Textbook Solutions from Chegg
Chegg's step-by-step math guided textbook solutions will help you learn and understand how to solve math textbook problems and be better prepared for class. Stuck on a math question that's not in your textbook? Chegg's math experts can provide answers and solutions to virtually any math problem, often in as little as 2 hours. Thousands of math guided textbook solutions, and expert math answers when you need them. That's the power of Chegg.
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Algebra 1 Course Now Available at Educator.com
Educator.com announces its new Algebra 1 online course. This course is in addition to 70+ subjects already available for high school, college, test prep, and professional subjects.
Los Angeles, CA (PRWEB) August 29, 2013
With the new school year coming right around the corner, Educator.com announces the release of our online Algebra 1 course with Professor Eric Smith.
The course is for the student who is a little stumped by Functions and Quadratics. It is for the ambitious student who wants to get ahead or review Inequalities. It is for the parent who wants to brush up on their Graphing skills to better assist their child. Algebra 1 contains the fundamental building blocks for higher level math later on, and simple everyday activities like finances and how much to tip. In Educator.com's latest math course, Professor Smith thoroughly and clearly explains everything from Order of Operations to Radical Equations and more. Students should feel more confident and knowledgeable in their Algebra classes after completion of this course.
Professor Eric Smith is a beloved instructor with a successful track record of teaching high school and college level math for over ten years. He is an expert at breaking down even the most complex problems into easy to understand, bite-sized pieces.
It is incredibly easy to access this invaluable resource and get started. Complete access to this course and Educator.com's 70+ others is available for the affordable price of $35 dollars a month. Get help in complementary courses like Algebra 2 and Biology, and other subjects like Language, Music, Computer Science, and SAT and AP Test Prep! Educator.com empowers students to learn anything, anytime, anywhere. Other super saver options include a 6-month or 12-month bundle plan for $150 and $240 a year, respectively.
Educator.com is proud to provide today's scholars with advanced digital study materials that meet both their academic and financial needs. New and exciting courses are frequently added. At this time, Educator's Algebra 1 lessons and accompanying free sample lessons are available for immediate viewing.
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Educator.com pairs students with the best university professors and educators in the country. Educator's goal is to provide high school, college, and professional students with a variety of academic subjects in an online video format that is affordable, accessible, effective, and comprehensive.
The most effective way to improve education is to have the best teachers teach. With the best instructor in a subject, learning anything is possible. Every student deserves an excellent education regardless of geographic location or socioeconomic status and with Educator.com's affordable pricing everyone can access the site's complete content. For more information about the company, please visit the About Us Page.
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Applications of mathematics in economics
Shows instructors what mathematics is used at the undergraduate level in various parts of economics. Separate sections provide students with opportunities to apply their mathematics in relevant economics contexts. Brings together many different mathematics applications to such varied economics topic...
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7.
MA1251 NUMERICAL METHODS 3 1 0 100AIMWith the present development of the computer technology, it is necessary to develop efficient algorithmsfor solving problems in science, engineering and technology. This course gives a complete procedure forsolving different kinds of problems occur in engineering numerically.OBJECTIVESAt the end of the course, the students would be acquainted with the basic concepts in numericalmethods and their uses are summarized as follows: i. The roots of nonlinear (algebraic or transcendental) equations, solutions of large system of linear equations and eigen value problem of a matrix can be obtained numerically where analytical methods fail to give solution. ii. When huge amounts of experimental data are involved, the methods discussed on interpolation will be useful in constructing approximate polynomial to represent the data and to find the intermediate values. iii. The numerical differentiation and integration find application when the function in the analytical form is too complicated or the huge amounts of data are given such as series of measurements, observations or some other empirical information. iv. Since many physical laws are couched in terms of rate of change of one/two or more independent variables, most of the engineering problems are characterized in the form of either nonlinear ordinary differential equations or partial differential equations. The methods introduced in the solution of ordinary differential equations and partial differential equations will be useful in attempting any engineering problem.1. SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 9 Linear interpolation methods (method of false position) – Newton's method – Statement of fixed point theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian elimination and Gauss-Jordon methods - Iterative methods: Gauss Jacobi and Gauss-Seidel methods - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method.2. INTERPOLATION AND APPROXIMATION 9 Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton's forward and backward difference formulas.3. NUMERICAL DIFFERENTIATION AND INTEGRATION 9 Derivatives from difference tables – Divided differences and finite differences –Numerical integration by trapezoidal and Simpson's 1/3 and 3/8 rules – Romberg's method – Two and Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpsons's rules.4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 9 Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order Runge – Kutta method for solving first and second order equations – Multistep methods: Milne's and Adam's predictor and corrector methods.
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Algebra 1 Online with Books (3rd ed.)
Algebra 1 for Distance Learning
Help develop your teenager's thinking skills with the Algebra 1 Distance Learning course from BJU Press. Algebra 1 provides the thinking skills and experience required for further education and future careers. Engaging lessons introduce basic algebraic skills in a logical order, including relations, functions, graphing, systems of equations, radicals, factoring polynomials, rational equations, probability and statistics, and quadratic functions. It also presents algebra as an important tool that your teen can use in exercising dominion over the earth as God commanded.
Teacher Information: Mr. Harmon teaches this course. Read more about him by clicking on the Instructor tab.
What's Included: Click on the Contents tab to learn more about what is included with this product.
Scheduling Information: 180 days; lessons are 30 minutes in length.
Register now! Your textbooks will be shipped right away. You will receive an email from BJU Press Distance Learning Online regarding login information for the online courses which will be available June 1, 2015. You will have through December 2016 to complete your online learning program.
* Unless otherwise noted, kits may not have any partial returns or substitutions.
Each subject includes a printed Student Worksheets/Handouts packet. An abridged Teacher's Edition, an eTextbook copy of the Student text (where available), and other resources are available when you log in to bjupressonline.com. Grades 5-12 take tests and quizzes online.
Mr. Bill Harmon, BS
Bill Harmon has loved science for as long as he can remember. After completing his B.S. in Chemistry, he returned to Florida where he gained experience teaching a variety of subjects: science, math, Latin, and computer courses. Now he works as a chemist in the Safety Services Office at BJU, teaches Distance Learning Physics and Algebra, and teaches Chemistry at Bob Jones Academy. He is currently pursuing an M.Ed. in Secondary Education. He and his wife Mary Ann have two children, Brian and Janette. His favorite Bible verse is II Timothy 3:14.
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Some sourses offered on MIT's online courseware have audio taped and video recorded lecture which you can download from itune for free. I do find this helpful rather than just reading the book. Some of them contain problem set and exam with keys.
Does somebody knows, where are the best books in the mathematical biology in the Internet?
Best regards.
In the explanation of given phenomena, no other things and no other grounds of explanation can be employed than those which stand in connection with the given phenomena according to the known laws of experience.
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International Mathematics Competition for University Students (IMC)
The International Mathematics Competition for University Students is an annual mathematics competition open to all undergraduate students of mathematics. It is held at a different location each year at the end of July or beginning of August. Students from over 170 universities from 43 countries have participated over the first seventeen competitions.
IMC runs over five or six days during which the competitors sit two five-hour examinations, each with six questions chosen by a panel and representatives from the participating universities. Problems are from the fields of Algebra, Analysis (Real and Complex), Combinatorics and Geometry. The working language is English.
Organizer
University College London (main organizer) and universities worlwide (local organizer)
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Can low achieving mathematics students succeed in the study of linear inequalities and linear programming through real world problem based instruction? This study sought to answer this question by comparing two groups of low achieving mathematicsAlliance College -- History; Polish Americans -- Education -- United States; Universities and colleges -- Pennsylvania -- Cambridge Springs; Polish National Alliance of the United States of North America
The purpose of this study was to determine if integrating a unit on functions would benefit students. Previous studies have shown that integrating science and mathematics increases students' understanding of certain topics in science. Typically,...
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This is a dynamic math website where students enter problems and where the site's math engine solves the problem. Students in most cases are given a step-by-step process for solving the problem that student enters immediately
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Prerequisite: COMPASS/ACT math placement test results
appropriate for this course within the last two years.
This course is for students who need to learn basic arithmetic
skills. No calculators will be used. Topics include operations with whole
numbers, fractions, decimals, integers, exponents; square roots; order of
operations; conversion between fractions, decimals and percents; solving
1-step equations. Applications include units of measurement and conversion
between units in same system; proportions; averages; area and perimeter of
rectangles and squares; percent problems.
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Finite Math—Semester B
When it comes down to it, life is all about luck. Whether you find twenty bucks sitting on the sidewalk or get struck by lighting, chance plays a bigger role in life than people admit. Even the very best Dungeon Masters and Texas Hold 'Em champions can't escape probability at work. Unless they're cheating.
In this Common Core-aligned course, we'll delve deep into the mysteries of counting theory, normal distributions, why so many people you know share the same birthday, and more. We'd tell you what else we'll cover, but we don't want to ruin the mystery.
On second thought, let's ruin the mystery. With loads of drills, examples, and projects, we'll cover
counting theory, Venn diagrams, and other ways to deal with large sets of numbers.
probability, experiments, and the famous Birthday Problem.
conditional probability, events, and using trees to represent them.
statistics, histograms, odds, and binomial events.
normal distributions, z-scores, and game theory.
What are the odds you'll finish this course knowing all there is to know about statistics and probability? We're betting pretty good.
P.S. Finite Math is a two-semester course. You're looking at Semester B, but you can check out Semester A here.
Course Breakdown
Unit 8. Counting Theory
You learned how to count back in preschool, so it's high-time you stepped up your counting game. We'll start out with sets, unions, and intersections, and even draw a few Venn diagrams. Then, we'll get factorials involved and talk about combinations and permutations and their many applications. By the time we're through, you'll be able to give the Count a run for his money.
$15.59add to cartremove
Unit 9. Probability
If probabilistic thinking is already intuitive to you, then great. You're ahead of the game. But for the rest of us, this unit is all about making probability as intuitive as how to eat the last Oreo. (Twist-and-lick, obviously.) From setting up experiments to probability properties and formulas, this unit contains more coin tosses and die rolls than you thought were possible.
$15.59add to cartremove
Unit 10. Conditional Probability
In this unit, we're going to learn how to tell if that third flip being heads depends on the first two being heads (spoiler alert: no). With the help of the Product Rule, trees, and Bayes' Theorem, we'll learn about a new kind of probability: one where the likelihood of an outcome can change in an instant—or at least in the blink of another event happening first.
$15.59add to cartremove
Unit 11. Statistics
We'll kick off the unit by discussing how to turn any kind of data into a table or graph that you trust. (Those histograms always looked a little shady to us.) After talking about probability and odds, we'll boil down our data into bite-sized summaries, like expected value, variance, and standard deviation. They're not as tasty as those mini-quiches and shrimp cocktails, but we promise they'll be more useful when it comes to data analysis.
$15.59add to cartremove
Unit 12. Normal Distributions and Game Theory
We won't lie to you: this unit's a biggie. Often, normal distributions can seem more abnormal than you'd think. Don't worry. We'll help you tackle with z-scores, bell curves, and binomial probabilities like a boss. After that, we'll take on game theory, talk about its different strategies, and learn how to kick your opponent's butt at Monopoly. Family game night will never be the same again
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The University Core in Mathematics
The University Core Requirement in mathematics is satisfied by taking one of the courses below. Keep in mind, however, that some majors (like Biology, Business, and Economics) will require specific courses in mathematics beyond the University Core.
Core Courses (one required)
MATH 100 Number, Magnitude, Form
MATH 110 College Algebra
MATH 120 Finite Mathematics
MATH 150 Functions
MATH 151 Calculus
The University uses a placement protocol, which includes a Mathematics Placement Exam, to assist students in the selection of a suitable core course. The placement exam is offered during freshman orientation. You can also make individual arrangements to take the placement exam by contacting the Department of Mathematics and Physics. Prospective students are encouraged to look through the practice questions to find out what to expect from the placement exam.
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...Chemistry and math go hand-in-hand and that is where most students get confused. However.
...I know all of the standard openings and am familiar with most of the standard reference works including Modern Chess Openings. Discrete mathematics is concerned with the relationships among mathematical structures that are discrete instead of continuous. For example, the arithmetic of integers...
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9780072937305MP: Calculus Single Variable w/ OLC Bind-In Card
The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.
The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems
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The Latest from Shmop
Shmoop Launches Calculus Guide for Students and Teachers
One of the most common questions that flits across a math student's mind is, "Why does this matter?" Understandably, it may be difficult to see at a glance how finding a solution to the derivative of an expression might directly correlate to one being able to tie their shoelaces.
Thank goodness for calculus. Admittedly, some of the concepts are tough, but along the way you begin to see its wicked practical applications. Rather than simply juggling numbers and variables, you are beginning to apply the mathematical concepts you have picked up along the way to solve real-world problems. Suddenly, math has a purpose! Huzzah!
Shmoop, a publisher of digital curriculum and online test prep, is proud to announce the launch of its new Calculus Guide. Here, students can learn that "dy is over dx." (Or is it in denial? It does still keep dx's photo in a frame on its desk…)
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Elementary and Intermediate Algebra
9780495389613
ISBN:
0495389617
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the "language of algebra," iNTERMEDIATE ALGEBRA, 4e provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approac...hes that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills. The authors' five-step problem-solving approach makes learning easy. More student-friendly than ever, the text offers a rich collection of student learning tools, including Enhanced WebAssign online learning system. With ELEMENTARY AND INTERMEDIATE ALGEBRA, 4e, algebra makes sense!
Alan S. Tussy is the author of Elementary and Intermediate Algebra, published 2008 under ISBN 9780495389613 and 0495389617. Two hundred eighteen Elementary and Intermediate Algebra textbooks are available for sale on ValoreBooks.com, ten used from the cheapest price of $3.99, or buy new starting at $74 Missing many pages. Heavy wrinkling from liquid damage. Does not affect the text... [more]
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Advice for Prospective Students
What are the different programs of study in mathematics that are available at Ave Maria University?
Every student at the University must take at least one math course to satisfy the University core requirement. In addition, we provide major and minor programs of study, both of which can be tailored to the individual student's needs and interests. You can consult the Program Requirements page for further details.
What if I am interested in engineering or computer science? Can I study that at Ave Maria University?
Although we do not have an engineering or computer science program per se, perhaps a degree in mathematics or physics will get you part way there. For more information, check out the "Whither Engineering" page.
How can I satisfy the University core requirement in mathematics?
The University core requirement is satisfied by taking one of the following courses: MATH 100, MATH 110, MATH 120, MATH 150, or MATH 151. Keep in mind, however, that some majors (like Biology, Business, and Economics) will require specific courses in mathematics. You should ask your academic adviser for more information.
How can I decide which math class to take to satisfy the University core requirement?
If you take our Mathematics Placement Exam, we can recommend the best math course for you. The placement exam is offered during freshman orientation. You can also make individual arrangements to take it by contacting the Department of Mathematics and Physics. We encourage you to look through the practice questions to get a better idea of what to expect from the placement exam.
How can I determine if I am prepared for University-level math classes?
You should be comfortable with the basic concepts of algebra, geometry, and trigonometry. Courses in precalculus and calculus, although optional, will definitely be useful. You can also take a look at the practice questions for the placement exam to get an idea of the sorts of questions that we might expect you to be able to answer when you arrive on campus.
What kind of calculator will I need in my math class?
It mostly depends on your professor. Although some professors will not let you use a calculator for exams, most will let you use one for homework. In any case, you should make sure that you own a stand-alone calculator that is separate from your ipod or cell phone. What ever brand of calculator you do choose to purchase, be sure that you become familiar with it, since your professor will probably not be.
What is the best home school program to prepare students for University-level math classes?
Although there are several good choices for home school programs in math, you should make sure that you choose one which exposes you to algebra, geometry, and trigonometry. Some reasonable options include:
Of course, this is by no means an exhaustive list, nor can we officially endorse any of the programs above. Whatever choice you do make, be sure to dedicate plenty of time for homework, read your textbook carefully, and practice taking timed exams.
What should I do if I have other questions about studying math at Ave Maria University?
You can send us an email, or look at our contact page for other ways of getting in touch with us.
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Why is algebra so important?
Last fall results from national math exams stirred up a tempest in a standardized test. It turns out math scores rose more quickly before No Child Left Behind was implemented, and fourth-grade math scores haven't improved since 2007. As reported in the New York Times, the achievement gap remains a chasm between the haves and the have-nots.
What does this mean for your child? While pundits and politicians battle over the big issues, it's up to parents to stay on top of the little ones: their own kids' academic development. Make sure your tween or teen is on track for high school math with this guide to algebra.
Why algebra matters
It is frequently called the gatekeeper subject. It is used by professionals ranging from electricians to architects to computer scientists. It is no less than a civil right, says Robert Moses, founder of the Algebra Project, which advocates for math literacy in public schools.
Basic algebra is the first in a series of higher-level math classes students need to succeed in college and life. Because many students fail to develop a solid math foundation, an alarming number of them graduate from high school unprepared for college or work. Many end up taking remedial math in college, which makes getting a degree a longer, costlier process than it is for their more prepared classmates. And it means they're less likely to complete a college-level math course. For middle-schoolers and their parents, the message is clear: It's easier to learn the math now than to relearn it later.
The first year of algebra is a prerequisite for all higher-level math: geometry, algebra II, trigonometry, and calculus. According to a study (pdf) by the educational nonprofit ACT, students who take algebra I, geometry, algebra II, and one additional high-level math course are much more likely to do well in college math.
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Algebra is not just for the college-bound. Even high school graduates headed straight for the work force need the same math skills as college freshmen, the ACT found. This study looked at occupations that don't require a college degree but pay wages high enough to support a family of four. Researchers found that math and reading skills required to work as an electrician, plumber, or upholsterer were comparable to those needed to succeed in college.
Algebra is, in short, the gateway to success in the 21st century. What's more, when students make the transition from concrete arithmetic to the symbolic language of algebra, they develop abstract reasoning skills necessary to excel in math and science.
Algebra I: Learn it now or later?
Students typically take algebra in eighth or ninth grade. The benefit of studying it in eighth grade is that if your child takes the PSAT as a high school sophomore, she will have completed geometry. By the time she's ready to take the SAT or ACT as a junior, she will have completed algebra II, which is covered in both of these college admissions tests.
There's a growing movement to require algebra in seventh grade, but many seventh-graders aren't prepared for it, math educators say.
"Some kids get turned off of math because they start math too early," says Francis "Skip" Fennell, president of the National Council of Teachers of Mathematics (NCTM). If you're wondering whether your child is ready to advance, he recommends talking to her current teacher. The goal is for your child to learn algebra well and stay engaged in math, not to push her through the curriculum as quickly as possible.
Is your child on track?
Math curriculum varies widely from state to state, so it can be difficult to determine whether your child is getting the right preparation for higher-level courses. For a better sense of how your child's schoolwork compares, look up your state's math standards. Or see what the NCTM recommends for preschool through high school.
W. Stephen Wilson, a math professor at Johns Hopkins University, reviewed K-12 math standards nationwide for the Thomas B. Fordham Institute and has strong opinions about which offer the best guidance. He calls California's the " gold standard" and recommends that parents who want to make sure their kids are prepared for high school and college compare their curriculum to the California standards.
The answer is in the homework
Wilson offers this advice to parents trying to evaluate their children's math instruction:"If a student isn't bringing home work that requires lots of manipulation and word problems, then there is probably a problem."
Fennell suggests talking to your child and her math teacher about how homework is used, specifically:
Are homework assignments corrected and returned in a timely way?
Is homework reviewed in class so students can learn from their mistakes?
Does the teacher change the pace or direction of his or her instruction, based on student feedback?
You don't need to be a mathematician to ask good questions about your child's curriculum, Fennell adds. "Ask the teacher, 'Is it a repeat of math that should have already been mastered? When my child finishes this year, will he be ready for high school math?'"
Bill Moore directs Washington's Transition Mathematics Project, which is working to better prepare students for college math. According to him, middle-schoolers need to have a solid foundation of "basic procedural skills that really make problem solving more fluid. There's a fundamental set of stuff that just has to be memorized, and then there's a sense of numbers, a sense of what's a reasonable answer."
Calculators: Tool or crutch?
How much should students rely on calculators? The issue has been debated by math teachers, university professors, and parents, but there is general agreement that calculators shouldn't be a substitute for learning basic arithmetic and standard algorithms. "In some cases," says Moore, "students go straight to calculators, and if the calculator says it's right, then it must be right."
"The calculator is an instructional tool," says Fennell. "It should support but not supplant anything. You don't use it for 6 x 7."
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Understand and use math concepts in order to design a financial or economic system.
Interpret technical information presented in mathematical or diagram form in order to work with things like real estate property valuations and stock market reports.
Work math problems quickly and accurately.
Understand and use computers and related equipment.
Speak and write clearly to report financial information.
Make decisions about the value of real estate and personal property based on inspection of the property, how you think its location will be affected by future plans of the community, as well as established facts like past tax values.
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you are returning to school, studying for an adult numeracy test, helping your kids with homework, or seeking the confidence that a firm maths foundation provides in everyday encounters, Basic Maths For Dummies, UK Edition, provides the content you need to improve your basic maths skills.
Based upon the Adult Numeracy Core Curriculum, this title covers such topics as:
Getting started with the building blocks of maths and setting yourself up for success
Dealing with decimals, percentages and tackling fractions without fear
Sizing Up weights, measures, and shapes
How to handle statistics and gauge probability
Filled with real-world examples and written by a PhD-level mathematician who specialises in tutoring adults and students, Basic Maths For Dummies also provides practical advice on overcoming maths anxiety and a host of tips, tricks, and memory aids that make learning maths (almost) painless - and even fun.
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He holds a PhD in Mathematics from the University of St Andrews and worked for several years on NASA's Living With A Star project at Montana State University, where he came up with an equation which is named after him. It's used to help save the world from being destroyed by solar flares. So far so good.
He became tired of the glamour of academia and returned to the UK to concentrate on helping students come to terms with maths and show that not all mathematicians are boring nerds; some are exciting, relatively well-adjusted nerds.
Colin lives in Dorset with an espresso pot, several guitars and nothing to prove.
Product Description
From the Back Cover
Make numbers dance to your tune in no time!
No head for numbers? Feel like maths isn′t your thing? Stop selling yourself short. Maths tutor Colin Beveridge believes that doing maths comes as naturally to humans as swimming does to fish, and he proves it in Basic Maths For Dummies. Encompassing the Adult Numeracy Core Curriculum, and using Colin′s proven formula for turning anybody even the most maths–phobic student into a natural number–cruncher, this book arms you with the confidence and skills you need to handle everyday maths challenges, return to school, pass skills and employability exams with flying colours, and help the kids with their homework.
Face down the competition overcome maths anxiety and set yourself up for success
Get a firm footing master the building blocks of maths, including addition, subtraction and long division
Take their measure size up weights, measures, rates, conversions and geometric shapes
Show ′em who′s boss give fractions no quarter, put decimals in their place and accept nothing less than 100% from percentages
Beat the odds discover how to decipher statistics, gauge odds and predict probabilities
Shoot from the hip learn simple tricks for making reliable estimates fast
Open the book and find:
Tricks for conquering maths anxiety
Addition, subtraction, multiplication and division made easy
Advice on money, weights, measures and shapes
How to read charts, tables and graphs at a glance
Guidance on conquering fractions, decimals and percentages
How to decipher statistics and probabilities
How to handle ballpark estimates and rough calculations in your head
Learn to:
Add, subtract, multiply and divide with confidence
Deal with decimals, tackle fractions and make sense of percentages
Size up weights, measures and shapes
Prepare effectively for maths tests
About the Author
Colin Beveridge holds a doctorate in mathematics from the University of St Andrews. He gave up a position as a researcher at Montana State University (working with NASA, among other projects) to become a full–time maths tutor, helping adults, GCSE, A–level and university students overcome their fear of maths a position he finds ′far more enjoyable than real work′.
Most Helpful Customer Reviews
I have found this book very very helpful. I have been phobic about maths my entire life but have recently decided on a career change that will involve studying science at university level. I bought this book as maths was by far my weakest point, in fact I had to work right from scratch.
This book takes you by the hand and leads the way, one baby step at a time, from the most basic of maths skills right up to things that I never imagined I would be able to do. Not only does it contain a huge amount of useful info presented in an easy to understand way but it even makes it enjoyable and very rewarding to work through.
I have this book as well as "Basic Maths Practice Problems for Dummies" and "Numeracy Tests for Dummies" they all go hand in hand and between them have covered a massive proportion of what I needed to know.
This book should be the first point of call for anybody who is looking to improve their maths.
This book reviews some of the most fundamental mathematics for school pupils, and for people who struggles with basic maths in daily situations. It is divided in comprehensive chapters, each of them focusing on a specific point. Chapters are very well organised with clearly indicated subtopics. It is full of simple tricks to make adding, subtracting, multiplying and dividing a piece of cake for example. It is also full of clever advices about how to use and understand maths. While being very serious on the topic, the style is very engaging and informal (you'll know everything about the author's obsession on large cappuccinos and carrot cakes). This book is ideal for school pupils, as well as for adults who were reluctant of mathematics at school. They won't be anymore, and realise that after all... maths is fun.
A well laid out and structured book, as a person who has struggled with Mathematics, I wish books like these were around when I was studying instead of the dry almost antique books that were in use in the past, The chapters are well divided into topics so that people can zero in on areas of interest. The various tips and tricks that can be used to help the learner along are invaluable tools for exams and indeed every day life.
However, some have commented, and rightly so, on the fact that the book is too wordy and also that there are no practice questions. This latter criticism is the real problem and really cannot be excused as the book is touted at the self-help market. As a person who struggled with the topic, one of the main ways to learn is practice and more practice, hence my 4 star rating.
I never thought I would buy a book on maths but when I found this Dummie one I thought I would give it a go. I never did maths at school and have always wanted to get the hang of it and I'm pleased to say that now I am working through this book I am getting a good understanding of what its all about. I'm really beginning to enjoy it!
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More About
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Overview
Mathematical Methods for Economics uses an applications-oriented approach to teach mathematical tools in the context of current and classic economic examples. This first edition is clearly written and successfully demonstrates how mathematics is used to solve economic problems across a wide range of fields including microeconomics, macroeconomics, economic growth, international trade, open-economy macroeconomics, finance, labor,
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Shipping prices may be approximate. Please verify cost before checkout.
About the book:
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics.
Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments.
The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book. Usually dispatched within 1-2 business days, A good reading copy. May contain markings or be a withdrawn library copy. Expect delivery in 2-4 weeks.
Hardcover, ISBN 0198531559 Publisher: Oxford University Press, 1975
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This book consist of 50 numerical problems for PMP exam and detailed answer at the end of book. These problems are relatively difficult compared to what actually PMP aspirants would come across. However, if participants are comfortable in these 50 questions, they would find numerical problems in PMP exam relatively easy.
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More About
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Overview
This book contains the essentials of the Differential Calculus well arranged for elemental study.
It gives a series of twenty-one easy lessons, showing first the purpose of this interesting branch of mathematics and then its relation to the Integral Calculus.
The main object of the writer is to show the student the real uses of these branches of study, while he is attempting to master elemental principles and methods peculiarly their own, and hold his attention to these things, neglecting as useless, if not hurtful, much of the details which are found in ordinary textbooks.
The author then states and proves the rules for work and applies them to all the topics ordinarily presented in the elementary calculus illustrating each with appropriate exercises, the solutions of which are fully given.
The book is evidently not intended as a textbook, for school or college use, in the sense of furnishing sufficient exercise in the application of the elements of the calculus; but it will be found very useful in review of principles, helpful in the meaning of operations, and instructive in the theories of limits and infinitesimals which so often trouble writers and teachers to explain. We think the author rightly combines the two opposing methods of limits and infinitesimals thereby practically escaping the bald fiction of the one and bridging the dark chasm of
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2008 Spiral-bound GoodMath Basics for the Health Care Professional helps trainees in a wide variety of healthcare professions to master a vital skill toward their career success. This workbook incorporates every aspect of math relevant to health care applications with a wealth practice opportunities throughout. The third edition continues to promote critical thinking through an organized presentation of instruction, practice, and self assessment. Its new features make for an even better guide to increase math proficiency. These new features include: a supplementary CD-ROM with additional sets of challenging practice tests; coverage of occupation-based units that are essential for health care personnel, including reading drug labels, medicine cups, syringes, and intravenous fluid, apothecary measurement and conversions, parenteral dosages, basic intravenous administration and basic dosage by weight units; two extra units reviewing pre-algebra basics and the metric system; and an appendix of extra practice unit tests with answer keys for easy self-checking.
Related Subjects
Meet the Author
Michele Benjamin Lesmeister is currently a full-time, tenured member of the faculty at Renton Technical College and has taught in two-year colleges for over 20 years. Michele has also been involved in developing transitional learning materials for native speakers and second language speakers for the health care fields for 18 years. As an active participant in the Universal Design for Learning initiative on the RTC campus, Michele tries to create materials that address learner barriers and improve access to learning for all students. Michele has authored several books, both of which she uses within her own classrooms. Michele is the Vice-President of the Renton Federation of Teachers as well as a member of the National Learning Disabilities Association, the League of Innovation, and the Council on Adult Basic Education. Michele also received the Faculty of the Year Award at RTC in 1989 and
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Prerequisite: MAT 1100 (or equivalent college transfer course) with a "C" or
better within the last three years or COMPASS/ACT math placement test results
appropriate for this course within the last two years
GE Outcomes: Critical Thinking, Quantitative Literacy
The study of the properties and characteristics of geometric
figures through an axiomatic approach that focuses
on proof and the building of a logical system. In
particular, the material includes angles, similarity and congruence
of triangles, parallel and perpendicular lines, quadrilaterals,
right triangles, circles, area and volume, and
constructions.
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CalcRef
A comprehensive Calculus review app written by a Math PhD. Functions, Limits, Derivatives and Integrals are all covered with 55+ worked examples. For quick access to equations, the "Equations" tab displays commonly used properties and equations for derivatives and integrals
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...
Show More understand concepts. Features incorporation of AMATYC and NCTM standards-reflected in an increased emphasis on visualization graphing, and data analysis. In addition, Martin-Gay's 4-step problem solving process-Understand, Translate, Solve and Interpret-is integrated throughout. Also includes new features such as Study Skills Reminders, "Integrated Reviews", and "Concept Checks." For those in need of a graphing utility resource in intermediate algebra, and for readers who need to prepare for advanced algebra or finite math143.00
Your Savings:$121.51
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Aimed at effectively delivering the 2008 framework, the Pupil Books are packed with functional maths questions and spreads and ensure progression by providing differentiated material for each level. Year 7 Pupil Book 2 is fully levelled with built-in progression helping students to progress from level 4 to level 5 and beyond. This Pupil Book: * Guarantees progression with colour-coded levelling and level boosters to help pupils work at the right level and progress with ease. * Enables pupils to develop vital functional skills and put maths into context with the help of the integrated functional maths questions and exciting real-world spreads. * Promotes personalised learning and self assessment using pupil-friendly learning objectives for every chapter. * Eases the class into understanding new concepts with worked examples. * Stretches and challenges the knowledge and skills of pupils using extension activities. * Provides rigorous maths practice with the hundreds of levelled questions. * Captures pupils' attention using the colourful design. * See the Teacher's Pack for more support and answers.
"synopsis" may belong to another edition of this title.
About the Author:
Collectively, Evans, Gordon, Speed and Senior have over 100 years of teaching experience, both in the classroom and leading maths departments. They all currently hold senior positions within examining bodies and have been extensively involved in the development and piloting of new specifications.
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1118457447
9781118457443
Details about Mathematics for Elementary Teachers:
This book establishes a solid math foundation for future teachers. Thoroughly revised with a clean, engaging design, the new Tenth Edition of Musser, Peterson, and Burger's best-selling textbook focuses on one primary goal: helping students develop a deep understanding of mathematical concepts so they can teach with knowledge and confidence. The components in this complete learning program—from the textbook, to the e-Manipulative activities, to the Children's Videos, to the online problem-solving tools, resource-rich website and Enhanced WileyPLUS—work in harmony to help achieve this goal.
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1.1 Limits and Their Properties
•What is Calculus?
•The Tangent Line Problem
•The Area Problem
What is Calculus?
• Calculus is the mathematics of change.
• Pre-Calculus is static while calculus is dynamic.
(see pp 43-44)
• Calculus is the reformation of precalculus
mathematics through the use of a limit
process.
The "Calculus Process"
Precalculus Limit Calculus
Math Process
Chapter P: Preparation for Calculus
Chapter 01: Limits and their Properties
Chapter 02: Differentiation
The Tangent Line Problem
• Animation: All the tangent lines to a curve.
• Tangents and Secants
• The Tangent Problem.gsp
The Area Problem
Finding the Area Under the Curve
• The Area Problem
Assignment:
• Section 1.1 (1-10)all
• Use the following window for problem 9
domain:(0,6) & range:(0,6)
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Holt McDougal Larson Algebra 1 Student Edition - 12 edition Suppo
rt the Common Core Teacher resources include correlations to the Common Core State Standards, differentiated pacing guides, and course planners with teaching support to ensure complete coverage of the Common Core State Standards. Support the Common Core Teacher resources include correlations to the Common Core State Standards, differentiated pacing guides, and course planners with teaching support to ensure complete coverage of the Common Core State StandardsHardcover Very Good 0547647131 Clean text. Edge wear on cover. Page edges have light dirt marks. Some pages may be creased. No Priority shipping available on this item. **NO international shipping....show more -5e- ...show less
$80.77 +$3.99 s/h
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AlphaBookWorks Alpharetta, GA
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Follett School Solutions, Inc. Woodridge, IL
0547647131 No excessive markings and minimal highlighting.CD Roms, access cards/codes, and other supplemental materials may or may not be included based on availability.
$83.41 +$3.99 s/h
Good
A Book Company Lexington, KY
May contain some highlighting. Supplemental materials may not be included. We select best copy available. - Student Edition - Hardcover - ISBN 9780547647135
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Overview
This user-friendly, Web-based software package makes it easy to help you develop the essential math skills you need to succeed in construction trades. An innovative, interactive teaching and learning resource, BUILDING MATH SKILLS ONLINE FOR CONSTRUCTION allows you to quickly assess baseline skill levels and assign personalized courses of study, with lessons and problems targeted to your individual needs and career interests. In addition to a strong focus on practical applications for real-world construction tasks and hands-on projects, instructional content is correlated to the Common Core Standards. BUILDING MATH SKILLS ONLINE FOR CONSTRUCTION, is a powerful new resource to support your success—in the classroom and your future career.
Product Details
ISBN-13: 9781133590422
Publisher: Cengage Learning
Publication date: 7/30/2012
Meet
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Section 6.1: Matrices Solutions to Linear Systems
When it is desirable to emphasize the notation used for individual entries we use [aij]
instead of capital A to name the matrix.
Example:
Example: Consider the following system of equations:
The corresponding coefficient matrix is:
and the augmented matrix is:
Example:
Elementary
Row Operations: 1. Interchange two rows
2. Multiply a row by a non-zero constant and replace that row with the product.
3. Add a multiple of a row to another row and replace one but not both of the rows with that sum.
DEFINITION:
Two matrices are row equivalent
if one can be obtained from the other by a sequence of elementary row operations.
The sample exercises referenced above are interactive. Instruction and learning depends on the reader pointing to items on the page to create pop-up explanations.
Minimal List of Exercises Page 5883 Exercise Set: All exercises 1 - 36.
Section 6.4: Multiplicative Inverses of Matrices and Matrix Equations
Information about finding the inverse of a square matrix is found in the PDF file HERE.
Minimal List of Exercises Page 6034 Exercise Set: 1 - 12, 15, 17, 19, 21, 2529, 30, 31, 32, 37, 39, 40.
Minimal List of Exercises Page 6165 Exercise Set: All of 1 - 10, 27 - 32, 41, 42, 44, 49, 50.
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Algebra 1: Units 1-5 Introduction and How to Guide Opening the Documents: Congratulations on your recent purchase of Algebra Class . This is the first step in really ...
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Integrated Algebra 1 is a new text for high school algebra that continues the approach that has made Amsco a leader in presenting mathematical ideas in a contemporary ...
Algebra 2 and Trigonometry is a new text for a course in intermediate algebra and trigonometry that continues the approach that has made Amsco a leader in presenting ... 2/Algebra 2 and Trigonometry.pdf
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Saxon Geometry includes all topics in a high school geometry course, presented through the familiar Saxon approach of incremental development and continual review. The homeschool kit includes the...
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Algebra 2 covers all topics that are traditionally covered in second-year algebra as well as a considerable amount of geometry. In fact, students completing Algebra 2 will have studied the equivalent...
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Saxon Geometry includes all topics in a high school geometry course, presented through the familiar Saxon approach of incremental development and continual review. The homeschool kit includes the...
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Seton Educational Media has the lowest prices on Saxon products!SAXON Teacher is the only official video supplement to the SAXON Math Homeschool program. Contains over 110 hours of...
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Product Description
Instead of memorizing formulas and equations, Videotext Algebra helps students to understand math through mastery learning, helping them to solidify each concept before moving on the next. This Module contains one copy of all print materials needed for this module.
Module B in Videotext Algebra, this unit covers:
Basic Relations (Solutions, Making Zeros, Making Ones, Combinations)
Complications (Grouping Symbols, Like Terms on the Same Side, Placeholders on Both Sides, Combinations)
After blowing through a standard Algebra program, we thought it best to continue on with Algebra 2 for my 13yo. But, curiously, he hit a math wall almost instantly in Algebra 2. Typically, we switched programs. Twice. We considered switching to Geometry and ditching Algebra for a year. Afterall, he has plenty of time. But then we found VideoText Interective. He has regained his confidence by beginning at the beginning and moving swiftly through module A. Module B has the same clear presentation that opens the eyes and lifts the spirit. Don't let the cost deter you because if you start with this, you won't waste money (and time) on the others.
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More About
This Textbook
Overview
Mathematics for Elementary Teachers, Third Edition offers an inquiry-based approach, which helps readers reach a deeper understanding of mathematics. Sybilla Beckmann, known for her contributions in math education, writes a text that encourages future teachers to find answers through exploration and group work. Fully integrated activities are found in her accompanying Activities Manual, which comes with every new copy of this text. As a result, readers engage, explore, discuss, and ultimately reach a true understanding of mathematics.
Related Subjects
Meet the Author
Sybilla Beckmann earned her undergraduate degree in mathematics from Brown University and a PhD in mathematics from the University of Pennsylvania. She taught and did research in mathematics at Yale University for two years. Since then, she has been at the University of Georgia. When she had children, she became very interested in helping prospective teachers understand and appreciate the mathematics they will teach. This interest led to her book. In her spare time, she enjoys playing the piano, weaving, attending classical music concerts, and traveling
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This lesson is wonderful for anyone who is just being introduced to the art of proofs. Induction is a great starter proof that helps a student who is new to proofs wrap his or her head around the idea. Not only is the basic structure of a proof by induction explained, several examples are included for additional practice and understanding. A really great crash course in Induction, but containing no additional resources.
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An ITS dealing with students' algebraic solutions to Physics problems needs to map the student variables and equations onto the physical properties and constraints involved in a known correct solution. Only then can it determine the correctness and relevance of the student's answer. In earlier papers we described methods of determining the dimensions (the physical units) of student variables. This paper describes the second phase of this mapping, determining which specific physical quantity each variable refers to, and which part of the set of constraints imposed by physics principles each student equation incorporates. We show that knowledge of the dimensions of the variables can be used to greatly reduce the number of possible mappings.
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Information Technology - Information Technology - Solutions - Customer Services
Tue, 26 May 2015 14:13:00 +0000Joomla! - Open Source Content Managementen-gbMathematica
Mathematica is a software package used for communicating scientific ideas in a variety of ways, whether this is visualization of a concept in an intro-level course, or creating a simulation of a new idea related to research.
Mathematica is available for free to UAB faculty, staff and students, thanks to funding from the College of Arts and Sciences and the School of Engineering.
{slide=How to Get Mathematica}
Campus machines
Follow the directions below to download software from Wolfram and request the appropriate activation key. If you do not have administrator access to your machine, please contact your IT support for assistance.
Resources for Educators
Learn how to make your classroom dynamic with interactive models, explore computation and visualization capabilities in Mathematica that make it useful for teaching practically any subject at any level, and get best-practice suggestions for course integration.
Access on-demand and live courses on Mathematica, SystemModeler, and other Wolfram technologies. {/slide}
{slide=Research with Mathematica} Rather than requiring different toolkits for different jobs, Mathematica integrates the world's largest collection of algorithms, high-performance computing capabilities, and a powerful visualization engine in one coherent system, making it ideal for academic research in just about any discipline.
Learn what areas of Mathematica are useful for specific fields. {/slide}
{slide=Comparison between Mathematica and Matlab} In general, Mathematica is a high-level complete system, while MatLab is a low-level core with specialist toolboxes. Most engineering colleges at research universities maintain both products, including UAB. Because MatLab has separate toolboxes, each toolbox can only assume the functionality of the basic, core system; Mathematica is an all-in-one software which is interconnected nicely. For example, in Mathematica, purely numeric commands can perform symbolic pre-processing for richer and more accurate results, which is not possible in MatLab because of the design. This overall concept applies to the vast majority of Mathematica's commands when compared to MatLab.
Engineers and other groups on campus value the following functionality, which is unique to Mathematica:
Very sophisticated symbolic algorithms for closed-form solutions to problems
Much easier to create mouse-driven interfaces to visualize variations in equations or simulations,
The highest quality and most accurate graphics engine available for symbolic and numeric graphics,
Support for both machine precision and arbitrary precision,
Automatic switching between algorithms for best results,
Solves any order ODE (rather than only first-order in MatLab),
Integration for any n-dimensions (rather than only 3 in MatLab),
Wolfram Language included to program in procedural, functional, object-oriented, or rule-based style makes language easier to learn (rather than procedural only in MatLab),
Mathematica's high-level language requires less code to develop algorithms or ideas than MatLab
Text and equation typesetting document interface with slideshow mode (not available in MatLab),
Load-on-demand data sets to use in addition to importing a wide variety of types of data
IDE based on Eclipse, which researchers more commonly know and work with (rather than MatLab's home-grown IDE).
{slide=Support for Mathematica} For assistance with using the Mathematica software:
College of Arts and Sciences users can contact the CAS IT help desk by phone at 205-975-4500, by e-mail at casit@uab.edu or online at uab.edu/casit
School of Engineering users can contact Tommy Foley at 205-934-8477 or by e-mail at tfoley@uab.edu
All other schools/departments should contact Tony Schaudt, Wolfram Research Inc., at 800-965-3726, ext. 5588, or by e-mail at troys@wolfram.com
{/slide}
]]>kwbean@uab.edu (Kerry Bean)Solutions - Customer ServicesFri, 19 Dec 2014 15:12:09 +0000Key performance indicators
IT has developed a set of Key Performance Indicators that report various statistics to help UAB IT better understand and improve on how we interact with customers and respond to their needs.
The KPI charts measure, for example, how tickets are submitted to AskIT, the kind of issues for which customers are seeking help, the length of time tickets are open and the scores from customer satisfaction surveys/feedback.
Setting goals, measuring the results, communicating to our customers and acting on these Key Performance Indicators are critical to UAB IT's becoming a more service-oriented organization.
If you are a student enrolled in a subscribed school, you will have an account. Currently subscribed schools are the Schools of Business and Education. For more information, contact AskIT, 205-996-5555.
If you or your school have not yet subscribed, see the information below regarding what is available, set-up and how to request a subscription.
UAB has an agreement in place with Qualtrics that provides a survey tool to the UAB campus community at a discounted price to what is available to individual users and schools direclty from Qualtrics. School-level subscriptions include faculty, staff, and students. All other subscription levels include only employees (faculty/staff). The licensing is for campus only and does not include the UAB Hospital. The agreement with Qualtrics includes a Business Associate Agreement that covers HIPAA as well.
If your school or department previously had a subscription directly with Qualtrics, those subscriptions are now included under the discounted campus agreement offering. Contact AskIT (askit@uab.edu) for information on migrating your surveys to the new subscription.
The Qualtrics Research Suite is a powerful online survey tool that allows you to build complex surveys that fulfill a variety of research needs. You can use this tool to build surveys, distribute surveys and analyze responses, all from one convenient online location!
UAB Information Technology strives to provide consistent, accessible, personalized and collaborative environments to enhance the student experience. The quicklinks below provide a 'get-started' list of the most common services students ask about. For even more information and resources available to the student community visit uab.edu/it/home/students.
BlazerID and Password
Most of UAB's secured online resources require you to log in using your BlazerID and password. You probably already have a BlazerID; however, if you are not sure or if you need to change your password, you can visit BlazerID Central at uab.edu/blazerid. As of January 1, 2014 a new password/passphrase standard is in effect. In accordance with the new standard student passwords will expire at 180 day intervals. You will receive multiple advance notifications of a pending password expiration date.
BlazerNet
Using your BlazerID and password, log into BlazerNet, UAB's student portal - uab.edu/blazernet. From there you will be able to link to class registration, grades, financial aid and other academic resources.
E-mail
Your UAB e-mail address (BlazerID@uab.edu) is the place to look for all official correspondence from UAB. To check or update your e-mail preferences, visit BlazerID Central at uab.edu/blazerid. To register a UAB account, click "Get A UAB Email Account" on the left side of the web page. UAB has transitioned students to Microsoft Office 365 email. This provides 1TB of storage plus other features. If your email account has been migrated to Office 365, you should use to access your mailbox. For help with email configuration, visit the FAQ link:touab.edu/it/email.
File Size & UAB Dropbox
Your Office 365 mailbox has 1TB of space, and the size limit for attachments is 30MB. Large attachments should be sent via the UAB Drop Box at uab.edu/dropbox.
Wireless Networks
Stay connected on campus by accessing the UAB WiFi network using your BlazerID and password:uab.edu/it/wireless. For information about Apogee ResNet in the dorms, click here.
Online courses are available via Canvas (log in with your BlazerID and password at uab.edu/canvas). Training and support opportunities are available at the site.
Recommended System Specifications & Computer Setup
UAB IT provides recommendations on computer specifications for Apple Macintosh and Microsoft Windows PC laptop and desktop systems, and guidance on how to prepare your computer for use at UAB (before you arrive on campus). Visit uab.edu/it/students and select from the available resources for more detail.
Software & Computers
UAB IT offers an extensive library of software for free or at discounted pricing, including antivirus software, Microsoft Office products and more. Microsoft Office products are available to students for free through their Office 365 accounts, along with free storage on OneDrive. Through UAB's relationship with Dell, many computer products are available at a discount to students (and parents on behalf of students). Visit uab.edu/it/students and select from the available resources for more details.
Computer Labs
UAB maintains several student computing labs which are open to all current students with a valid BlazerID. For locations and hours, visit uab.edu/it/labs.
The Higher Education Opportunity Act (HEOA) includes provisions to reduce the illegal uploading and downloading of copyrighted works through peer-to-peer (P2P) file sharing of movies, videos, music, etc. More information, including how UAB detects and responds to illegal downloading activity, can be found at uab.edu/it/heoa.
IT Policies
Individuals who use UAB technology resources are required to read the Acceptable Use Policy in its entirety. This and other IT policies, standards and best practices can be found on the UAB IT website: uab.edu/it/policies.
Help Desk
For support with all things IT contact AskIT, UAB's IT help desk. Many self-help articles and FAQs are available on the AskIT website. To access the FAQs, open a ticket or chat with an agent visit uab.edu/askit, or call AskIT at 205-996-5555. Hours of operation vary and are posted on the website.
eNotify
Students can register their cell phone for various notifications from around campus. From notifications about postings in the learning management system, to reminders about registration deadlines, to being able to reset your BlazerID password remotely (24x7)...it all starts with registering your cell phone and selecting which services you want to take advantage of. Visit uab.edu/enotify and sign up today.
The VMware Academic Program, provided as a service to the UAB STEM Community through UAB IT, accelerates instruction and research in the rapidly expanding area of virtualized infrastructure by providing faculty and students involved with science, technology, engineering, and math courses (STEM) with access to the virtualization technologies most widely used in commercial production environments.
STEM Faculty can use VMware software under specific usage guidelines in a variety of areas of academic research and classroom instruction.
STEM Students can use this software free of charge for one year with yearly renewals as part of qualified coursework or research projects.
{slide=Who Has Access to the VMWare Academic Program?}
With UAB's annual subscription qualified members of the academic community in a STEM course can utilize the VMware Academic Program in the following areas:
Instruction – STEM Faculty within member institutions gain access to VMware software licenses free of cost for the purpose of classroom instruction. STEM Students taking qualified courses can also install program software on their personal computers.
Research – STEM Faculty within member institutions gain access to VMware software licenses free of cost as a part of their research projects. Program software can be installed in research labs (open a ticket with AskIT (uab.edu/askit) to inquire about lab installations) as well on the personal computers of faculty and students involved in research projects.
Use of VMware software for instruction and research is governed by specific program guidelines and the conditions described within the VMware Academic Program EULA (End-User License Agreement) and all faculty/students installing VMWare products should be familiar with the licensing and comply. The use of software for infrastructure purposes is governed by the VMware Commercial EULA and not included under this Academic Program.
{/slide}
{slide=What are the Licensing/Compliance Requirements for Using the VMWare Products?}
VMWare maintains strict compliance guidelines for the Academic Program and the following links are provided to ensure that specific licensing details are always the most up to date version and available to the UAB Community. Each user of this program is responsible for ensuring they understand and are in compliance with the licensing requirements at all times.
The free single use licenses provided through The VMware Academic Program may be used for instruction and non-commercial research only. Please refer to the definitions of instructional and research use below
Lab licenses may only be installed in lab environments where the lab is primarily used for instructional and research purposes.
Program software installed in shared lab environments can be used across different courses offered by different faculty members.
Faculty members as well as staff directly involved in administering systems and providing support for program software may install the software on their personal computers
Students taking qualified courses or conducting research can access program software within lab machines or download programs software on their personal computers. Students receiving licenses through a qualifying course or research project may use the licenses after the course or project is concluded.
Multiple academic groups in an institution may join the Program if each group meets the eligibility requirements.
Every copy of the software must be a true and complete copy and it must include all copyright and trademark notices. All software made available must include all of the files.
Examples of Unacceptable Use
Students who are in an approved department but are not taking courses that lead to credit or a certificate or who are not involved in relevant research projects are not eligible to use the software.
Students, faculty members, or other parties that received a license under the program but no longer attend or are employed by the institution.
Staff members who are not directly involved with system administration related to the program, such as administrative assistants, may not install the software on their personal computers.
Software that is part of the program may not be shared with non-approved departments. However, it may be installed on shared labs if the approved department's students regularly use that lab.
The designated Program Administrator for the member approved may not be a teaching assistant or a student. However, teaching assistants or students may help the Program Administrator with the program.
The software provided by VMAP may not be sold, rented, leased, or transferred to any third party including contractors, consultants, other companies, and other department personnel.
Software cannot be used for infrastructure purposes. Licenses acquired through the VMware Academic Program are for instructional, research and personal use only.
The software provided by VMAP may not be used for any purpose outside of instructional, research and personal use.
vSphere licenses provided under this program may not be used for desktop virtualization.
Use of free VMware software for instruction and research is governed by the specific program guidelines and the conditions described within the Academic EULA and the use of software for infrastructure purposes is governed by the VMware EULA for each of the products.
Definitions of Instructional, Research and Infrastructure Use
Instructional use is defined as conducting educational classes, labs, or related programs for teaching or learning concepts related to the products that are part of this program.
Research use is defined as conducting not-for-profit research projects.
Infrastructure use is defined as use of software as a part of the institution's or department's infrastructure that's not intended for specific classroom instruction or research project
IMPORTANT: These guidelines are provided for your convenience only. Please refer to the VMware Academic Program EULA for specific license rights.
{/slide}
{slide=What Products are Included?}
For STEM students and faculty/staff
VMware Workstation
VMware Fusion
VMware Player
VMware eLearning
VMware Sales Professional Certification
For STEM faculty/staff only
VMware vSphere Enterprise
VMware vCenter Server Standard
VMware vCloud Director
{/slide}
{slide=How to Obtain Software}
Software is available by download only to faculty/staff/students via the website below. Logon using your BlazerID and Password. UAB will validate your participation in the program and pass the appropriate information to the web store. All UAB users can logon to the site, but only those faculty/staff/students validated as STEM will be allowed to actually order products.
Through UAB's relationship with Dell, many products are available to students (and parents on behalf of students) and faculty/staff for purchase for home use. Check this page often as Dell regularly provides notices of sales and discounted items and they will be posted here. Remember, these are Dell's prices and are not negotiated by UAB, but simply discounted offerings that Dell is making available to the education community. You will need the UAB Member ID provided below.
Beginning April 30, 2014, UAB has been upgrading students to Microsoft Office 365, a new cloud-based platform for e-mail, file storage and Microsoft Office applications (Word, PowerPoint, Excel). This new service is free of charge for students and provides the following benefits:
Students who prefer to work offline will be able to download the Office applications and continue using their preferred e-mail clients. For more details about Microsoft Office 365 for students, click here.
UAB maintains both a Campus agreement and a Select agreement with Microsoft. Each user of software under the Microsoft agreements must use it subject to and strictly in accordance with the terms, conditions, limitations, and restrictions contained in the agreements. All software products are (a) licensed by Microsoft and (b) may not be copied or transferred to a third party.
Software included in the Campus Agreement is licensed on an annually recurring basis. UAB does not have a perpetual license to the software, but only the right to use the software as long as the agreement is renewed/paid annually. Under the agreement UAB receives rights to install the software on all UAB owned/leased systems, home-use rights for faculty/staff (with limitations-see below), student-use rights (with limitations-see below) and all version upgrades that MS may release during the term of the agreement. While the Campus Agreement reduces the complexity of licensing and paying for these campus-wide applications, it does not give UAB users the right to install the applications in any way that violates the rights granted by Microsoft.
Software under the Select Agreement is for UAB Faculty/Staff only and is mostly licensed on a one-time purchase basis with optional Software Assurance for version upgrades. Software under the Select agreement must be purchased prior to installation...no software under Select is available for use without first purchasing the applicable license.
CALs for Windows Terminal Server are included only up through Windows Server 2003.
Windows Upgrade requires that a full operating system already be licensed on the system. Only a right to upgrade is included here.
UAB faculty and staff may continue to use and install previous versions.
Microsoft Campus Server Platform
UAB's campus agreement covers the following server applications and all associated CALs for faculty, staff, and students:
Windows Server - all editions
SharePoint Server - all editions including Internet sites
Exchange Server - all editions
System Center Config Manager - server and ML Std & Enterprise
All external connectors
SQL Server
BizTalk Server
MS Desktop Optimization Pack (faculty/staff only)
All CALs for the above server product
Windows Remote Desktop CALs (old Windows Terminal Server)
Software should be requested via the IT Software Library website for installation on UAB owned systems.
Microsoft Select Products - Exclusively for Faculty/Staff purchases for use on UAB owned equipment, all other Microsoft products not included under the Campus Agreement must be purchased separately and can be obtained at a discount through our Microsoft Academic Select agreement. This would include all of the server products and other frequently requested items such as Visio and Project.
Virtually all software purchased under the Select agreement is granted as a perpetual license with a one-time payment. Software Assurance (SA) is available for an extra fee that provides upgrades to any new versions released during the time the purchase is covered by SA. SA must be purchased for the full remaining time the Select Agreement is scheduled to be in effect. UAB's Select Agreement runs through November 2013, thereby requiring that any SA purchases also run through November 2013. SA is sold for the remaining months left in the Select agreement, so if you purchase a product with SA in September of 2011, you will pay for 2 years and 2 months of SA (September 2011 through November 2013).
Once SA benefits expire the user still owns the perpetual license and any version upgrades that were released during the SA term. While SA is not required and not always cost effective, users should pay close attention to when new version upgrades/releases are planned by MS as it may make sense to purchase SA especially if a purchase must be made immediately and a new release is only a few months away.
Contact AskIT at 205-996-5555 or submit a ticket online at for questions related to the MS Select Agreement.
Office for Mac Professional includes: Word, Excel, PowerPoint, and Entourage.
Windows Upgrade: requires that a full operating system already be licensed on the system. Only a right to upgrade is included here. Students should note that this is a limited license that requires removal of the upgraded operating system when the student graduates or is no longer a student of the University. Careful consideration should be given prior to utilizing this upgrade option as removal of an upgrade may pose significant risk to the overall functionality of the student's system.
Home use installations may not use the same media as provided to faculty/staff for installation of the applications on UAB owned equipment, but must use the specific media and license keys provided through the Bookstore or downloaded from the Kivuto website.
Use of the software must be for the exclusive use of the faculty/staff (home) and must be deleted upon termination of the Campus Agreement or upon leaving the University.
Users mus accept a Use Acceptance Form at the time of license purchase indicating their understanding and acceptance of the license rights.
{/slide}
{tab=Students}
For installation on personally owned systems only, these Microsoft products are available to students:
At no cost to students:
Microsoft Office 365, with cloud storage and access to Office programs. Click here for instructions on registering and downloading.
Installations on UAB owned systems should be running Windows 7 Enterprise and Office 2010 Enterprise Windows 8 and Office 2013 are currently available only to TIMGroup members for testing.
{slide=Windows 7 and Windows 8}
Windows 7 and 8 employ the same licensing model as Windows Vista requiring a 'key server' at UAB to 'authorize' each installation of Vista. Where systems are not connected to the network for long periods of time, an alternate method utilizing a limited-use key will be available but on a restricted basis. UAB IT has set up a key server for testing and is making Windows 8 available to the TIMGroup members for testing within their areas.
Click here to be directed to the Software login page. Once logged in select Windows 7 in the dropdown box.
Additional information on Windows 7 (including hardware requirements) is available from Microsoft at:
According to Microsoft "DreamSpark is simple: it's all about giving students Microsoft professional-level developer and designer tools at no cost so that students can chase their dreams and create the next big breakthrough in technology - or just get a head start on their career." While most of the software is free, some items are at a small cost and if ordered you must provide a valid form of payment. However, those fee-based products should not be required as part of any course at UAB.
DreamSpark helps educators teach the latest technologies and experiment in research. To make learning more motivating, relevant, and engaging for today's students requires a diverse set of resources. DreamSpark gives educators the resources to ensure their classrooms always have the latest technologies to challenges, motivate, and keep students engaged in new ways.
Access to the Dreamspark program is through an external webportal managed by UAB IT. Login using your BlazerID and strong password (don't worry, the authentication takes place using a secure connection back to UAB...your password is never provided to the external website).
NOTE: While anyone with a valid BlazerID can login to the Dreamspark site, only those students and faculty engaged in a STEM program are currently authorized to order/download any software. Your ability to participate in the program is based on the information UAB passes to Dreamspark during the login process.
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Before financial problems can be solved, they need to be fully understood. Since in-depth quantitative modeling techniques are a powerful tool to understanding the drivers associated with financial problems, one would need a solid grasp of these techniques before being able to unlock their full potential of the methods used. In The Mathematics of Financial Models, the author presents real world solutions to the everyday problems facing financial professionals. With interactive tools such as spreadsheets for valuation, pricing, and modeling, this resource combines highly mathematical quantitative analysis with useful, practical methodologies to create an essential guide for investment and risk-management professionals facing modeling issues in insurance, derivatives valuation, and pension benefits, among others. In addition to this, this resource also provides the relevant tools like matrices, calculus, statistics and numerical analysis that are used to build the quantitative methods used.
Financial analysts, investment professionals, risk-management professionals, and graduate students will find applicable
information throughout the book, and gain from the self-study exercises and the refresher course on key mathematical topics. Equipped with tips and information, The Mathematics of Financial Models - Provides practical methodologies based on mathematical quantitative analysis to help analysts, investment and risk-management professionals better navigate client issues - Contains interactive tools that demonstrate the power of analysis and modeling - Helps financial professionals become more familiar with the challenges across a range of industries - Includes a mathematics refresher course and plenty of exercises to get readers up to speed
The Mathematics of Financial Models is an in-depth guide that helps readers break through common client financial problems and emerge with clearer strategies for solving issues in the future.
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READ MORE >
DR. KANNOO RAVINDRAN consults with corporations on investments, derivatives trading, modeling, and risk management. He also lectures around the world on these topics and runs a private equity fund. Dr. Ravindran pioneered the use of derivatives to manage risks embedded in variable annuity
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Mathematics 309 - the elementary geometry of wave motion
Topics covered on this page:
Part I - Scaling and Shifting Graphs Part II - Wave functions in 1D Part III - Affine Functions in 2D and 3D Part IV - Waves in 2D and 3D and the Wave Equation
Part I - scaling and shifting
One way of obtaining one
graph from another is by scaling and shifting
either x
or y or both, so
that the graph y=f(x)
becomes the graph
y = af(bx + c) + d. The way to see what happens
to the graph is to understand what happens in simple steps
with just one change at a time.
y = f(x)
y = 2f(x)
All y-values on the graph are scaled by 2.
In subsituting cf for f,
vertical distances are scaled by c.
y = f(x)
y = f(x)+1 1 is added to all y values.
y = f(x)
y = f(2x)
The height at x on the new graph is
equal to
the height at 2x on the old one.
The new graph is obtained by
compressing
the old one horizontally by 2.
In substituting cx for x,
horizontal distances are scaled by 1/c.
y = f(x)
y = f(x+1)
The height at x on the new graph
is equal to
the height at x+1 on the old one.
The new graph is obtained by
shifting
the old one 1 to the left.
y = f(x)
y = f(2x-1)+1
Only the last one is tricky,
since it involves
a sequence of substitutions.
In order to see which ones,
we unravel the process.
The function f(2x-1)+1 is obtained
from f(2x-1) by adding 1.
The function f(2x-1) is obtained
from f(x-1) by substituting 2x
for x.
Part II - Wave functions in 1D
This section should be read by high school graduates with the
minimum of grade 12 knowledge of math. Some physics from secondary school will
also be useful for this page. But the author of this website assumes that the
reader carries certain basic knowledge about trigonometry.
GOAL: The main goal of this section is to introduce wave functions in one
dimension while using parameters that have been traditional to physics when
involving light as a wave. (The other properties of light will not be discussed
here as it digresses from the discussion of waves.) In this first section of
wave functions of the first dimension we look at the basic building block; the
function y = cos (x) and it's relations to waves before discussing changes that
can be made to this wave function. Look at the graph below to see what the graph
looks like. (In this case we use radians as the x value.)
We first start off by introducing vocabulary that will help us in our
discussion about wave equations.
CYCLE: A cycle of a periodic function is a part of its graph from any point
to the first point where the graph starts repeating. In the case of the cosine
graph a cycle is repeated every horizontal length of 2 . So one cycle consists
of 2 , 2 cycles consist of 4 , 3 cycles consist of 6 and so on.
CRESTS: The peak height of of a periodic function. In the case of cos(x) there is a crest at every n x 2.
WAVELENGTH: This is the horizontal length between two consecutive crests. In the 1st graph just above the wavelength is 2 . In the following functions we will denote wavelenth with the Greek letter lambda ().
PERIOD: The time it takes to go through one cycle.
VELOCITY: The speed that an object travels with a specific direction. In this case our object is a wave and will be denoted by the letter C.
FREQUENCY: There are two ways to define frequency they are 1) cycles/second or 2) if dealing with radians we would define it as radians per second. The frequency is denoted by the Greek letter omega ().
AMPLITUDE:This is the vertical distance in which a trough and crest are away from a horizontal line. (Sidenote: A trough is the lowest point in periodic graph.) So for example the Amplitude for a cos(x) graph would be 1, since 1 unit is the distace away from a crest and a trough with the horizontal line being y=0. We denote the amplitude for one dimensional wave graphs with the capital letter A.
Now that we're done all this terminology and Greek letter referencing we can now begin to move onto the more interesting material of wave functions.
Let us suppose that we want the equation of a wave that has not been changed horizontally or vertically at time zero. Then what would it's graph be? ANSWER: The graph would be y=cos(x) since nothing has changed.
But what if the wave starts to move and in a horizontal direction, what would the new function look like after time t?
ANSWER: It is important to note here that the graph has shifted a certain amount of distance away from the origin. The key word being here is distance. The formula for distance in this case is velocity*time (C*t). So our new graph with just horizontal movement occuring is y=cos(x-Ct) if the wave moves in the positive direction and is y=cos(x+Ct) if the wave moves in the negative direction of the X-axis.
The Following graph shows a horizontal shift of in the positive X-axis direction. The velocity in this case is radians per second and the time for the shift to happen is 1 second.
Now that we know how to shift, is there a way to determine what the cosine function if the wavelength is no longer 2? For example what if we noticed that the the graph has compressed or stretched in the horizontal direction compared to f(x)=cos(x). What would the new wave equation be then?
ANSWER: To determine the new equation we need to know what the new wave length of the graph is. Once we know this information then we can proceed to find the equation of the wave. The equation of the graph that deals with compression and stretching is f(x)= cos[(2/)*x].
If 2 < 1 then the graph is being stretched by a factor of /2 with comparison to the f(x)=cos(x) graph. If it happens that 2 >1 then the opposite occurs and the graph is shrunk by a factor of /2 Let us suppose our new wave function has a wave length of 4, then our function is written as follows. f(x)=cos[(2/4)*x]=cos([1/2]*x).
The following graph shows the difference between cos(x) and cos([1/2]*x)
Say that we are given the function instead of the wave length, can we determine the wave length from such a function?
ANSWER: A simple answer is yes. Let cos(Ax) be our graph, with A > 1, then we have a graph that is compressed by a factor of 1/a, then using the following equation we get the wave length of the graph. 2/=(A), then we isolate then =2/A.
The next thing to tackle is the vertical compresion or stretching of the graph. How is this done?
ANSWER: We put the compression or stretching factor in front of the function. There is a direct relationship when we put this number in front of the cosine function. So for example if we wanted a vertical stretch of 2, then the new function would be f(x)=2cos(x). If we wanted to compress the graph vertically by a factor of 1/2 for the cosine graph then our new function would then become f(x)=(1/2)cos(x).
The following graph shows a stretching and compressing of a cosine graph.
Now that we know the basics of waves and the different equations, we can get fancy and combine two or more together to produce a more sophisticated graph. For example the graph below is f(x)=2cos((1/2)(X-)).
To get the above graph we would shift in the right direction by a value of Pi, then expand horizontally by a factor of 2 and then stretch vertically by the factor of 2 when using the cos(x) graph as the comparison. The graph represents at time t=1.
If you've noticed, none of the equations have used frequency directly. It must be noted that = (2C)/
So our equation can be manipulated into the following form
y=Acos ((2)/)(x-Ct))
y=Acos((2/)x-(2C)/)t)
So now we replace terms and use frequency directly into the function and Voila we get...
y=Acos((2/)x-t)
It should be noted that if we are given two of the following three, velocity, wave length. For example manipulating the formula /2=C
The period can be found by letter T=period and having T=2/ y=Acos((2)x-(2C)/)t)
Part III - Affine functions in 2D and 3D
Hmm. Where do we start with this topic? First of all, you need to know what
an affine function is. An affine function is any function that can
be represented as:
f(x) = ax + b,
where a and b are some arbitrary constants and x is a variable. That was the 1D form. In 2D, we add another variable to the equation, and
this changes the function form to:
f(x, y) = ax + by + c,
where c is another arbitrary constant and y is the extra variable that has been
added.In 3D, this equation takes the form:
f(x, y, z) = ax + by + cz + d,
where d is another arbitrary constant and z another variable that we need to
worry about. Now, let's take a look at how these functions behave in 2D (3D functions behave in the
same manner, except that you have to add another dimension to the graph. Since this is
hard to convey on graphs, we will be restricting our discussion to 2D graphs).
We will set f(x) = 0. In the grand scheme of things, this is usually done because we can
always rewrite this equation as C = ax + by where C is the combination of f(x)
and c.
There are many different cases to consider. Let us now take a look at them.
a = 0
The equation reduces to by = c. These equations are just horizontal lines.
b = 0
The equation reduces to ax = c. These equations are just vertical lines.
Ok, so now we want to express all the above cases in a simpler model. Let's look at
level lines (a level line is a curve where a function has a single value) of the function
ax + by = C
If you look at the equation ax + by = C and set C to 0, then we see that
this is [ a b ].[x y]' = 0, from linear algebra. This means that [x y] is perpendicular
to the vector [a b]'.
In fact, if we put C back into the equation, we see that all level lines are
perpendicular to [a b]'. In the graph below, [a b] was chosen to be [1 1] as an example.
One thing that is useful and handy to know concerning affine functions - that would be
the distance between level lines in a set (C varies, but [a b] is chosen and stays
constant within the set).
To figure this out, think of the vector [a b] as the distance between level lines.
Calculating the length of the vector would be equivalent to calculating the distance between level
lines! Since the distance from the line ax + by = 0 would be c1 / sqrt( a^2 + b^2 ) (using
our knowledge of vector algebra), the general formula for this would be:
distance = (c2-c1) / sqrt( a^2 + b^2 )
This effectively calculates the distance between level lines. This distance is also
signed (positive or negative), indicating the direction in which the level line lies.
Part IV - Waves in 2D and 3D and the Wave Equation
In order to understand waves in multidimensions, namely in 2 and 3 dimensions, we must have a good
grasp of the wave equation in 1 dimension. Please refer to the second section of this page titled "Wave Functions in 1 Dimension".
In the one dimensional case, we have:
1) f(x)=Acos[(2/)*(x-ct)]
A = amplitude, or height of the wave
= 3.14159265358979323846264338327950288419716939937510....
= the wavelength
Whereas in the 2 and 3 Dimensional case respectively, consider
2) f(x,y)=Acos(ax+by-ct)+g
3) f(x,y,z)=Acos(ax+by+cz-dt)+g
In the 2 dimensional case, a and b are the stretching/compressing factors on the axises x and y respectively. (This
equation is actually the wave equation as a function of space x,y and time t.)
Similarly, in the 3 dimensional case, a, b, and c are the stretching/compressing factors on the axises x, y, and
z axises accordingly. (Here, the wave equation as a function of x,y,z and t. This would make it impossible to graph since
it would require using four axises.)
What does it mean by stretching and compressing factors? Let's take a look at the the wave equation in 2D.
Here are some graphs of the 2D equation (in 3D). Remembering what you already know from the section on "Wave Functions
in 1D", apply this knowledge to the 2D case. We have the amplitude A which is going to stretch all values of f(x,y) by a factor of A. If A<1, then the waves will appear shallow, whereas when A>1, the waves will appear to be taller in comparison to the case when A=1.
For a and b >1, points on the x and y axises are compressed by a factor of 1/a and 1/b respectively. However, if a and b <1, then points on the x and y axises are stretched out because of the factor 1/a and 1/b.
At time t=0, f(x,y)=Acos(ax+by) where [a,b] is the vector perpendicular to the waves (level lines) and is a multiple of [a,b]. The signed distance from level 0 to level 2 is 2/[(a^2+b^2)^0.5], also the length of . However, as time increases, the wave moves in the positive xy plane given c is the velocity in the equation
f(x,y)=Acos(ax+by-ct)
However, it would move in the opposite direction in the negative xy plane if c were negative, changing the wave equation to
f(x,y)=Acos(ax+by+ct).
Finally, in the equation f(x,y)=Acos(ax+by-ct)+g, the graph is shifted by a factor of g on the f(x,y) axis.
We would apply similar shifting and scaling techniques for graphs of 3 dimensions if it were at all possible to conceive.
And now, a couple of final animations to leave you with (which mimicks wave-like motion)
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A full course in differential equations involves applications of derivatives to be studied after two or three semester courses in calculus. A derivative is the rate of change of one quantity with respect to another; for example, the rate
Although Wikipedia is a great place to find information, it's subject to incomplete citations, biased views, and inaccuracies. And when you absolutely have to have undisputable facts, that's just not good enough.
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Should you grade homework? NO, I don't think so (at the freshman level). It could be LOTS of work for you, and hard to tell what is the student's work and what is his/her tutor's work (or the work of a classmate). However, a daily or weekly quiz (consisting of 1 or 2 problems) might be a good idea. Your main obligation is getting your M.S. degree - you may need to budget your time wisely.
3. Tests
Make test questions similar to the in-class examples - maybe exactly the same... copy problems out of the book!
No more than about 10 questions per test (depending on difficulty - this is maybe not a reasonable number of multiple choice questions, though).
Spread problems out through the material to reflect amount of class time spent on the topics.
Type the test,preferably in LaTeX so that you become proficient in this software and ready to type your thesis in LaTeX (you don't want to have to type your thesis, or any other mathematical work, in Word or WordPerfect!).
GIVE PARTIAL CREDIT!!! (Unfortunately, this does not apply to multiple choice tests [which are the norm in Probability and Statistics, MATH 1530].) Make sure the students are aware that you only give partial credit when answers are partially correct! Grading is hard, messy and partial credit is subjective!
Bonus questions are a good idea.
Write out a detailed solution for each test (the "key"), post it and put a copy on reserve in the library.
Leave space on the test for answers and maybe a box for their final answer.
Grade the tests "assembly line" style. This keeps a bit of anonymity of the students, objectivity, and uniformity of partial credit.
4. The Lectures
BE ORGANIZED!!! Start at the upper left-hand side of the board. Lecture "linearly." Don't go back and change the notes on the board or lecture by drawing arrows all over the place. Imagine yourself as the student and trying to write down a coherent version of the notes (at the same time, listening and trying to learn this new material).
Write in complete sentences. Use equal signs and respect all mathematical symbols.
DON'T WRITE INCORRECT THINGS ON THE BOARD!!!
Bring two colors of chalk to class to correct errors.
Work examples from the book (even numbered problems maybe).
Don't write on the board and then stand in front of it while lecturing - keep on the move!
Make eye contact with everyone in the class.
If you get stuck on a problem, don't start lying! If you don't know the answer right then and there, say "I don't know!" "Punt" and give a detailed and correct solution during the next class period after you have had time to think it through.
Don't be arrogant! you know much more than the students on the topic and you have nothing to prove. Above all, don't start making up stuff! It's okay to speculate or guess (sometimes it's even fun) if you don't know the answer, but make sure you label it as such.
Erase the board at the end of class. It's a nice thing to do for the next person using the room, but more importantly it gives the students time to approach you in a more informal setting.
5. Conclusion
Ask for help from the faculty.
Talk with your graduate student colleagues.
Mimic the teaching style of someone you consider a good teacher.
Lead by example: show that you understand the math and you work hard at preparing for class. If you are sloppy and unprepared, you will certainly be leading by example, unfortunately!
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It was the most interesting and interactive presentation of basic Calculus I had encountered to date, and have used similar methods for explanation and teaching since. In addition to my academic and teaching credentials, C++ was the main computer programming syntax for the majority of my Master'...
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Mathematics Course Descriptions
(A grade of "C" or better must be earned in the course used to satisfy the general education mathematics requirement.)
MATH 0803: Beginning Algebra
Content of this course is as follows: the language of algebra, fundamental operations, signed numbers, equations and problem solving 0803 must repeat the course in each subsequent semester until he or she earns a grade of C or better. Students who make a grade of C or better in MATH 0803 must enroll in MATH 0903 the following semester.
MATH 0903: Intermediate Algebra
Prerequisites: One unit of high school algebra, grade of C or better in MATH 0803, or consent of the Mathematics Department.
The purpose of this course is to prepare for college level mathematics those students whose mathematics background is inadequate. Content of the course is fundamental operations, linear equations, special products and factoring, fractions, functions, graphs, and systems of linear equations 0903 must repeat the course in each subsequent semester until he or she earns a grade of C or better.
MATH 1003: College Mathematics
ACTS Common Course - MATH1003
Prerequisites: Score of 19 or above on the mathematics subscore of the Enhanced ACT, score of 460 or above on the quantitative portion of SAT, score of 41 or above on the quantitative portion of the COMPASS mathematics section, or make a grade of C or higher in Math 0903.
The course focuses upon the mathematics of contemporary life. Topics include Planning and Scheduling schemes from Management Science, Data Analysis, Probability and Inference from Statistics, Voting Systems and Division Schemes from the science of Social Choice, and various Growth Models.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 1113: College Algebra
ACTS Common Course - MATH 1103
Prerequisites: Score of 19 or above on the mathematics portion of the ACTE exam, or score of 460 or above on the quantitative portion of SAT, or score of 41 or above on the COMPASS mathematics section, or grade of "C" or better in MATH 0903.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
Note: May not be taken for credit after completion of MATH 2703 or any higher level mathematics course.
MATH 1203: Plane Trigonometry
ACTS Common Course - MATH1203
Prerequisite: MATH 1113 or consent of Mathematics Department.
A study of the properties of the trigonometric functions and their graphs, solution of right and oblique triangles, formulas and identities, inverse functions, and trigonometric equations.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 1914: Precalculus
ACTS Common Course - MATH1305
Prerequisites: Completion of high school algebra I and II with a grade of C or better and a score of 19 or above on the mathematics portion of the ACTE exam, or score of 460 or above on the quantitative portion of the SAT, or score of 41 or above on the COMPASS mathematics section, or a grade of A*, B*, or C* in MATH 0903.
This course is designed to provide additional mathematical background before enrolling in the calculus sequence.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2033: Mathematical Concepts I
Prerequisite: MATH 1113, elementary education major
Elementary set theory, numeration systems, elementary number theory and the real number system.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2043: Mathematical Concepts II
Prerequisites: MATH 2033, elementary education major
A continuation of MATH 2033, including a study of the elementary concepts of probability and statistics, and an informal study of geometry.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2703: Discrete Mathematics
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2914: Calculus I
ACTS Common Course - MATH2405
Prerequisites: Math ACTE score of 24 or higher, or a grade of C or higher in MATH 1914 or MATH 1203 or consent of instructor.
This is the first of two courses covering the calculus of functions of a single variable. The content covers differentiation of all single variable functions and introduces integration of functions.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2924: Calculus II
ACTS Common Course - MATH2505
Prerequisite: MATH 2914 or equivalent
This is the second of two courses covering the calculus of functions of a single variable.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2934: Calculus III
ACTS Common Course - MATH2603
Prerequisite: MATH 2924 or equivalent
This is the third course in the elementary calculus sequence. It covers the calculus of functions of several variables.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 2981,2982,2983: Special Topics in Mathematics
Prerequisites: Math ACTE score of 22 or higher, or MATH 1113, or consent of instructor.
This course will be offered on an as-needed basis to cover topics in mathematics that are not otherwise covered in the curriculum. The content and credit for this course will vary according to the interests and needs of the student. This course may be repeated for credit if the course content differs.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 3003: Foundations of Number Systems
Prerequisite: MATH 2703
A brief review of elementary set theory, followed by the construction of the natural numbers, the integers, the rational numbers, the real numbers and the complex numbers accompanied by a development of the order and field properties.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 3033: Methods of Teaching Elementary Mathematics
Prerequisite: MATH 2043 and admission to Stage II.
A course on methods of teaching the mathematics of the elementary school using mathematical concepts and principles taught in these grades.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 3123: College Geometry
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 3153: Applied Statistics I
Prerequisite: MATH 2924
A balanced approach emphasizing both theory and applications will be taken. Topics include descriptive statistics, exploratory data analysis, probability and probability models, discrete and continuous random variables, confidence intervals, hypothesis testing, and control charts. Students will be required to collect data, use a current statistical software package to analyze the data, and make inferences based upon the data analysis as part of an individual and/ or group project.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 3173: Math Methods for Engineers
Offered: Annually
Cross-listed: ELEG 3173
Prerequisite: MATH 3243
This course is designed to give the undergraduate student an introduction to a variety of advanced mathematical techniques used in solving engineering problems. The course will cover linear algebra, complex variables, discrete mathematics, and applied statistics.
MATH 3203: Introduction to Analysis
Prerequisite: MATH 3003
A careful development of the real number system and the theory of calculus on the real line.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 3243: Differential Equations I
Prerequisite: MATH 2924
A study of differential equations of the first order; linear equations of higher order including the methods of undetermined coefficients and variation of parameters; linear equations with constant coefficients; special equations of order two and systems of linear first-order differential equations using matrices.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
Note: MATH 5103 may not be taken for credit after completion of MATH 4103 or equivalent.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4113: History of Mathematics
Prerequisite: MATH 2934
A study of selected topics from the history and nature of mathematics from ancient to modern times. Emphasis will be placed on the historical development of mathematics through a study of biographies of prominent mathematicians and the evolution of some important mathematical concepts. The fundamental role of mathematics in the rise, maintenance, and extension modern civilization will be considered.
Note: MATH 5113 may not be taken for credit after completion of this course.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4123: Mathematical Modeling
Prerequisites: MATH 2703 and MATH 3243
This course provides an introduction to the mathematical modeling process and applies this process to problems that may be modeled with pre senior level mathematics. Emphasis will be placed on connections of mathematics to application areas such as business, industry, economics, physical sciences, biological sciences, medicine and social sciences.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4133: Abstract Algebra II
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4153: Applied Statistics II
Prerequisite: MATH 3153
This course is a continuation of MATH 3153 with emphasis on experimental design, analysis of variance, and multiple regression analysis. Students will be required to design and carry out an experiment, use a current statistical software package to analyze the data, and make inferences based upon the analysis.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4173: Advanced Biostatistics
Prerequisites: An introductory statistics course or permission of instructor.
This course will include analysis of variance, one factor experiments, experimental design with two or more factors, linear and multiple regression analysis, and categorical data analysis.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4243: Differential Equations II
Prerequisites: MATH 3243 and MATH 4003 or consent of the instructor.
A continuation of MATH 3243 with emphasis on higher order and systems of differential equations.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4263: Mathematical Statistics
Prerequisite: MATH 3153
This is an introductory course in mathematical statistics. Topics include distribution functions (both discrete and continuous), multivariate distributions, distributions of functions of random variables, and statistical inference.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4273: Complex Variables
Prerequisite: MATH 2934
An introduction to complex variables. This course will emphasize the subject matter and skills needed for applications of complex variables in science, engineering, and mathematics. Topics will include complex numbers, analytic functions, elementary functions of a complex variable, mapping by elementary functions, integrals, series, residues and poles and conformal mapping.
Note: MATH 5273 may not be taken for credit after completion of this course.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4343: Introduction to Partial Differential Equations
Prerequisites: MATH 2934 and MATH 3243
This course is an introduction to partial differential equations with emphasis on applications to physical science and engineering. Analysis covers the equations of heat, wave, diffusion, Laplace, Dirichlet and Neumann equations. Course is suitable for senior level or first year graduate students in Mathematics, Physics, and Engineering.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4703: Special Methods in Mathematics
Prerequisites: SEED 2002 and junior standing or permission of the instructor.
This course, designed for prospective junior and senior high mathematics teachers, will provide the student with knowledge of current research and practice in mathematics education, a setting in which to apply that knowledge, and the opportunity to assess their teaching performance and formulate a plan for improvement.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4772: Mathematics Teaching Practicum
A course designed to provide mathematics education majors with experience in teaching mathematics and assessing student performance.
Note: A grade of C or better must be earned in the course used to satisfy the general education mathematics requirement.
MATH 4951,4952,4953,4954: Undergraduate Research in Mathematics
Offered: On demand
Prerequisite: Departmental approval
Advanced students carry out independent research activity relating to a significant problem in a major field of study. Supervised by faculty member. Formal report and presentation required. One to four credits depending on problem selected and effort made.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
MATH 4971: Mathematics Senior Seminar
Prerequisites: MATH 3203 or MATH 4033, or departmental approval.
Students will engage in a research project under the guidance of faculty research advisors. The research area will depend on the interests of the students and available expertise of faculty advisors. The students will present their findings before their peers, faculty advisors, and members of the Mathematics Department Assessment Committee.
MATH 4991,4992,4993,4994: Special Problems in Mathematics
The content and credit for this course will be designed to meet the needs of the student.
Note: A grade of C of better must be earned in this course if being used to satisfy the general education mathematics requirement.
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Valuation and risk management, two sides of the quant business, must be treated with equal sophistication, with equal respect, and with equal suspicion. And there must be closer interaction between them.
In education, valuation should not be the domain of the most abstract of mathematicians with risk management its more primitive partner. In practice, quants must not produce models that risk managers cannot understand.
At every stage of valuation and model development you must be asking questions about risk and robustness. It is dangerous to come up with some fancy model and only afterwards start asking questions about model error. Anyone who has ever calibrated a model knows that the methods used to mitigate model risk almost come as an afterthought, and are totally inconsistent with the original model. This need not be the case.
In the CQF we treat valuation and risk management as equals. The structure of the CQF is unashamedly mathematical. Module by module we add mathematical flexibility, and in each lecture you will see model risk and model robustness discussed alongside the theory of valuation. This is how quantitative finance ought to be taught. This is the mature approach to the subject, and it will help to resolve many of the discrepancies between finance theory and finance practice.
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Course in Enumeration
9783540390329
ISBN:
3540390324
Pub Date: 2007 Publisher: Springer
Summary: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more ...about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result.
Aigner, Martin is the author of Course in Enumeration, published 2007 under ISBN 9783540390329 and 3540390324. Three hundred nineteen Course in Enumeration textbooks are available for sale on ValoreBooks.com, fifty two used from the cheapest price of $61.64, or buy new starting at $61.64
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Pre Algebra Mathematics Prerequisite: DMAT 0066 or an appropriate assessment test score. Course Description: This course is designed to develop an understanding of fundamental operations using integers, fractions, decimals, percentages, and perimeter and area of basic geometric figure concepts, and to strengthen basic skills in mathematics. The course is planned primarily for students who need to review basic mathematical processes. (3 Lec.)
Coordinating Board Academic Approval Number 3201045119
Developmental Mathematics Prerequisite: An appropriate assessment test score or DMAT 0090. Course Description: This is a course in algebra which includes operations on real numbers, polynomials, special products and factoring, and linear equations. Also covered are graphs, systems of linear equations, exponents, quadratic equations and an introduction to complex numbers. (3 Lec.)
Coordinating Board Academic Approval Number 3201045119
Intermediate Algebra Prerequisite: An appropriate assessment test score or DMAT 0305. Course Description: This course is a study of relations and functions with special emphasis on linear and quadratic expressions and equations, including complex solutions. Also covered are absolute value, polynomial, radical and rational expressions and equations, and linear and absolute value inequalities. (3 Lec.)
Coordinating Board Academic Approval Number 3201045219
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A Mathematics Sampler: Topics for the Liberal Arts
This work presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics - including computers, perfect numbers and four-dimensional geometry - to exemplify its distinctive features.
Hardcover, 602 pages
Published
January 1st 2001
by Ardsley House
(first published January 1st 1988)
Community Reviews
This was a very informative book, and I really enjoyed working through its examples. It provides a moderately gentle introduction to set and group theory, and helped me understand some of the mathematical underpinnings of probability and statistics, including the assumptions that must be made for statistical theory to hold.
I couldn't list all the topics covered, but it did a good job on each one of them.
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The key things developed in the course are capability with fractions, ability to recognize patterns in solving problems, and applying the skills to solving word problems. Precalculus can be thought of as "Algebra 3," giving students the most difficult and complex Algebra problems and scenarios t
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...
More About
This Book
manipulative, pictorial, and independent practice. Lessons include worksheets or patterns and answer keys, and each section ends with a practice test and answer key.
What People Are Saying
From the Publisher
"This volume should be highly useful to all mathematics educatorsconcerned with increasing the achievement of students faced withhigh-stake tests based on currently accepted standards."
—David E. Boliver, professor of mathematics and statistics,University of Central Oklahoma
"The well-designed sequences of activities proceeding from theconcrete to pictorial to symbolic provide the needed structure forhelping students who struggle with high school math."
—Bill Juraschek, associate professor, University of Colorado atDenver
"The expertise that Dr. Thompson supplies to the field ofsecondary mathematics teaching is phenomenal. MathEssentials is a resource that will save countless hours ofresearch and preparation."
—Jim Wohlgehagen, secondary mathematics coordinator, Plano ISD,Plano, Texas
Related Subjects
Meet the Author
Frances McBroom Thompson, Ed.D., is professor of mathematics at Texas Woman's University. She has taught mathematics in junior and senior high schools and served as a K-12 mathematics specialist, and she is now an educational consultant for grades K-12. Dr. Thompson received her doctorate in mathematics education from the University of Georgia, and she is the author of numerous books including Hands-On Math!, Hands-On Algebra!, and Math Essentials, Middle School Level (all published by Jossey-Bass).
Read an Excerpt
Math Essentials, High School Level
John Wiley & Sons
Chapter One
Section 1
ALGEBRAIC THINKING AND APPLICATIONS
Objective 1: Simplify Algebraic Expressions Involving One or Two Variables
Students have great difficulty recognizing the differences among linear, quadratic, and constant terms in algebraic form. Exponents seem insignificant to them. Viewing each type of term as an area helps students visualize the role each term plays in an expression. The following activities provide experience with such visualization in the combining of like terms. It is assumed that students have already mastered the four operations with integers.
1. Give each pair of students a packet of tiles, two copies of Worksheet 1-1a, and a sheet of plain paper or tagboard (approximately 8.5 inches by 14 inches) for a building mat. If preferred, laminate the mats to make them more durable. Mats define a specific space on which to represent a problem being solved. If teacher-made tiles are used, each packet should contain the following in different colors of laminated tagboard: 8 square (quadratic) variable tiles, each 3 inches by 3 inches (color #1); 8 square variable tiles, each 3.25 inches by 3.25 inches (color #2); 12 rectangular (linear) variable tiles, 0.75 inches by 3 inches (color #1); 12 rectangular variable tiles, 0.75 inch by 3.25 inches (color #2); and 20 unit tiles, 0.75 inch by 0.75 inch (color #3). Each tile should have a large X drawn on one side to show the inverse of that tile. Use tagboard that is thick enough so that the X will not show through to the other side. Commercial tiles are also available for two different variables, but a large X must be drawn on one of the largest faces of each tile in order to represent the inverse of that tile when the X faces up.
2. The meaning of a large square tile needs to be connected to a long rectangular tile of the same color. Have students place a rectangular variable tile of color #1 (call it variable A) horizontally on the mat. Then have them place two more variable tiles below and parallel to the first tile on the mat. Ask: "If a single variable tile A is considered to cover an area of 1 by A, or A, how can we describe the arrangement indicated by these tiles on the mat?" ("3 rows of A.") "What product or area is this?" ("3A.") Ask: "How can we show A rows of A on the mat if we do not know what the value of A is?" Show students how to build several rows of one variable tile each, using one variable tile A as the multiplier, or "ruler," that indicates when to stop putting tiles in the product on the mat (see the illustration below). When the product is finished, the multiplier tile should be removed from the mat. Depending on the dimensions used to make the tiles, whether commercial or teacher-made, the width across several rectangular tiles placed with their longer sides touching may or may not match the length of the longer side of the same type of tile. Such a match is not important and should be deemphasized since the variable tile A is not considered to have a specific length or value in unit tiles. Therefore, although the width of 4 of the variable tile A may appear to match to one variable tile length as shown on the mat below, do not allow students to say that 4 rows of A equal 4A.
3. Ask: "Is there another single block that will cover the same surface area on the mat that the product A of A, or A(A), covers?" ("Yes. The large square tile in color #1; its side length equals the length of the variable tile A.") Again, discuss the idea that the large square tile in color #1 may or may not fit perfectly on top of the "A rows of A" tile arrangement; it will be close enough. Since both the square and rectangular tiles in color #1 are representing variables without known values, we want to maintain their variable nature as much as possible. Physical models like the tiles naturally have specific dimensions that affect or limit areas being built with the tiles, but for our purpose, we will assume that only the unit tiles may be used to represent exact amounts of area. We will now assign the large square tile in color #1 the name of A-squared, or [A.sup.2]. Hence, A rows of A equal [A.sup.2]. From now on, whenever A rows of A are needed, the large square tile will be used to show that amount of area on the mat.
4. Similarly the areas of the square and long rectangular variable tiles in color #2 might be described as B-squared, or [B.sup.2], and B, respectively. If an X appears on the top side of a variable tile, the inverse or opposite of the tile's area will be indicated. For product example, a B-squared tile with X on top will be called "the opposite or inverse of B-squared" and written as (-[B.sup.2]). Each small square tile in color #3 represents an area of 1 by 1, or 1 square unit of area. If a given set of unit tiles all have an X showing-for example, 5 tiles with X-then the tile value will be the "negative of 5 square units of area" and written as (-5). Note that area itself is an absolute measure, neither positive nor negative. Area, however, can be assigned a direction of movement in real applications; hence, we can consider the opposite or negative of a given area.
5. After the area of each type of tile is identified, have students do the exercises on Worksheet 1-1a. For each exercise, they should place a set of tiles on the building mat to show the first expression. Then they will either add more tiles to this initial set or remove some tiles from the set according to the second expression of the exercise.
6. After combining tiles that have the same amount of area, students should record an expression for the total or remaining area on the worksheet.
7. Discuss an addition exercise and a subtraction exercise with the class before allowing students to work the other exercises independently.
Have students place 3 large square (quadratic) variable tiles, 2 long rectangular (linear) variable tiles, and 5 negative unit tiles on the building mat to represent the first expression. Any such group of tiles is called a polynomial, that is, a combination of variable tiles and/or unit tiles. Leaving this set of tiles on the mat, have students place additional tiles on the mat below the initial tiles to represent the second expression. The second set should contain a quadratic variable tile with X showing, 3 linear variable tiles, and 2 unit tiles:
Ask: "Can any 0-pairs be made through joining, then removed from the mat?" (One 0-pair of the large quadratic tiles and two 0-pairs of the small unit tiles should be formed and removed from the building mat.) "Can you now describe the total in tiles still on the mat?" Since tiles for two of A-squared, 5 of A, and -3 remain on the mat, students should complete the recording of Exercise 1 on Worksheet 1-1a: (3[A.sup.2] + 2A -5) + (-[A.sup.2] + 3A + 2) = 2[A.sup.2] + 5A -3
Have students place tiles on their mats to show the first group. There should be 4 of the quadratic variable tile, 3 of the linear variable tile with the X-side showing for the inverse variable, and 4 positive unit tiles on the building mat. Discuss the idea that the subtraction symbol between the two polynomial groups means to remove each term in the second group from the first group. Ask: "Can we remove one quadratic variable tile from the original four? ("Yes; 3 quadratic variable tiles, or 3[A.sup.2], will remain.") "Can 2A be removed from -3A?" Since only inverse variable tiles are present initially, 0-pairs of A and -A tiles will need to be added to the mat until two of the variable A are seen. Then 2A can be removed, leaving 5 of -A on the mat. Similarly, -2 will be removed from +4 by first adding two 0-pairs of +1 and -1 to the mat. Then -2 can be removed from the mat, leaving +6. The mat arrangement of the initial tiles and the extra 0-pairs of tiles is shown here before any tile removal occurs. Have students complete Exercise 2 on Worksheet 1-1a by writing an expression for the tiles left on the mat: (4[A.sup.2] -3A + 4)-([A.sup.2] + 2A -2) = 3[A.sup.2] -5A + 6.
Remind students that when they use 0-pairs of a tile and remove one form of the tile (for example, positive), then the other form (for example, negative) remains to be added to the other tiles on the mat. Show students that when they needed to remove 2A from the mat earlier, two 0-pairs of A and -A were placed on the mat. After 2A was removed to show subtraction, the two inverse variable tiles, -2A, still remained on the mat to be combined with the other tiles for the final answer. Hence, a removal of a tile from the mat is equivalent to adding the inverse or opposite of that tile to the mat.
To confirm this, have students place the original group of tiles (4[A.sup.2] -3A + 4) on the mat again. The opposites needed (-[A.sup.2], -2A, and +2) should then be placed on the mat and combined with the original tiles. See the illustration below. Remove any 0-pairs formed, leaving tiles for 3[A.sup.2], -5A, and +6 on the mat as the answer. Finally, have students write another equation below Exercise 2 on Worksheet 1-1a, this time showing the alternate method that uses addition: (4[A.sup.2] - 3A + 4) + (-[A.sup.2]-2A = 3[A.sup.2]. - 5A + 6. Encourage students to use whichever of these two methods seems comfortable to them.
In the answer key for Worksheet 1-1a, when the coefficient of a final variable is 1, the number 1 will be written with the variable. This approach seems to be helpful to many students. Nevertheless, discuss the idea with the class that the 1 in such cases is often not recorded but simply understood as being there.
Building Sums and Differences Name ___________________ with Tiles Date ___________________
Build each polynomial exercise with tiles. Different variables require different tiles. Record the result beside the exercise. For each subtraction exercise, also write the alternate addition equation below the subtraction equation.
1. (3[A.sup.2] + 2A - 5) + (-[A.sup.2] + 3A + 2)
2. ([4A.sup.2] - 3A + 4) - ([A.sup.2]) + 2A - 2) =
3. (5[B].sup.2] + 3) - (2[B.sup.2] + 1) =
4. 2[A.sup.2] - 3A + 1) + (4A-5) =
5. (4A-2+[B.sup.2]) + (-6-2A)
6. 3A-(-[A.sup.2]-5)= 7. (5B.sup.2]-4)-(5[B.sup.2]-4[-[A.sup.2]) =
8. 3A-2[A.sup.2]-5+B-8+3[A.sup.2] =
Activity 2
Pictorial Stage Materials
Worksheet 1-1b Regular paper and pencil
Procedure
1. Give each student a copy of Worksheet 1-1b. Have students work in pairs, but they should draw the diagrams separately on their own worksheets. Large squares will be drawn for the quadratic variable, a long rectangle whose length equals an edge length of the large square will be drawn for the linear variable, and a small square will represent the integral unit. A large X should be drawn in the interior of a shape to show the inverse of that shape. If an exercise involves two different variables, letters need to be written on the drawn shapes to identify the different variables. The product of two different variables, for example, A and B, should be shown as a large rectangle similar in size to the quadratic squares and labeled as AB. The notation AB simply means A rows of B, or the area AB.
2. For addition exercises, students should draw the required shapes and connect any two shapes that represent a 0-pair. The remaining shapes will be recorded in symbols to show the sum.
3. For subtraction exercises, students will be asked to use either the removal method or the alternate method, which involves addition of inverses. To remove a shape, students should mark out the shape. When needed, two shapes should be drawn together as a 0-pair. For the alternate method, inverses of the subtrahend expression should be drawn and combined with the first expression to produce a sum. The result will be recorded symbolically.
4. When checking students' work after all are finished, allow time for students to explain their steps; do not just check for answers. Students need to practice expressing their ideas mathematically. Such verbal sharing is also very beneficial to auditory learners.
5. Discuss Exercises 1 and 2 on Worksheet 1-1b with the class before allowing partners to work together on their own.
Consider Exercise 1: (-3[B.sup.2] + B + 2) + ([B.sup.2]-4B + 1)Students should draw the necessary shapes on their papers to represent each polynomial group. The shapes for the first polynomial group may be drawn in a row from left to right following the order of the given terms. The shapes for the second polynomial group should be drawn as a second row below the first row, but students may rearrange the shapes and draw them below other like shapes in the first row. Since only one variable is involved, no labeling is needed for the shapes. Any 0-pairs should be connected. Remaining shapes will then be counted and recorded as the answer. A sample drawing is shown here:
The final equation will be as follows and should be recorded on Worksheet 1-1b: (-3[B.sup.2] + B + 2) + ([B.sup.2] - 4B + 1) = -2[B.sup.2] -3B + 3. At this point, begin to encourage students to record the terms of a polynomial with their exponents in decreasing order.
Now consider Exercise 2: ([A.sup.2] + 5A - 3) - (2[A.sup.2] + 3A + 2). Since the removal process is required for this exercise, students should draw shapes for the first polynomial group and then draw any 0-pairs below that group, which will be needed in order to mark out the shapes shown in the second group. The shapes remaining or not marked out in the finished diagram will be the difference. Here is the completed diagram:
The final equation should be recorded on Worksheet 1-1b as follows: ([A.sup.2] + 5A - 3)- (2[A.sup.2] + 3A + 2) = -[A.sup.2] + 2A - 5. It may be helpful for some students to write -1[A.sup.2] instead of -[A.sup.2] . This is acceptable notation
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Mathematics for Grob Basic Electronics
9780078271281
0078271282
Summary: Provides students with the mathematical principles needed to solve numerical problems in electricity and electronics. 13 chapters cover keeping track of the decimal point when multiplying and dividing; working with fractions; manipulating reciprocals; finding powers and roots of a number; powers of 10; logarithms; metric system; solving equations; trigonometry; binary and hexadecimal numbers; and complex numbers. ...> Bernard Grob is the author of Mathematics for Grob Basic Electronics, published 2002 under ISBN 9780078271281 and 0078271282. Three Mathematics for Grob Basic Electronics textbooks are available for sale on ValoreBooks.com, two used from the cheapest price of $21.89, or buy new starting at $116.95.[read more]
Ships From:Salem, ORShipping:Standard, ExpeditedComments:Has minor wear and/or markings. SKU:9780078271281-3-0-3 Orders ship the same or next business day... [more]
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Text Sets can be used to compile alternative texts for the students use. A big importance of text sets is that they contain materials that vary in length, difficulty, and text structure. This is crucial because you want to have material that can fit the needs of all students. Those below level, at level, and above. Some examples of text sets are…
In an algebra class system of equations will be a topic that you will encounter. Some students have a difficult time with this. An example question is
y= -3x – 2, 6x + 2y = -4. Here is an example text set that will help you with your students.
Khan Academy:
From their website it says for students: "Students can make use of our extensive library of content, including interactive challenges, assessments, and videos from any computer with access to the web."
This is a great resource for teachers to use to help students who either need additional help or to push students who need to be challenged. It is a free resource for any to use and walks you through step by step how to use the site. There is no level too low. This starts from the bottom and will allow the student to accomplish certain mathematical principles that they may have thought would have been impossible.
YouTube is full of instructional videos on a wide variety of levels and the brilliant thing about YouTube is that if one video does not make sense then just go to another. Here are two examples.
Purple Math is a website that students can visit and its purpose is to try and help struggling students gain an understanding. This does well about explain not only how to do the problem but how the problem would come up.
Wikipedia. I know this will make some people cringe but there are loads of useful information on the website. One benefit of Wikipedia is that whatever word the student does not know in the explanation they can usually click a link that will then explain to them that word.
This is just a short list of a text set and many will include different textbooks. And some students may not have Internet access to being able to provide a student with print outs from these websites could be extremely useful.
"Savvy teachers build upon the power of reading recommendations. Although face-to-face conversations about favorite selections can serve as powerful reading motivators for many students, social cataloging websites allow readers to connect, share, discuss, and archive their reading suggestions within and beyond their school settings."
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Math SolverFree for Windows 8 is a handy tool for performing frequently used operations used for solving math problems. You can use this tool for solving quadratic Equations or calculating the angles of a...
FGES - First Grade EquationSolver is an easy-to-use Command Line-based Open Source application that can solve Equations. Now you can use this C written software to solve the mathematical Equations that...
DeadLine is a Free program useful for solving Equations, plotting graphs and obtaining an in-depth analysis of a function. Designed especially for students and engineers, the Freeware combines graph plotting...
Quadratic Equation has the form ax2 + bx + c = 0. It will generally have two solutions; that is, two different values of x that make the Equation true.
It can happen that both solutions are the same...
Berkeley Madonna is arguably the fastest, most convenient, general purpose differential EquationSolver available today. It is relatively inexpensive and runs on both Windows and Mac OS. Developed on the...
MathGenius is a graphical tool intended to simplify your work in mathematics. By now it includes a graphical function plotter, a mechanism (still in development) to derive functions, and an EquationSolver....
OPEN DESIRE: experiment-protocol script interpreter and differential-EquationSolver for up to 20,000 scar or vector differential Equations. 13 integration rules. Compiles and executes immediately on command...
The Chasys Math was designed to be a suite of math utilities that includes a calculator featuring graph-plotting, complex numbers and visually-perfect algebraic method (Chasys Math Calculator), and a matrix...
Simple Solver is a Free Windows application that can simplify computer logic systems, Boolean Equations, and truth tables. The application includes six different tools:Logic Design Draw, Logic Simulation,...
FreeMat is a Free environment for rapid Engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB from Mathworks, and IDL from Research Systems, but is...
Simple Solver is a Free Windows application that can simplify computer logic systems, Boolean Equations, and truth tables. The application includes six different tools:Logic Design Draw, Logic Simulation,...
Universal Math Solver is a software package which, until now, students could only dream of. Universal Math Solver is a mathematical software which was designed to help you solve all the math problems....
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Should College Classes Ditch the Calculator?
Should College Classes Ditch the Calculator?
According to Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research and Development Center, using calculators in college math classes may be doing more harm than good. In a limited study conducted with undergraduate engineering students and published in the British Journal of Educational Technology, King has determined that our use of calculators may be serving as an alternative to an actual, deep understanding of mathematical material.
"We really can't assume that calculators are helping students," says King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
King, along with co-author and director of the Mathematics Education Centre at Loughborough University, Carol Robinson, conducted the study by interviewing 10 second-year undergraduate students who were enrolled in a competitive engineering program. The students were given a number of mathematical questions dealing with sine waves, which are mathematical curves that describe a smooth repetitive oscillation. To help solve the problems, the students were given the option of using a calculator instead of completing the work entirely by hand. Over half of the students questioned opted to utilize their calculators in order to solve the problems and plot the sine waves.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," says King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the work, King and Robinson interviewed the students about how they approached the material. One student who used the calculator stated that she had trouble remembering the rules for how sine waves operate, and found it generally easier to use a calculator instead. In contrast, however, a student who opted to complete the work without a calculator stated that they couldn't see why anyone would have trouble completing the question, but did admit that it would likely be easier with a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," says King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
Given the small sample size used in the study, it is entirely possible that King's findings are largely anecdotal in how our usage of calculators and understanding of mathematical concepts may positively or negatively correlate. However, King does stress that while all the evidence may not be in, his study does raise important questions regarding how, when and why students choose to use calculators, and in doing so, we may develop a more holistic approach to math instruction
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Getting into the nation's most competitive universities requires more than a good SAT score, it requires a perfect score. Perfect 800: SAT Math gives advanced students the tools needed to master the SAT math test. Covering areas including arithmetic concepts; algebra; geometry; and additional topics such as probability and weighted average, the book... more...
Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. This uncorrected soft cover reprint of the second edition places the emphasis on applications and... more...
This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coherent presentation of the state of art of the theory including detailed proofs and its applications to... more...
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation. more...
LearningExpress's 20 Minutes a Day guides make challenging subject areas more accessible by tackling one small part of a larger topic and building upon that knowledge with each passing day. Practical Math Success in 20 Minutes a Day features: ? A walkthrough of the fundamental concepts of pre-algebra, algebra, and geometry ? Hundreds of practice... more...
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Now you have all useful math formulas and definitions handy and can always refer to them. There are a lot of drawings (including 3D), explaining all symbols used in formulas. Range of material - high school.
The content is divided into sections and subsections so that it is easy to find any formula, definition or equation.
Many people have asked about integrals - already are, but here only at the secondary level. Advanced integrals are already available in a twin Matma2 application dedicated to the students.
There is also a paid version of the Math (MathPro), which does not show ads, and includes material from both Math and Math2 apps.
This is the first part of A-Level Maths e-notes. It includes several topics included in A-Level maths. (Numbers, Surds, Polynomials, Modulus, Inequalities, Trigonometry, Trigonometric identities, Triangles, Small angles, The Straight line, Functions, Limits, Differential Calculus, Higher Order Derivatives, Integration, Areas under curves, Logarithms, Rules of differentiation, Implicit Differentiation). Select a topic from the list or flip through the pages in portrait or landscape mode. Designed for all-size devices.Solving Equations as easy as using a pocket calculator. Any equations with an equals sign and the varable x can be entered. The solutions are calculated listed. Generally valid equations and insoluble equations are identified. Quadratic equations or higher degree equations are also solved, such as equations with exponential and logarithmic functions or trigonometric functions. The entered term is calculated if the entry has neither a variable nor an equals sign (pocket calculator function).
This is a Smart Worksheet on indices and logs. It consists of over 100 questions. The idea here is that you have a go at the problems first and then check out the video solution.
There are also useful tools embedded including an on-line calculator and an on-line equation solver. There is also an emailque button where you can ask a question about indices and logs and send it in.
Hope you enjoy the worksheet and any feedback is always appreciated. Cheers, Mark
When solving logarithm equations, we can only rely on our knowledge of the logarithm properties. Understanding what the properties mean will help you in the long run. Review with Mr. Defining Wizard all properties so you are prepared for any problem you face.
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Note: Algebra 1 and 2 sources are included here to ensure coverage of concepts that may be found on the CLEP (college level) test.
Choose one of the algebra textbooks as your main source. Work through the book, using the lectures/lessons found at the HippoCampus or SAS algebra 1 websites to help you understand each concept. Visit the Prentice Hall site for video lessons, and practice quizzes. In addition, print the worksheets found at the Kuta software site to reinforce your learning. The other sources are provided for further studying, if needed. (If, for instance, you find you are struggling with one textbook, try the other to see if it better suits your learning style.) Finish with the practice tests and end-of-course exams.
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handyCalc Calculator
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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Mathematics, "The Queen of Sciences" as called by Carl Friedrich Gauss, is the science of number, quantity, and space, either as abstract concepts or as applied to other disciplines (such as physics and engineering).
The distinguished authors of the top-quality books and textbooks listed under Research and Markets' Mathematics category are the world's leading researchers. These publications cover all the key areas in today's research. They are invaluable references, comprehensive and
readily accessible. When available, pre-publication titles are also included, so you can be sure not to miss the latest developments in your research field.
The readership of this category includes both graduate and undergraduate students, as well as researchers and mature mathematics.
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Johnson provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters have been updated with real–world data to make...
Text Mining: Applications and Theory presents the state-of-the-art algorithms for text mining from both the academic and industrial perspectives. The contributors span several countries and scientific...
When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized...
This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and...
This book provides an essential understanding of statistical concepts necessary for the analysis of genomic and proteomic data using computational techniques. The author presents both basic and advanced...
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic
In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions...
The fourth edition gives readers the skills to apply calculus on the job. It highlights the applications' connection with real–world concerns. The problems take advantage of computers and graphing calculators...
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field,...
Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically...
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This is an applied handbook for the application of data mining techniques in the CRM framework. It combines a technical and a business perspective to cover the needs of business users who are looking...
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Plenty of physics is taught via math, right? Like, this physical concept is embodied by this formula, etc. Is there any resource that goes the other way, i.e. follows general mathematical concept introduction order (e.g. derivatives, then integrals, and so on), but ties those concepts to physical processes as it does so, perhaps making them more concrete?
I don't know if it meets your criteria exactly, but I read about halfway through "A Tour of the Calculus" with my math-hating, physics-loving son to help teach him some math and convince him math was his friend. posted by Michele in California at 4:35 PM on June 20, 2012
Quite a few calculus books do this! Rule of thumb: the larger, heavier, more picture-filled, and less yellow a calc book is (Serge Lang, I'm looking at you), the more likely it is to have a lot of story problems. A large fraction of those are likely to be based in physics (mostly mechanical, but you definitely get some E/M stuff in e.g. Stewart). posted by AkzidenzGrotesk at 4:52 PM on June 20, 2012
There is a set of textbooks which go through a course of "mathematical physics". The course is different mathematical techniques (primarily in calculus) and all of the illustrations are physics problems. The one we used the most when I was in school was Arfken.
(Thirty years and four editions ago that was considered the best though there likely are better ones now.) posted by bukvich at 5:17 PM on June 20, 2012
I think most physics classes also teach the math as they go, even if it's only on a cursory level, or as review. I don't think you'll really learn the math completely that way, but it's usually enough so that you can follow along with the relevant material. At least the iTunesU classes I've watched on physics all do, and so do the khan academy physics videos. posted by empath at 5:55 PM on June 20, 2012
What level of math do you want? This may be higher than you need, but I gotta say, I never really understood the hard parts of multivariable calculus until I read Purcell's Electricity and Magnetism (and I am a 100% pure mathematician who doesn't even like physics.) I also really like Sternberg's Group Theory and Physics. (This corresponds roughly to a course that would be called "Abstract Algebra" -- usually taken after multivariable calculus, but for many people substantially easier.) posted by escabeche at 6:53 PM on June 20, 2012
The one we used the most when I was in school was Arfken.
*grimace* Arfken is a bit advanced, save that for learning bessel functions, not intro calc.
Try an intro physics book, of the sort used to teach physics to first-years in the major.
Halliday and Resnick, Physics, 3rd Ed, teaches the derivative when it teaches the concept of velocity, and introduces the integral with the copy of work. Tipler, Physics - extended version, 3rd Ed, teaches the derivative when it teaches the concept of velocity and introduces the integral a short bit later at the end of that section on motion in one dimension.
Either one should be fine; and cheap. Get the 1990, 1991 version; newer ones may have a more info-box filled style which can be tedious. posted by sebastienbailard at 7:23 PM on June 20, 2012
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This ebook is available for the following devices:
Presents a comprehensive picture of the current state of the field of discrete and computational geometry
Includes an expanded preface, with a set of photographs of groups and individuals who have played a major role in the history of the field in the past 20 years
Contains 28 major articles, chosen for the importance of their results, the breadth of their scope, and to show the intimate connections between discrete and computational geometry and other areas of both computer science and mathematics
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ti-smartview emulator is an easy-to-use, demonstration tool for leading the classroom instruction of math and science concepts. Based on the popular ti-84 plus family of graphing calculators (compatible with the ti-83 plus family), the ti-smartview emulator complements classroom calculator use by displaying an interactive representation of the calculator, plus offers many unique instructional capabilities. TI 34 MultiView scientific calculator was designed
with educator input in mind for use in middle grades math and science classes including Middle School Math, Pre Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology. In Classic ...
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Take your teaching into the future with the
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Geometry: Expanded Edition is the third book in the Life of Fred High School Mathematics Series, and is designed for students in 11th grade who have already finished the preceding Beginning Algebra, Expanded Editionand Advanced Algebra, Extended Edition. This new edition of Geometry replaces the both the earlier Life of Fred Geometry; it also contains all problems completely worked out. Thirteen chapters plus six honors-level half chapters with multiple sub-lessons are included. Each lesson ends with a Your Turn to Play segment with a small number of thought- provoking questions. Answers are provided on the next page for students to go over themselves after attempting to solve the problems. Chapters conclude with three problem sets, each of which is named after a city, and their answers...
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The topic of this course is a new approach to the foundation of linear signal processing (SP), termed algebraic signal processing theory (ASP), that was developed by the instructor and his collaborators. Linear signal processing is built around the fundamental concepts of signals, filters, spectrum, z-transform, Fourier transforms, and many others. ASP generalizes these concepts, and thus linear SP, to provide a unifying approach to many existing SP methods and to enable the derivation of many new ones. This is made possible through the connection between linear SP and abstract algebra that ASP reveals and explores.
Specifically, the course will provide a new look at standard time SP but then introduce various other forms of SP including the non-standard space SP in one and higher dimensions, separable and nonseparable. In each case there will appropriate z-transforms, Fourier transforms, etc.These different SP methods will be derived as instantiations of the general, axiomatic ASP theory. ASP provides detailed insights into existing and novel transforms, their properties, and their fast algorithms, and naturally connects to linear statistical SP (Gauss-Markov random fields and Karhunen-Loeve transforms) as will be discussed in detail. Other topics will include uncertainty relations, sampling theorems, and shift-variant SP.
The course is mathematical in nature. The mathematics needed for ASP will be introduced in the course and learned through concrete exercises. In particular, no background in abstract algebra is needed. The instructor's emphasis regarding math is "hands-on" rather than "abstract."
The course is targeted for graduate students who are interested in enhancing their understanding of the foundation of SP. For any questions please contact the instructor.
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Elementary Geometry for College Students
9781439047903
ISBN:
1439047901
Edition: 5 Pub Date: 2010 Publisher: Brooks Cole
Summary: If you want to rent Elementary Geometry for College Students online, we can help you. This text book, written by Daniel C Alexander and Geralyn M Koeberlein, was published by Brooks Cole in 2010. Now you can get cheap Elementary Geometry for College Students here in its 5th edition for an affordable price. We specialize in providing great deals that are heavily discounted for previously owned copies. You can buy Elem...entary Geometry for College Students online here for a price far lower than you might think, and sell back later on too. We provide the whole deal for every college student.
Alexander, Daniel C. is the author of Elementary Geometry for College Students, published 2010 under ISBN 9781439047903 and 1439047901. Two hundred fifty nine Elementary Geometry for College Students textbooks are available for sale on ValoreBooks.com, nineteen used from the cheapest price of $5.17, or buy new starting at $5239047903-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:97814390479 getting across the basics of geometry. I found this book very effective because it gave you review and test questions/answers which was very helpful when preparing for a test. Most of the time teachers will use problems from here for quizzes or test so practicing these problems is crucial. The examples in each chapter are very helpful as well because they give a break down of each problem.
If I could change one thing about this book it would be to provide all the answers for every other problem. Sometimes in certain chapters, answers to the odd problems would be missing. But other than that this book was very helpful in helping me pass with an A this semester!
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Mathematics 2, Essential
When we paint a room, put up a fence, buy a rug, or wrap a present, we are using shapes. Essential Math 2 deals with the nature and property of shapes such as circles, triangles and squares. In doing so, this course provides an introduction to geometry and algebra. Essential Math 2 also acquaints students with the metric system of measurement.
What others are saying:
The American School really helped me. Being a senior, I have so much going on, and night school would have been a hassle to fit into my busy life. Thanks to the American School, I could do it in my spare time and worked at my own speed. — Katie, Michigan
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Algebra for College Students (3rd Edition)
9780136129080
ISBN:
0136129080
Edition: 3 Pub Date: 2007 Publisher: Pearson
Summary: "Algebra for College Students "is typically used in a very comprehensive 1-semester Intermediate Algebra course serving as a gateway course to other college-level mathematics courses. The goal of the Intermediate Algebra course is to provide students with the mathematical skills that are prerequisites for courses such as College Algebra, Elementary Statistics, Liberal-Arts Math and Mathematics for Teachers. This Alge...bra for College students text may also be used in a 1-semester, lower-level College Algebra course as a prerequisite to Precalculus.
Allen R. Angel is the author of Algebra for College Students (3rd Edition), published 2007 under ISBN 9780136129080 and 0136129080. Three hundred four Algebra for College Students (3rd Edition) textbooks are available for sale on ValoreBooks.com, one hundred nine used from the cheapest price of $48.60, or buy new starting at $99.29edited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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This lesson from Illuminations has students study equivalence and systems of equations while identifying and using related functions. It includes an interactive applet that can be used in class. Discussion questions are simplifying algebraic expressions using multiplication. The unit's activities include defining the terminology associated with algebraic operations, using the fundamental...
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Precalculus Mathematics for Calculus - Text - 5th edition stu
dents develop insight into mathematical ideas. The authors' attention to detail and clarity, as students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the market leader. ...show less
Overview. Angle Measure. Trigonometry of Right Triangles. Discovery Project: Similarity. Trigonometric Functions of Angles. The Law of Sines. The Law of Cosines. Review. Test. Focus on Modeling:Surveying495109976-5-0
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This expanded new edition presents a thorough and up-to-date
introduction to the study of linear algebra
Linear Algebra, Third Edition provides a unified introduction to
linear algebra while reinforcing and emphasizing a conceptual and
hands-on understanding of the essential ideas. Promoting the
development of intuition rather than the simple application of
methods, the book successfully helps readers to understand not only
how to implement a technique, but why its use is important.
The book outlines an analytical, algebraic, and geometric
discussion of the provided definitions, theorems, and proofs. For
each concept, an abstract foundation is presented together with its
computational output, and this parallel structure clearly and
immediately illustrates the relationship between the theory and its
appropriate applications. The Third Edition also features:
A new chapter on generalized eigenvectors and chain bases with
coverage of the Jordan form and the Cayley-Hamilton theorem
A new chapter on numerical techniques, including a discussion
of the condition number
A new section on Hermitian symmetric and unitary matrices
An exploration of computational approaches to finding
eigenvalues, such as the forward iteration, reverse iteration, and
the QR method
Additional exercises that consist of application, numerical,
and conceptual questions as well as true-false questions
Illuminating applications of linear algebra are provided
throughout most parts of the book along with self-study questions
that allow the reader to replicate the treatments independently of
the book. Each chapter concludes with a summary of key points, and
most topics are accompanied by a "Computer Projects" section, which
contains worked-out exercises that utilize the most up-to-date
version of MATLAB(r). A related Web site features Maple
translations of these exercises as well as additional supplemental
material.
Linear Algebra, Third Edition is an excellent undergraduate-level
textbook for courses in linear algebra. It is also a valuable
self-study guide for professionals and researchers who would like a
basic introduction to linear algebra with applications in science,
engineering, and computer science.
Richard C. Penney, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. Dr. Penney is the author of numerous journal articles and has received several major teaching awards.
A new section has been added on computational linear algebra to reflect the increase in the power, speed, and availability of computers. More extensive discussions of the condition number as well as the numerical computation of eigenvalues are included.
Two new chapters are provided on numerical linear algebra and the Jordan normal form
Full sections on both Hermitian and Unitary matrices have been added, as well as sections on computational linear algebra and wavelets.
An increase in the amount of exercises and the True-False questions is evident in this new edition. The exercises continue to be "conceptual but not theoretical" in nature, and they compliment the approach and style of the book.
A student solutions manual is available, which contains worked
out examples, hints for some of the exercises, and translations of
the computer exercises into various platforms, i.e.
MapleTM, MATLAB®, and TI
calculators.
All exercises have been updated to reflect the most up-to-date
versions of Maple and MATLAB.
A sample syllabus for a two semester class has been added
to the front matter. November 2008)
"This book should make a good text for introductory courses."
(Computing Reviews, September 30, 2008) Nov 2008)
"This book should make a good text for introductory courses."
(Computing Reviews, September 30, 2008
| 677.169 | 1 |
Math for Strategists
Abstract
Great strategists rely heavily on numbers as they go about their work. Offers an overview of the high- and low-brow quantitative tools that students encounter during the Strategy course. The class explores high-brow tools in detail; the focus here is on low-brow calculations. Such calculations come up often in class but because they seem so simple, they get little airtime or explanation. From past class experience, roughly 20% of the students in each section come into the course with the intuition and experience to do these simple calculations themselves. The other 80% understand the calculations after they see them and grasp their value, but don't spot the opportunities to do the math themselves, before class
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...
Show More NCTM (National Council of Teachers of Mathematics) Standards-based curricula. Contains geometry which middle school mathematics teachers will actually have to teach, as well as additional material to deepen future teachers' knowledge and understanding of geometry. Demonstrate the presentation and use of geometry in the middle school to assist students in linking the typical college geometry course with the standards-based concepts taught by middle school teachers. Includes a variety of activities designed to deepen the connections between the geometry students are studying now and the geometry they will teach. For anyone interested in learning more about geometry.
Show Less
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Numbers deals with the development of numbers from fractions to algebraic numbers to transcendental numbers to complex numbers and their uses. The book also examines in detail the number pi, the evolution of the idea of infinity, and the representation of numbers in computers. The metric and American systems of measurement as well as the applications... more...
Shows how well-meant teaching strategies and approaches can in practice exacerbate underachievement in maths by making inappropriate demands on learners. As well as criticizing some of the teaching and grouping practices that are considered normal in many schools, this book also offers an alternative view of attainment and capability. more...
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding... more...
Deals with the specific characteristics of mathematical communication in the classroom. This book offers a presentation and an application of the fundamental research method in mathematics education that establishes a reciprocal relationship between everyday classroom communication and epistemological conditions of mathematical knowledge. more...
This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge... more...
Education in any social environment is influenced in many ways by the traditions of these environments. This volume reflects the structure of the conference in four sections of papers, integrating insights, results and implications from the comparative discussions. more...
Italian mathematics between the two World Wars was shaped by a colorful array of strong personalities who concentrated their efforts on a select number of fields and won international recognition and respect in an incredibly short time. This book describes Italian mathematics in the period between the two World Wars. more...
Mathematics and Teaching uses case studies to explore complex and pervasive issues that arise in teaching. In this volume, school mathematics is the context in which to consider race, equity, political contexts and the broader social and cultural circumstances in which schooling occurs. This book does not provide immediate or definitive resolutions.... more...
Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve... more...
The book contains a selection of 43 scientific papers of the great mathematician, Ennio De Giorgi. All papers are written in English and 17 of them appear also in their original Italian version. The editors provide also a short biography of Ennio De Giorgi and a detailed account of his scientific achievements, ranging from his seminal paper on the... more...
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More About
This Textbook
Overview
This is a reprint of "A First Course in Calculus," which has gone through five editions since the early sixties. It covers all the topics traditionally taught in the first-year calculus sequence in a brief and elementary fashion. As sociological and educational conditions have evolved in various ways over the past four decades, it has been found worthwhile to make the original edition available again. The audience consists of those taking the first calculus course, in high school or college. The approach is the one which was successful decades ago, involving clarity, and adjusted to a time when the students'background was not as substantial as it might be. We are now back to those times, so it's time to start over again. There are no epsilon-deltas, but this does not imply that the book is not rigorous. Lang learned this attitude from Emil Artin, around 1950.
Editorial Reviews
From the PublisherFrom the Publisher
From the reviews:
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Product Description
The Algebra 1: The Complete Course DVD Series will help students build confidence in their ability to understand and solve algebraic problems.
In this episode, students will learn to visualize concepts with the aid of manipulatives. The properties of the reciprocal function and also the general form of a rational function are also taught. Grades 5-9. 30 minutes on DVD.
DVD Playable in Bermuda, Canada, United States and U.S. territories. Please check if your equipment can play DVDs coded for this region. Learn more about DVDs and Videos
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Mathematical Structures for Computer Science
9780716768647
ISBN:
071676864X
Edition: Sixth Edition Pub Date: 2006 Publisher: W. H. Freeman
Summary: This edition offers a pedagogically rich and intuitive introduction to discrete mathematics structures. It meets the needs of computer science majors by being both comprehensive and accessible.
Judith L. Gersting is the author of Mathematical Structures for Computer Science, published 2006 under ISBN 9780716768647 and 071676864X. Two hundred thirty six Mathematical Structures for Computer Science textbooks a...re available for sale on ValoreBooks.com, seventy one used from the cheapest price of $0.92, or buy new starting at $18
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College Algebra
MAT 110 or the equivalent with a minimum grade of C or appropriate score on the Mathematics Assessment Test; and MAT 080 or geometry proficiency.
III. Course (Catalog) Description
A study of the following functions and their graphs: polynomial, rational, exponential, logarithmic, and special functions; systems of equations and inequalities, sequences and series, and the binomial theorem.
IV. Learning Objectives
1. Classify functions and their graphs, and identify their domain and range. 2. Identify and apply transformations of graphs. 3. Solve linear and non-linear equations. 4. Solve polynomial and rational inequalities algebraically and graphically. 5. Sketch the graph of polynomials using zeros and end behavior. 6. Sketch the graph of rational functions using zeros, asymptotes, and end behavior. 7. Find, graph, and interpret the inverse of a function. 8. Graph exponential and logarithmic functions, and use their properties to simplify and solve equations involving them. 9. Classify and sketch the graphs of conic sections. 10. Model and solve applications using the elementary functions studied in the course. 11. Use technology to graph, evaluate, and interpret functions, and to solve equations involving themMethods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate. Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
(To be completed by instructor.)
IX. Instructional Materials
Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes.
Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".
Textbooks can also be found at our Mathematics Textbooks page.
A graphics calculator is required. A TI-83/84 will be used for instructional purposes.
X. Methods of Evaluating Student Progress
(To be completed by instructor.)
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam
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From angles to functions to identities - solve trig equations with ease Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner.... more...
If you're preparing for The American Institute of Professional Bookkeepers' (AIPB) bookkeeping certification test, you need an easy- to-follow test-preparation guide that gets you up to speed quickly in all of the bookkeeping basics, from setting up a company's books and recording transactions to managing employee payroll, handling government paperwork,... more...
From genetics to ecology ? the easy way to score higher in biology Are you a student baffled by biology? You're not alone. With the help of Biology Workbook For Dummies you'll quickly and painlessly get a grip on complex biology concepts and unlock the mysteries of this fascinating and ever-evolving field of study. Whether used as a complement... more...
Gruber's Complete SAT Math Workbook includes shortcuts and tips, strategies and practice tests. It also features the exclusive Gruber system that has raised actual SAT scores by more than 600 points! more...
Helpful instruction and plenty of practice for your child to understand the basics of multiplication and division
Understanding multiplying and dividing is essential for your child to do math problems with confidence. Practice Makes Perfect: Multiplication and Division gives your child bite-sized explanations of the subjects, with engaging... more...
Helpful instruction and plenty of practice for your child to master the basics of vocabulary
Having a strong grasp of vocabulary is essential for your child to read and write with confidence. Practice Makes Perfect: Mastering Vocabulary gives your child bite-sized explanations of the subject, with engaging exercises that keep her or him motivated... more...
Instant revision notes, with self-check questions and grade-boosting tutorials in a unique e-book. Written by senior examiners and experienced teachers who know what students need for that final ? instant ? check! There are sections covering all the important reading and writing topics needed in the GCSE English exam, with example material taken... more...
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development plan for educators, staff and administrators was designed with a month long flipped on-lined training for participants to learn essential skills and functionality necessary on their own pace in order to advance to the 3 hours faceMatific is a fantastic maths resource with over 750 interactive
episodes for K-6 maths and follows the new Australian curriculum.
Matific is available across all platforms PC, Mac, IPad and Android.
It is available either via the website ( or as an app from the app store or Google play
It is the most interactive and engaging product on the market today.
Matific teaches fundamental maths concepts using manipulation of familiar objects.
The algorithm within each episode is randomly generated so the student will never be able to just learn the answer by repetition.
A truly great product.
Factoring polynomials, especially trinomials, are main subject of high school math. So far, the factoring AC Method has been the most popular method to factor binomials. This method could be improved if we apply the Rule of Signs of Quadratic functions into its operational approach.
The New AC Method works simpler and faster than the existing AC Method. The most important advantage is it can avoid the lengthy factoring by grouping.
| 677.169 | 1 |
More About
This Textbook
Overview
Make mathematics fun and satisfying for everyone
Math can be a living source of powerful ideas that transcend mathematics; a window into mind-opening philosophical concepts such as infinity, fourth dimensions, chaos, and fractals; and a practical training ground for developing skills in analysis, reasoning, and thought—if you have the right approach and the right guide.
The Heart of Mathematics: An Invitation to Effective Thinking—now in its third edition—transforms mathematics into an engaging, relevant experience even for the most math-phobic student. Infusing this book with humor and enthusiasm, Edward B. Burger and Michael Starbird—both recipients of the Mathematical Association of America's foremost national teaching award and countless state, regional, and campus-wide teaching honors—introduce students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
Richer and more rewarding than ever, this new edition features:
An emphasis on mathematical methods of investigation
Visualization techniques that make key concepts easier to understand
Accessible, friendly writing style that encourages critical thinking
"Life Lessons"-effective methods of thinking that students will retain and apply beyond the classroom
End of section Mindscape activities for the development of application, problem-solving, and argumentation skills
Meet the Author
Edward B. Burger is professor of mathematics in the Department of Mathematics and Statistics at Williams College. He graduated from Connecticut College in 1985, where he earned B.A. Summa Cum Laude with Distinction in Mathematics, and received his Ph.D. in mathematics from the University of Texas at Austin. He did his postdoctoral work at the University of Waterloo in Canada. Dr. Burger has received numerous awards including: the Award of Excellence, for "educational mathematics videos that break new ground from the Technology & Learning magazine, and the Distinguished Achievement Award, for Educational Video Technology from The Association of Educational Publishers. He was honored as one of the "100 Best of America", Listed in Reader's Digest's Annual Special Issue as Best Math Teacher. He also received the Residence Life Academic Teaching Award, University of Colorado at Boulder and the Robert W. Hamilton Book Award, for "The Heart of Mathematics".
Michael Starbird Michael Starbird is a University Distinguished Teaching Professor of Mathematics at The University of Texas at Austin. He has received more than a dozen teaching awards including the Mathematical Association of America's 2007 national teaching award and several university-wide teaching awards based largely on his course in mathematics for liberal arts students. Starbird brings intriguing mathematics to general audiences through his classes, lectures, books, and video courses. In 1989, Starbird was UT's Recreational Sports Super Racquets Champion
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Enter your mobile number or email address below and we'll send you a link to download the free Kindle Reading App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property.
Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math
Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation
This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.
{"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":23.88,"ASIN":"1118095707","moqNum":1,"isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":28.46,"ASIN":"0941355845","moqNum":1,"isPreorder":0}],"shippingId":"1118095707::hYQLkN0Xn3FL83lzIGg9re%2B7%2F69YWwfbZaCyHgZ4vb11NOitW1xtuLoylpJg%2FvcwY7KseRfShl9VTLaewZVk2XljvVsEsHydYEXR7BI9SGtx9QO6oIvjcQ%3D%3D,0941355845::9en2sgrGfAk3jNRbjXupvWBMhsQDYZux5nVNqiWc6b4YpENzYje8AiQyV964slxPpSVxCRZsLwUwN6o6FVP1x51mNeBKrFobdHMdjQ0%2B9Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at only a superficial level. Written to inspire "aha" moments, this important new book offers teachers the tools they need to help their students identify and comprehend the nuances and true meanings of essential math concepts—such as multiplication, division, fractions, place value, and much more—by exploring them through the lenses of language and symbolism.
The Problem with Math Is English explains how language-focused conceptual instruction leads students to a deeper understanding than traditional procedural-based teaching methods. By placing emphasis on truly understanding math concepts, Dr. Molina shows that teaching math becomes easier when teachers are able to communicate the language, symbolism, and representation of math to all of their students.
"Teachers of mathematics of all levels who read and spend time with this fun and challenging book will strengthen their content knowledge and find confidence in their own ability to think and reason. When teachers truly understand and embrace the mathematics/language connections so richly illustrated in the book, they will be able to pass on to all of their students a depth of mathematical insight and joy they may never have imagined before."
"In this easy to read book, Como Molina—with rare humor, insight and thoughtfulness—shares many of the lessons he has learned while providing professional development for mathematics teachers in U.S. public schools. Como delightfully challenged my own understandings of the important relationships between mathematical ideas and the language we commonly use to teach them."
About the Author
Concepcion Molina, Ed.D., is a program associate with SEDL, a private, nonprofit education research, development, and dissemination corporation based in Austin, Texas. Dr. Molina supports systemic reform efforts in mathematics and works to assist state and intermediate education agencies in their efforts to improve instruction and student achievement.
Most Helpful Customer Reviews
I found the first 3-4 chapters uninspiring, pedantic, and repetitive but I kept at it because I felt as if it could get good at any minute and am I glad I did!
I have always felt that math education suffers too much from a focus on procedure and a lack of emphasis on understanding the underlying concepts. The author has written a great book that addresses that specific issue. He peels back the onion on many topics. For example, he examines order of operations (PEMDAS), and asks why it may be so. He shows how it follows naturally from other more simple properties of math.
I have been struck numerous times while reading this book by my own lack of understanding of the fundamental underlying principles for the "rules" I have learned to apply so well.
While the book is targeted at primary and middle grades, I wish every math teacher at all levels would read this book. The attitude it inspires is important at all levels.
this book is amazingly pertinent to math education and should be required reading for anyone who is going to teach math. so many habits of our own school years are exposed and corrected. the emphasis on deep definitions, clear language, and contextual coverings for naked numbers leaves one excited about implementing these ideas. there were parts that i found difficult because i didnt have the mathematical skills that were the subject of discussion, but overall, extremely clear and accessible writing makes it easy to understand.
I am a Hugh school math teacher and I leaned quite a bit from this book. I learned that my use of language is really hurting my students. I never realized how easily what I say in class could be interpreted incorrectly. I have already changed the way I speak to my students and am planning to retool many of my lessons based on the ideas presented in this book. I will also be recommending it to other math teachers. Thank you for making me think differently.
This is the second time I've bought this for Kindle. There was something about having a copy on too many devices and the book was important enough that I wanted to buy it again. The information is clear and it's ideas are clearly transferable from the text to the classroom. Some things, (The Distributive Property), Ive been doing for several years before I read it in the book. I used some problems to challenge students who are too stuck on the crutch of the calculator. I strongly agree that understanding the underlying structure of the language and translating that understanding to applications/problems builds a better, stronger student whose knowledge lasts past the next test.
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Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples strewn throughout the text demonstrate how the language can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics and a range of other fields. The book will appeal to students, researchers and programmers wishing to further their understanding of Mathematica. Designed to suit users of any ability, it assumes no formal knowledge of programming so it is ideal for self-study. Over 275 exercises are provided to challenge the reader's understanding of the material covered and these provide ample opportunity to practise using the language. Mathematica notebooks containing examples, programs and solutions to exercises are available from
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Managing the Mean Math Blues 1st edition
0130431699
9780130431691
Details about Managing the Mean Math Blues:
Dear Reader,My fondest wish is that this book will assist you to succeed with math. Feel free to read it in any order that works for you. This is a book for you to control. The techniques and exercises are here to help you, not to overwhelm or discourage you. If you feel overwhelmed or discouraged, back off and return later. But do return. The rewards are many and great.I have included information I have found useful to math students during 30 years of teaching, so pick and choose. Refer to this book when you need a new and different strategy.Dawn Bigelow, a superb third-grade teacher I taught beside, told me that when she went to a conference she wanted to return withthree new ideas.More than three and she would be too overwhelmed to try them. Fewer than three and she had wasted her time going to the conference.Three was the magic number. When Dawn returned to her third-graders with three new ideas, she could easily incorporate them into the classroom system she already had in progress.You have a system in progress for learning. You only need three new ideas each time you come to this book. More than that and you will be overwhelmed. Fewer than that and you will be wasting your time. Modify your learning system slowly and surely. Incorporate winning ideas and strategies that fit who you are and what you want to accomplish.Skim over the Contents. Mark the topics that look the most promising. Chapter 2, along with the list below, can direct you according to your needs.Features of this book and their purpose are:Introduction and Chapter 1: Motivation to excite you and help you gather courage to confront the blues.Chapter 2: Explanation of routes through this book based on your needs.Chapters 3-6: Effective methods to control overwhelming negative thoughts and feelings about math (or life).Chapters 7-9: Self-discovery about who you are and how you learn best.Chapters 10, 13, 14, and 15: Study skills to use in math class.Chapters 11 and 12: Discussion of shyness and classroom/teacher issues.Chapter 16: Problem-solving strategies.Chapter 17: Test-taking strategies."Pushing Your Limits," Chapters 1-17: Journal activities to help you question, ponder, plan, and evaluate your math life."Mastering Math's Mysteries," Chapters 3-6: Practice with numbers and patterns."Mastering Math's Mysteries," Chapters 7-13: Fraction practice to shore up skills that math students tend to avoid."Mastering Math's Mysteries," Chapter 15: Practice with spatial visualization."Mastering Math's Mysteries," Chapters 14, 16, and 17: Practice with strategies discussed in the chapters."More Mastering Math's Mysteries," in the Appendix: More challenging math practice for the brave of heart.Solutions to "Mastering Math's Mysteries" exercises, in the Appendix.This book is not designed as a math textbook but rather to accompany a math textbook or to prepare you for a math textbook. The math exercises here are just for you to wet your feet. Because I know that every math student brings different experiences and needs, I had difficulty deciding which math topics to include. I chose fractions because they are universally avoided and disliked. The potential exists for you to feel terrific soon if you face them. Be patient with yourself as you wade into new territory. Being curious and willing to experiment can help you to swim sooner than you ever thought possible. Use a life preserver when you need it and never swim alone.My best,
Cheryl Ooter
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Rent Managing the Mean Math Blues 1st edition today, or search our site for Cheryl textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Prentice Hall.
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About 82 results for "quadratic equations"
Im very well acquainted… with matters mathematical, I understand equations, both the simple and quadratical, About binomial theorem Im teeming with a lot o news, With many cheerful facts about the square of the hypotenuse. Im very good at ...Cato Institute, 1 week ago
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Book Summary of Master Sat Ii Math 1c And 2c 4th Ed (Mas...
(Paperback)
With detailed reviews and expert test-taking strategies, this guide helps prepare you for the exam. It includes extensive review of math subjects ranging from algebra and geometry to trigonometry and statistics. Additional resources include, review questions and full-length practice tests at the end of each chapter to reinforce what you have learned.
Feature and benefits include: - Four full-length practice tests - Diagnostic tests to help students identify the areas in which they need improvement - Detailed review of fundamental subject principles, followed by practice questions
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