text stringlengths 8 1.01M |
|---|
Thomas' Calculus - 11th edition
Summary: The new edition of Thomas is a return to what Thomas has always been: the book with the best exercises. For the 11th edition, the authors have added exercises cut in the 10th edition, as well as, going back to the classic 5th and 6th editions for additional exercises and examples.
The book's theme is that Calculus is about thinking; one cannot memorize it all. The exercises develop this theme as a pivot point between the lecture in class, and the understand...show moreing that comes with applying the ideas of Calculus.
In addition, the table of contents has been refined to match the standard syllabus. Many of the examples have been trimmed of distractions and rewritten with a clear focus on the main ideas. The authors have also excised extraneous information in general and have made the technology much more transparent.
The ambition of Thomas 11e is to teach the ideas of Calculus so that students will be able to apply them in new and novel ways, first in the exercises but ultimately in their careers. Every effort has been made to insure that all content in the new edition reinforces thinking and encourages deep understanding of the material136 |
Finite Mathematics 235 - J. A. Macias
Winter break is gone! It is time to hit the books. I will be your mathematics instructor this semester.
These are some of the reasons why you will like this class:
-This is an applied mathematics class.
It marks the end an era; previous classes promised math would be useful one day. This class is all about uses and applications of mathematics.
-This is a sampler class.
A remarkable amount of topics and their uses are covered, and you are invited to decide which branch is better suited for your career goals. Think of it as a sampler at your favorite restaurant; taste a little of each and decide which one you want.
-No more training wheels.
Whereas most prior courses in mathematics provided you exercises using "nice" numbers and answers that usually turned out to be integers, the textbook does not shy away from ugly fractions and long decimals. Kind of like the real world.
-It is old! It is new!
The Pythagorean theorem has been around since Pythagoras in the 5th century B.C. Even calculus was developed centuries ago. This class exposes you to recent creations developed only a few decades ago due to the demands of the second world war.
-Counterintuitive ideas are proved.
There are some strange phenomena that defy intuition, yet can be proved mathematically.For example, if there are just 23 students in the class, there is a chance higher than 1 in 2 someone else in the class has the same birthday as you!
Let's do this!
What, when, where
Our class will meet in the Northeast building, room 225 at 12:45 sharp.
Ahem, excuse me!
Please silence your phones upon arrival; we do not want to hear your phone sing 'La Cucaracha' in the middle of an exam. Please refrain from texting, checking your Facebook account, etc. Bottom line, please come prepared for class and leave the world outside, if only for two hours.
I have office hours before class. This provides you an excellent chance to come and talk to me if you need to clarify something we discussed in class, need help with your homework, or for any other issue you have in mind. Not only is your education my job, I actually enjoy addressing your concerns! I am there for you, I am a great resource for you; use me!
Syllabus
Click here to obtain the syllabus we will use in the class. Information on exam dates, class policies etc. can be found there. Best of all, I am giving away the syllabus for free!
Homework postings
You can follow this link to see the homework assignments for the class.
Etcetera
If you need help with some Algebra topics or want a second opinion on some topic we discuss in class take a look at
This organization posts videos on many academic topics, including the one you want.
You can also review Algebra material on This website has interactive content in addition to instructional material. Check it out!
Why study mathematics?
Yeah, why? Well.......often people think they have no use for the material learned in class and ask me what the point of taking mathematics is. I could go on and on about this topic but if you want a concise reason I can say 'jobs' and 'money'. Need reassurance? Look at the two links below and see how those who can play with numbers are better suited to take on good paying positions: |
powerful tool for building mathematical graphs. The perfect tool for students, teachers and anyone involved in math: - supports standard graphs in Cartesian coordinate system, parametric graphs, graphs in polar coordinates and parametric graphs in polar coordinates, point graphs; - simple and easy to use intuitive interface; - 46 mathematical functions, built-in constants; - any number of graphs on one screen; - save graphs as images with various options; - work in real time, gesture support, two virtual keyboard to choose, examples, help section, history, settings and more.
You can draw a graph of any function as simple 2-D or 3-D. After that, You can draw graphs of functions that you wonder as you want. In 2D mode or 3D mode, you can draw easily many graphs. This is a fun job if you prefer. I wonder how the graphs of functions change when the function's parameters change.
Normal functions, logarithmic functions, exponential function, the absolute value function, trigonometric functions, inverse trigonometric functions, and many more can easily draw a graph of the function.
In three-dimensional graphics, sphere, Moebius strip, Cone, and many more can draw graphs of three-dimensional shapesUsing VisualGraph 3D, you can draw 3D graphs with full commands on functions like f(x,y) and parametrical or spherical functions and much more. You can view your 3D graph from 360 view, that means you can fully rotate and animate your graph. You can also zoom to see small variation clearly and view the contour of the graph.
Create your customized graph with trigonometric, logarithmic or exponential-functions and make screenshots. You can change the range of X-Y-Z axis to see full details.
The app is very easy to use and help to almost all student which have mathematics and engineering as their subject.
You can save and name your functions. A few good examples are already available, like damped oscillation and sphere-functions.
It's a graphical calculator with dynamic range result tables and you can differentiate and simplify your functionsA simple app that draws 3D graphs. The free version supports graphs in the form y = f(x, y), but the paid version supports other forms, including functions in cylindrical and spherical polar coordinates, parametric surfaces, and parametric curvesAn app designed to help students and other in understanding functions. Draw functions on a Cartesian plan. Several functions can be drawn on the same graph. Assign different colors to functions. Zoom in and out. Explore by moving the plan. Adjust density to get a precise graph without compromising responsiveness. Soon, you'll be able to save your graphs, print them, or email them.Features under development: - function to export the graph image. - calculations such as integration, derivatives, max and min - graph view (with x, y, z coordinates) - please let us know of any additional features you would like!
Function Solver is designed to solve a second degree function (parabola) With Function Solver you will receive not only an answer but also a way to solve Also you can see the graph of the function. and min&max points ,and intersection points I made this app to help those who have difficulty now you can be able to learn and solve Function ! I call it easy math !
So go download it and recommend to your friends If you have suggestions or questions: itsik932@walla.com Successfully! Function solver ItzikSelect Simple ODE Solver mode if your problem has only an equation or System ODEs mode if you has a System or Ordinary equations.
1) Enter the initial value for the independent variable, x0. 2) Enter the final value for the independent variable, xn. 3) Enter the step size for the method, h. 4) Enter the given initial value of the independent variable y0. 5) Select from the combo the integration method (default Euler method is selected). 6) Enter the function f(x, y) of your problem, for example. |
The relations between stress and strain in linear viscoelastic theory are discussed from the viewpoint of application to problems of stress analysis. This consideration includes some important diff... More: lessons, discussions, ratings, reviews,...
The ToKToL online adaptive learning platform contains a large (2000) set of maths questions and associated explanatory texts. Questions are selected to adjust to the ability of the student so that whe... More: lessons, discussions, ratings, reviews,...
A very powerful graphing program that is also especially easy to use. You can graph functions in two or more dimensions using different kinds of coordinates. You can make animations and save as movies activity demonstrates one of the many ways Sketchpad can be used in a calculus or math analysis class. Students manipulate a tangent line to a curve to investigate what it means for a curve to ha... More: lessons, discussions, ratings, reviews,...
In this activity, students will look at the graph of a function g(x), defined to be the integral of a function f(x), with the goal of understanding Part 1 of the Fundamental Theorem of Calculus. Speci |
Summary: CONTEMPORARY MATHEMATICS FOR BUSINESS AND CONSUMERS, BRIEF is a 14-chapter educational adventure into today's business world and its associated mathematical procedures. The book is designed to provide solid mathematical preparation and foundation for students going on to business courses and careers. It begins with a business-oriented review of the basic operations, including whole numbers, fractions, and decimals. Once students have mastered these operations, they a...show morere introduced to the concept of basic equations and how they are used to solve business problems. From that point, each chapter presents a business math topic that utilizes the student's knowledge of these basic operations and equations. In keeping with the philosophy of "practice makes perfect," the text contains over 2,000 realistic business math exercises--many with multiple steps and answers designed to prepare students to use math to make business decisions and develop critical-thinking and problem-solving skills. Many of the exercises in each chapter are written in a "you are the manager" format, to enhance student involvement. The exercises cover a full range of difficulty levels, from those designed for beginners to those requiring moderate to challenge-level skillsBrand New Title. We're a Power Distributor; Your satisfaction is our guarantee!
$229.68 +$3.99 s/h
New
PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI
0324658648 |
Starting with an overview of elementary operations, the text defines vectors, explores their fundamental ...
More About
This Book
Starting with an overview of elementary operations, the text defines vectors, explores their fundamental properties and linear combinations, and discusses auxiliary point technique and uniqueness of representations. Subsequent chapters examine vectors in coordinate systems, properties and formulas of inner products, and elements of analytic geometry—the straight line, analytic methods of proof, and circles, spheres, and planes. The text concludes with surveys of cross products, plane and spherical trigonometry, and additional geometric concepts, including segments and convexity and linear programming. Exercises appear throughout the book, with solutions at the end.
Related Subjects
Table of Contents
Elementary Operations 1
Introduction
Definition of vector
Fundamental properties
Linear combinations of vectors
Auxiliary point technique
Uniqueness of representations
Vectors in Coordinate Systems 40
Rectangular systems and orientation
Basis vectors and applications
The complex plane
Inner Products 60
Definition
Properties of inner product
Components
Inner product formulas
Work
Analytic Geometry 76
Our point of view
The straight line
Analytic geometry of the line continued
Distance from a point to a line
Analytic method of proof
Circles
Spheres
Planes
Determining a plane by points on it
Distance from a point to a plane
The straight line in three dimensions
Angle between two lines
Intersection of a line with a plane
Angle between a line and a plane
Cross Products 135
Cross products
Triple scalar product
Distance from a point to a plane
Distance between two lines
Triple cross products
Trigonometry 151
Plane trigonometry
Spherical trigonometry
More Geometry 160
Loci defined by inequalities
A few booby traps
Segments and convexity
Linear programming
Theorems arising in more general geometries
Applications of parametric equations to locus problems
Rigid motions
Appendix 204
Answers 206
Index 211 |
People you are a fan of:
5 online
Write a New Message
Forgot Your Password?
Enter Your Email
hba
Name:
School:
About:
If you have any questions or queries or you need help with studies,please email me right away.
-----------------------------
Tutorials Requested by users-
My tutorial (1st part) on waves-
My log-sheet to help students-
A trick-
Complex numbers- |
PBS Teachers: Math - PBS Teachers
The Public Broadcasting System's Math Service, combining computing and telecommunications technologies to offer interactive data services and interactive video and voice services for education based on the NCTM Standards. The site features: resources,
Peter Ash's Thoughts on Math and Education - Peter Ash
Musings on doing and teaching mathematics, book reviews, and math problems both elementary and advanced from the creator of Cambridge Math Learning. Blog posts, which date back to August of 2007, include "Very Proper Fractions"; "Physical Models for Non-Euclidean
...more>>
Physics and Math Help Online - Bryan Gmyrek
Tutoring available through e-mail. Previously answered questions are archived on the site, and a tutorial on The Plank Radiation Law - Blackbody Spectrum is available. The author also provides a physics help newsletter and a list of sites for further
...more>>
Plot Graphs - Philipp Wagner
Plot multiple two- or three-dimensional graphs, including of parameterized functions and derivatives, in one and the same graph. Key in equations with the WYSIWYG formula editor.
...more>>
Poliplus Software
Educational computer algebra, geometry, trigonometry, calculus software for Windows and Macintosh, and Java. Formulae 1 (F1) is a computer algebra system designed for the teaching and exploration of Mathematics. EqnViewer is a Java applet that allows
...more>>
The PostCALC Project - Duke University
The PostCALC Project is a branch of the Connected Curriculum Library that presents interactive, mathematically-based modules designed for high school students who have finished a year-long course in calculus. These modules, each appropriate for several
...more>>
Powell's Books
Located in Portland, Oregon, USA; the largest independent bookseller in the United States, specializing in technical books and new, used, hard-to-find, and antiquarian titles. An extensive subject and keyword list is available - search database of titles,
...more>>
Power Maths - A pre-calculus project - Sidney Schuman
A pre-calculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra,
...more>>
PreCalculus - Trevor Roseborough
An introduction to calculus for the student who is about to learn the subject. It makes clear the connection between the integral and the derivative and suggests a more consistent notation before the student becomes hopelessly confused.
...more>>
Problem of the Week - Purdue University
A panel in the Mathematics Department publishes a challenging problem once a week and invites college and pre-college students, faculty, and staff to submit solutions. Solutions are due within two weeks from the date of publication and should be sent
...more>>
The Problem Site - Douglas Twitchell
Math puzzles, brainteasers, strategy games, web quizzes, and informational pages. Flash-powered math games include Adders, Zap (slide tiles to move digits and add up to a specified sum), Side By Side (number re-arrangement), One To Ten (given four numbers,
...more>>
Problems of the Week - Math Forum @ Drexel
Our goal with the Problems of the Week is to engage students in non-routine, constructed-response mathematics investigations that integrate writing with problem solving in the math classroom. In addition to the Current PoWs and the Problems of the Week
...more>>
Productive Struggle
Group blog, with most contributions by secondary math and science teachers, that aims to "push teachers to learn in the same way that we push our students to learn" and "work together to make our struggles productive." Posts, which date back to March,
...more>>
Project Based Learning Pathways - David Graser
A blog about real life projects suitable for college math courses such as algebra, finite math, and business calculus. Most of these applied math projects include handouts, videos, and other resources for students, as well as a project letter. Graser,
...more>>
Public Domain Materials - Mike Jones
A collection of public domain instructional and expository materials from a US-born math teacher who teaches in China. Microsoft Word and PDF downloads include a monthly circular consisting of short problems, "The Bow-and-Arrow Problem," and "Twinkle
...more>> |
Created by Nathan Kahl for the Connected Curriculum Project, the purpose of this module is to study properties of the graphs of the basic trigonometric functions, sine and cosine. This is one within a much larger set...
Created by David Smith for the Connected Curriculum Project, the purpose of this module is to study data that may be modeled by sinusoidal functions; in particular, to determine average level, period, frequency,...
Created by Lang Moore for the Connected Curriculum Project, the purpose of this module is to provide an introduction to the elementary complex transcendental functions -- the exponential, sine, and cosine functions....
This lesson from Illuminations teaches students the features of sine and cosine graphs. Students use uncooked spaghetti to demonstrate the properties of the unit circle, which they will then represent with graphs. It is...
The Center for Cultural Design presents this site on breakdancing as a way of teaching mathematical concepts. Specifically, rotation and sine function are demonstrated. The cultural and social background of breakdance... |
Roadmap to the Regents: Mathematics B
If Students Need to Know It, It' s in This Book This book develops the mathematics skills of high school students. It builds skills that will help ...Show synopsisIf Students Need to Know It, It' s in This Book This book develops the mathematics skills of high school students. It builds skills that will help them succeed in school and on the New York Regents Exams. Why The Princeton Review? We have more than twenty years of experience helping students master the skills needed to excel on standardized tests. Each year we help more than 2 million students score higher and earn better grades. We Know the New York Regents Exams Our experts at The Princeton Review have analyzed the New York Regents Exams, and this book provides the most up-to-date, thoroughly researched practice possible. We break down the test into individual skills to familiarize students with the test' s structure, while increasing their overall skill level. We Get Results We know what it takes to succeed in the classroom and on tests. This book includes strategies that are proven to improve student performance. We provide - content review based on New York standards and objectives - detailed lessons, complete with skill-specific activities - three complete practice New York Regents Exams in Mathematics B |
Gets Them Engaged. Keeps Them Engaged. In a Shorter Text!Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the reader by opening their minds to learning (2) keeping the reader engaged on every page (3) explaining ideas directly, simply, and clearly so they don't get "lost" when studying and reviewing. Prerequisites: Fundamental Concepts of Algebra; Equations and Inequalities; Functions and Graphs; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Systems of Equations and Inequalities. For all readers interested in college algebra. |
Summary: Also available as a two-volume set, this text is intended to give students depth and perspective in their knowledge of the mathematics taught in elementary school. The author believes that some key elements in achieving this depth and perspective are for students to write clear, logical explanations, for students to enhance their intuition by working with examples and by looking for patterns and connections, and for students to use mathematics in a variety of applica...show moretions. The book is centered around "class activities," which are designed for students to work on in class in small groups. The class activities foster engagement, exploration and discussion of the material, rather than passive absorption. Many exercises and problems are included at the end of each chapter. Working on these exercises and problems and justifying their solutions carefully and clearly is crucial to achieving depth of understanding of the material. Both students and instructors should find this material fun, interesting, and rewarding. ...show less
The Concept of Measurement. Measurable Attributes. Converting From One Unit of Measurement to Another. The Moving and Combining Principles About Area. The Pythagorean Theorem. More Ways to Determine Areas. Areas of Triangles. Areas of Parallelograms. Areas of Circles and the Number Pi. How are Perimeter and Area Related? Principles for Determining Volumes. Volumes of Prisms, Cylinders, Pyramids, and Cones. Areas, Volumes, and Scaling.
4. Functions and Algebra.
Patterns, Sequences, Formulas, and Equations. Functions.
5. Statistics.
Designing Investigations and Gathering Data. Displaying Data. The Center of Data: Average and Median. The Spread of Data: Percentiles, Range.
6. Probability.
Some Basic Principles of Probability. Fraction Multiplication and Probability.
Appendix A: Cutouts for Exercises and Problems.
List Price: $76.00
Used Currently Sold Out
New $6.00
Save $70.00 (92%)
FREE shipping over $25
In stock
30-day returns
Condition:
Brand New
Order this book in the next 16 hours and 16 minutes and it ships by Noon CT tomorrowSuperFlyBooks AZ Phoenix, AZ
2002 Other Good |
Chantilly ACT MathThis means that they have to master a new level of abstraction in math. This can be challenging and take time, but it's worth it. They'll use algebra in every future math class and throughout their lives, so it's important to build a strong foundation in this class |
Product Information
Product Reviews
BJU Geometry Teacher's Guide Grade 10, Third Edition
4
5
1
1
If you are looking for a Geometry Text that has many examples and ways to teach the principles this is the book. The down side is that there are many ways to teach the principles and it is hard to decide which way to teach the lesson. The key is to know the student(s).
November 2, 2008 |
mathematicsUsing Maple, available from Adept Scientific (Letchworth, Herts), instructors can easily create interactive mathematical applications that help their colleagues and students solve problems, visualise solutions and explore conceptsAllThis fundamental underlying question has never been answered...until now. "MathspeedST: Leapfrogging LightspeedST FASTER Than The Speed of Light" is the complementary other half of "LightspeedST: Leapfrogging @ The Speed of Light."
Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students' understanding of music through mathematics.
Using Maple, available from Adept Scientific (Letchworth, Herts), instructors can easily create interactive mathematical applications that help their colleagues and students solve problems, visualise solutions and explore concepts.
Lanika announces Maplesoft's major new initiative to support teaching and learning. The Möbius Project makes it easy to create rich, interactive mathematical applications, share them with everyone, and grade them to assess understanding.
ThinkMath App is just the right mobile companion which prods you to think in a mathematically logical way. It guides you away from calculators and computing gadgets, so that you can solve simple to complex mathematical problems on your own.
For the third consecutive year, President Barack Obama used his State of the Union address to call for increased investment in science and technology. More than 40,000 Wisconsin students heed this call each day.
The Hong Kong Polytechnic University (PolyU) signed today (22 January) an agreement with the Australian Mathematics Trust (AMT) to launch the "Mathematics Challenge for Young Australians" (MCYA) in Hong KongThrough a careful treatment of number theory and geometry, Number, Shape, and Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofsMyAcademicWorkshop™ is a differientated online assesment system that helps place students into appropriate mathematics courses and helps increase student engagement and sense of accomplishment for students struggling in mathematics.
This book presents advanced mathematical descriptions and methods to help readers achieve more thorough results under more general conditions than what has been possible with previous results in the existing literature.
Physical Oceanography: A Mathematical Introduction with MATLAB® demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame.
Inner-city students are notoriously the poorest performers in SATs tests, and other exams, therefore, EIE program has teamed up with organisations, and companies to give FREE revision seminars for inner-city students on the 3rd, 10th, &17th of May.
NSF Center of excellence in advanced technological education at HCC in Brandon is taking a delegation of students, faculty members and administrators from Florida's community and state colleges on a 21 day technician training program to Spain. |
More About
This Textbook
Overview
Ooten Back Cover Copy
With over 50 combined years teaching basic math through calculus as well as consulting with math anxious students, Cheryl Ooten and Kathy Moore offer a wealth of creative ideas for all math students to overcome negative perceptions about math and develop the needed math study skills for success.
Managing the Mean Math Blues teaches students how to develop their own power to produce the desired proficiency in math. Students turn failure into success as they uncover secrets of successful math students and practice these new techniques with universal basic math concepts.
The second edition offers:
--Stronger and more math study skills content
--Added chapter to practice new skills on algebra
--Increased focus on the powerful "flow with math" technique
--The best strategies for overcoming math anxiety
--Teacher Resource Booklet
Watch students flourish as they put these cutting-edge techniques into practice and achieve a new level of confidence in the math abilities in the classroom."
"It's a great book! I hope math. faculty will take advantage of having a book available that combines the cognitive and affective combined approaches to teaching math."
Joan TottenFerris State University
"This is the book that I wish I had 35 years ago when I first started teaching math. The book neatly packages ideas, strategies, and tools in a way that readers understand, accept, and apply to learning math and any other challenging topic….Managing the Mean Math Blues, 2e is first book to clearly incorporate psychology, cognitive behavioral therapy, neuroplascity, visualization, relaxation, study skills, into a book that addresses and offers tools and strategies to overcome math anxiety."
Justine Wong
"The content is sound, the tone of the book is very supportive, and there is just enough content but not too much."
Related Subjects
Meet the Author
Cheryl Ooten , Mathematics Professor Emeritus, Santa Ana College, has taught all levels of mathematics from basic math through calculus counseling math anxious students for over 30 years. A licensed psychotherapist, Cheryl is currently a Ph.D. student at Claremont Graduate University pursuing her continuing interest in student success and math education.
Kathy Moore, Mathematics Professor, Santiago Canyon College, enjoys sharing her love of mathematics with the math anxious student. Outside of teaching people mathematics, she trains and shows her five dogs in obedience competitions around the country. Kathy lives in Norco, California with her husband and the canine pack |
MAT543 Real Analysis I
Part of a two-semester sequence covering the following topics: The real number system, topology of Rn, measure theory, and the Lebesque integral. Convergence theorems, differentiation, and Lebesque decompositions. Fubini's theorem, Radon-Nikodym theorem, and other advanced topics. |
Topics usually covered in Algebra I include number systems, properties of real numbers, order of operations (PEMDAS), prime numbers and factoring, exponents, simplifying expressions, solving equations and inequalities of one variable, properties of linear equations and inequalities, solving syste... |
crete Mathematics: A Foundation for Computer Science
This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's ...Show synopsisThis book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline201558025 WE HAVE NUMEROUS COPIES. HARDCOVER....Very Good. 0201558025 WE HAVE NUMEROUS COPIES. HARDCOVER. Library book in new condition. Light shelf wear to cover, edges, and corners. School barcode on/in book. Library sticker on binding and library stamps inside book as well as on outside edge of pages. Checkout sleeve inside front cover. Pages appear free of markings/writing.
Reviews of Concrete Mathematics: A Foundation for Computer Science
I am trying to catch up on lost ground on computer programming. For me there were some concepts in my knowledge of maths which fell into two categories. Either I did not know or had forgotten. This book has easily filled both of these gaps. The text is fun to read and takes the strain out of the ...
More
This book should be read by everyone who's serious about computers. It will give you the necessary background to work on optimization software, cryptographic algorithms, analysis of algorithms and several other subjects that are far beyond just "writing programs".
It is not an easy book, however. You |
A high-content, award-winning puzzle site that is divided into six main categories: puzzles & tests, optical illusions,...
see more
A high-content, award-winning puzzle site that is divided into six main categories: puzzles & tests, optical illusions, custom puzzles, teachers' resource, curiosities, art & language. Among the myriad of fun things, visitors will find number games, riddles, puzzles with downloadable pieces, oxymorons, and even a gift shop. A principal objective throughout the site is the enhancement of critical thinking skills. Here's a quote from Scientific American (May 27, 2003): "This virtual lab borrows the empirical spirit and creative curiosity that Archimedes brought to his work and invites visitors to explore with the same expectations for mind-blowing discovery."
This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It...
see more
This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It has chapters (parts of the book) with lessons (parts of the chapter about one idea). A lesson has five parts: 1.Vocabulary - gives special words you need for the lesson. 2.Lesson - gives a new idea and how to use this idea. 3.Example Problems - gives the steps to do problems using the new idea. 4.Practice Games - gives places for amusement where you do problems. 5.Practice Problems - You do problems.״
This is a free, onlne textbook. According to the authors, "We are two college mathematics professors who grew weary of...
see more
This is a free, onlne textbook. According to the authors, "We are two college mathematics professors who grew weary of forcing our students to purchase expensive college algebra textbooks whose mathematical content has slowly degraded over the years. Our solution? Write our own. The twist? We made our college algebra book free and we distribute it as a .pdf file under the Creative Commons License. What's more, the LaTeX source code is also available under the same license.״
״Here are my online notes for my Algebra course that I teach here at Lamar University, although I have to admit that it's...
see more
״Here are my online notes for my Algebra course that I teach here at Lamar University, although I have to admit that it's been years since I last taught this course. At this point in my career I mostly teach Calculus and Differential Equations.Despite the fact that these are my "class notes", they should be accessible to anyone wanting to learn Algebra or needing a refresher for algebra. I've tried to make the notes as self contained as possible and do not reference any book. However, they do assume that you've has some exposure to the basics of algebra at some point prior to this. While there is some review of exponents, factoring and graphing it is assumed that not a lot of review will be needed to remind you how these topics work.״
״Prepares college students for the mathematics they need in the social sciences, computer science, business, economics, and...
see more
״Prepares college students for the mathematics they need in the social sciences, computer science, business, economics, and the physical sciences up to the pre-Calculus level. It is also intended to serve a course that has as its objective an introduction to, or review of, what is currently called "pre-Calculus" topics. Some of the topics that are amplified in modern discrete mathematics and finite mathematics courses are introduced.״Please note that this site will try to sell supplements and you must create an account. However, there is no charge for the download of the textbook. As noted on the website, "Free access to the online book. Includes StudyBreak Ads (advertising placed in natural subject breaks)."
In this two-player game, players take turns assigning a value to one of the entries in a three by three matrix. Player N can...
see more
In this two-player game, players take turns assigning a value to one of the entries in a three by three matrix. Player N can select any free entry and give it a value of 1, while Player S can assign any entry the value 0. Player S wins if the matrix becomes singular; i. e. have a zero determinant. Otherwise, Player N winsElementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is...
see more
Elementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The...
see more
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated as it is the basis of all mathematical modeling used in applications found in all disciplines.Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Elementary Algebra, is the first part written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.John Redden's Elementary Algebra takes the best of the traditional, practice-driven algebra texts and combines it with modern amenities to influence learning, like online/inline video solutions, as well as, other media driven features that only a free online text can deliver. Using the online text in conjunction with a printed version of the text could promote greater understanding (at a lower cost than most algebra texts).From the traditional standpoint, John employs an early and often approach to real world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. Elementary Algebra has applications incorporated into each and every exercise set. To do this John makes use of the classic "translating English sentences into mathematical statements" subsections in chapter 1 and as the text introduces new key terms.A more modernized element; embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today.In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.While algebra is one of the most diversely applied subjects, students often find it to be one of the more difficult hurdles in their education. With this in mind, John wrote Elementary Algebra from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. |
GCSE Maths: Higher Level
Essential information written by Key Stage 3 SATs, GCSE and AS Level examiners, presented as bullet points and concise notes with key points ...Show synopsisEssential information written by Key Stage 3 SATs, GCSE and AS Level examiners, presented as bullet points and concise notes with key points highlighted to aid revision. Covers all the topics needed for every syllabus and written especially for 2001 exams. The notes include examiners tips to ensure important information is highlighted, and less formal student tips offering suggestions on where extra marks can be gained. Letts revision notes help condense course content into the essential points but also offer exam practice and each topic is followed by a short test so that students can monitor their progress. The books also have internet support available from Letts website. For every topic there is available a topic test on the website that allows students extended practice in examination style questions GCSE revision & exam preparation.. Colour illustrations GCSE revision & exam preparation.. |
Course Catalog
Course Descriptions
Mathematics Courses
This course will strengthen a student's foundation in quantitative reasoning in preparation for the science curriculum and QFR requirements. The material will be at the college algebra / precalculus level, and covered in a tutorial format with students working in small groups with the professor. Access to this course is limited to placement by a quantitative skills counselor.[ more ]
Have you ever wondered what keeps your credit card information safe everytime you buy something online? Number theory! Number Theory is one of the oldest branches of mathematics. In this course, we will discover the beauty and usefulness of numbers, from ancient Greece to modern cryptography. We will look for patterns, make conjectures, and learn how to prove these conjectures. Starting with nothing more than basic high school algebra, we will develop the logic and critical thinking skills required to realize and prove mathematical results. Topics to be covered include the meaning and content of proof, prime numbers, divisibility, rationality, modular arithmetic, Fermat's Last Theorem, the Golden ratio, Fibonacci numbers, coding theory, and unique factorization.[ more ]
Calculus permits the computation of velocities and other instantaneous rates of change by a limiting process called differentiation. The same process also solves "max-min" problems: how to maximize profit or minimize pollution. A second limiting process, called integration, permits the computation of areas and accumulations of income or medicines. The Fundamental Theorem of Calculus provides a useful and surprising link between the two processes. Subtopics include trigonometry, exponential growth, and logarithms. [ more ]
Mastery of calculus requires understanding how integration computes areas and business profit and acquiring a stock of techniques. Further methods solve equations involving derivatives ("differential equations") for population growth or pollution levels. Exponential and logarithmic functions and trigonometric and inverse functions play an important role. This course is the right starting point for students who have seen derivatives, but not necessarily integrals, before. [ more ]
Applications of calculus in mathematics, science, economics, psychology, the social sciences, involve several variables. This course extends calculus to several variables: vectors, partial derivatives, multiple integrals. There is also a unit on infinite series, sometimes with applications to differential equations. [ more ]
Applications of calculus in mathematics, science, economics, psychology, the social sciences, involve several variables. This course extends calculus to several variables: vectors, partial derivatives and multiple integrals. The goal of the course is Stokes Theorem, a deep and profound generalization of the Fundamental Theorem of Calculus. The difference between this course and MATH 150 is that MATH 150 covers infinite series instead of Stokes Theorem. Students with the equivalent of BC 3 or higher should enroll in MATH 151, as well as students who have taken the equivalent of an integral calculus and who have already been exposed to infinite series. For further clarification as to whether MATH 150 or MATH 151 is appropriate, please consult a member of the math/stat department.[ more ]
Who should have won the 2000 Presidential Election? Do any two senators really have equal power in passing legislation? How can marital assets be divided fairly? While these questions are of interest to many social scientists, a mathematical perspective can offer a quantitative analysis of issues like these and more. In this course, we will discuss the advantages and disadvantages of various types of voting systems and show that, in fact, any such system is flawed. We will also examine a quantitative definition of power and the principles behind fair division. Along the way, we will enhance the critical reasoning skills necessary to tackle any type of problem mathematical or otherwise.[ more ]
What is mathematics? How can it enrich and improve your life? What do mathematicians think about and how do they go about tackling challenging questions? Most people envision mathematicians as people who solve equations or perform arithmetic. In fact, mathematics is an artistic endeavor which requires both imagination and creativity. In this course, we will experience what this is all about by discovering various beautiful branches of mathematics while learning life lessons that will have a positive impact on our lives. There are two meta-goals for this course: (1) a better perspective into mathematics, and (2) sharper analytical reasoning to solve problems (both mathematical and nonmathematical).[ more ]
As a complement to calculus, which is the study of continuous processes, this course focuses on the discrete, including finite sets and structures, their properties and applications. Topics will include basic set theory, infinity, graph theory, logic, counting, recursion, functions, and number theory. The course serves as an introduction not only to these and other topics but also to the methods and styles of mathematical proof and problem solving. In the spring semester, students will attend class plus one conference section each week.[ more ]
Historically, much beautiful mathematics has arisen from attempts to explain physical, chemical, biological and economic processes. A few ingenious techniques solve a surprisingly large fraction of the associated ordinary and partial differential equations, and geometric methods give insight to many more. The mystical Pythagorean fascination with ratios and harmonics is vindicated and applied in Fourier series and integrals. We will explore the methods, abstract structures, and modeling applications of ordinary and partial differential equations and Fourier analysis.[ more ]
This course covers a variety of mathematical methods used in the sciences, focusing particularly on the solution of ordinary and partial differential equations. In addition to calling attention to certain special equations that arise frequently in the study of waves and diffusion, we develop general techniques such as looking for series solutions and, in the case of nonlinear equations, using phase portraits and linearizing around fixed points. We study some simple numerical techniques for solving differential equations. A series of optional sessions in Mathematica will be offered for students who are not already familiar with this computational tool. [ more ]
Many social, political, economic, biological, and physical phenomena can be described, at least approximately, by linear relations. In the study of systems of linear equations one may ask: When does a solution exist? When is it unique? How does one find it? How can one interpret it geometrically? This course develops the theoretical structure underlying answers to these and other questions and includes the study of matrices, vector spaces, linear independence and bases, linear transformations, determinants and inner products. Course work is balanced between theoretical and computational, with attention to improving mathematical style and sophistication. [ more ]
This course will be a study of mathematics education, from the practical aspects of teaching to numerous ideas in current research. This is an exciting time in mathematics education. The new common core state standards have sparked a level of interest and debate not often seen in the field. In this course, we will look at a wide range of issues in math education, from content knowledge to the role of creativity in a math class to philosophies of teaching.
In addition to weekly tutorial meetings that focus on some of the key questions in math education, we will also meet weekly as a group to discuss the mechanics of teaching. Each student will also be responsible for teaching bi-weekly extra sessions for MATH 200 at which they will make presentations, field questions, and offer guidance on homework questions. Students will also attend the MATH 200 lecture, and do some grading for the course.[ more ]
Gauss said "Mathematics is the queen of the sciences and number theory the queen of mathematics"; in this class we shall meet some of her subjects. We will discuss many of the most important questions in analytic and additive number theory, with an emphasis on techniques and open problems. Topics will range from Goldbach's Problem and the Circle Method to the Riemann Zeta Function and Random Matrix Theory.
Other topics will be chosen by student interest, coming from sum and difference sets, Poissonian behavior, Benford's law, the dynamics of the 3x+1 map as well as suggestions from the class. We will occasionally assume some advanced results for our investigations, though we will always try to supply heuristics and motivate the material. No number theory background is assumed, and we will discuss whatever material we need from probability, statistics or Fourier analysis. For more information, see edu/~sjmiller/williams/406.[ more ]
The complex numbers are amazingly useful in mathematics, physics, engineering, and elsewhere. We'll learn the meaning of complex multiplication and exponentiation, as in Euler's famous eiπ = -1. We'll study complex functions and their power series, learn how to integrate in the complex plane, including residue calculus, and how to map one domain to another (conformal mapping). We'll see the easiest proof of the Fundamental Theorem of Algebra, which says that every algebraic equation has a solution as long as you allow complex numbers.[ more ]
Mathematical models are extensively used to understand biological phenomena. In this course we will study how differential and difference equations can be used to model various ecological systems ranging from predator-prey interactions to infectious disease dynamics. We will explore how to formulate these models, and methods for analyzing these systems including local and global stability analysis will be introduced.[ more ]
The study of numbers dates back thousands of years, and is fundamental in mathematics. In this course, we will investigate both classical and modern questions about numbers. In particular, we will explore the integers, and examine issues involving primes, divisibility, and congruences. We will also look at the ideas of number and prime in more general settings, and consider fascinating questions that are simple to understand, but can be quite difficult to answer.[ more ]
Living in the information age, we find ourselves depending more and more on codes that protect messages against either noise or eavesdropping. This course examines some of the most important codes currently being used to protect information, including linear codes, which in addition to being mathematically elegant are the most practical codes for error correction, and the RSA public key cryptographic scheme, popular nowadays for internet applications. We also study the standard AES system as well as an increasingly popular cryptographic strategy based on elliptic curves. Looking ahead by a decade or more, we show how a quantum computer could crack the RSA scheme in short order, and how quantum cryptographic devices will achieve security through the inherent unpredictability of quantum events efficientlyIn the last twenty years computers have profoundly changed the work in numerical mathematics (in areas from linear algebra and calculus to differential equations and probability). The main goal of this tutorial is to learn how to use computers to do quantitative science. We will explore concepts and ideas in mathematics and science using numerical methods and computer programming. We will use specialized software, including Mathematica and Matlab. [ more ]
What can computational biology teach us about cancer? In this capstone experience for the Genomics, Proteomics, and Bioinformatics program, computational analysis and wet-lab investigations will inform each other, as students majoring in biology, chemistry, computer science, mathematics/statistics, and physics contribute their own expertise to explore how ever-growing gene and protein data-sets can provide key insights into human disease. In this course, we will take advantage of one well-studied system, the highly conserved Ras-related family of proteins, which play a central role in numerous fundamental processes within the cell. The course will integrate bioinformatics and molecular biology, using database searching, alignments and pattern matching, phylogenetics, and recombinant DNA techniques to reconstruct the evolution of gene families by focusing on the gene duplication events and gene rearrangements that have occurred over the course of eukaryotic speciation. By utilizing high through-put approaches to investigate genes involved in the MAPK signal transduction pathway in human colon cancer cell lines, students will uncover regulatory mechanisms that are aberrantly altered by siRNA knockdown of putative regulatory components. This functional genomic strategy will be coupled with independent projects using phosphorylation-state specific antisera to test our hypotheses. Proteomic analysis will introduce the students to de novo structural prediction and threading algorithms, as well as data-mining approaches and Bayesian modeling of protein network dynamics in single cells. Flow cytometry and mass spectrometry will be used to study networks of interacting proteins in colon tumor cells.[ more ]
Take a piece of string, tie a knot in it, and glue the ends together. The result is a knotted circle, known as a knot. For the last 100 years, mathematicians have studied knots, asking such questions as, "Given a nasty tangled knot, how do you tell if it can be untangled without cutting it open?" Some of the most interesting advances in knot theory have occurred in the last ten years.This course is an introduction to the theory of knots. Among other topics, we will cover methods of knot tabulation, surfaces applied to knots, polynomials associated to knots, and relationships between knot theory and chemistry and physics. In addition to learning the theory, we will look at open problems in the field.[ more ]
It is easy to convince oneself that the shortest distance from equatorial Africa to equatorial South America is along the equator. This illustrates the fact that "straight lines" on a sphere are described by so-called great circles. It is somewhat more difficult to describe the shortest path between two points on the surface of, for example, a doughnut, reflecting the fact that a doughnut curves in space in a more complicated way than the sphere. Differential geometry is the mathematical language describing these curvature properties. In this course we will learn this language and use it to answer many interesting questions. We will also develop the tools needed to begin the more advanced study of "Riemannian" geometry, which describes (among other things) Einstein's Relativity Theory.
Topics: Curves in space, the Frenet-Serret Theorem, the first and second fundamental forms, geodesics, principal/Gaussian/mean/normal curvatures, the Theorema Egregium, the Gauss-Bonnet formula and Theorem, introduction to n-dimensional Riemannian manifolds/metrics/curvature.[ more ]
Set theory is the traditional foundational language for all of mathematics. We will be discussing the Zermelo-Fraenkel axioms, including the Axiom of Choice and the Continuum Hypothesis, basic independence results and, if time permits, Goedel's Incompleteness Theorem. At one time, these issues tore at the foundations of mathematics. They are still vital for understanding the nature of mathematical truth.[ more ]
The subject of computational geometry started just 25 years ago, and this course is designed to introduce its fundamental ideas. Our goal is to explore "visualization" and "shape" in real world problems. We focus on both theoretic ideas (such as visibility, polyhedra, Voronoi diagrams, triangulations, motion) as well as applications (such as cartography, origami, robotics, surface meshing, rigidity). This is a beautiful subject with a tremendous amount of active research and numerous unsolved problems, relating powerful ideas from mathematics and computer science.[ more ]
The thorough study of Euclidean geometry has been a cornerstone of a complete education for thousands of years. In this course, we trace the origins of modern geometry by studying its classical roots, including ancient Greek geometry, conic sections, triangle centers, circle theorems, trigonometry, and analytic geometry. Other topics include the impossibility of doubling the cube or trisecting an angle, non-constructable polygons, non-Euclidean geometry, and geometry in higher dimensions.[ more ]
Using math competitions such as the Putnam Exam as a springboard, in this class we follow the dictum of the Ross Program and "think deeply of simple things". The two main goals of this course are to prepare students for competitive math competitions, and to get a sense of the mathematical landscape encompassing elementary number theory, combinatorics, graph theory, and group theory (among others). While elementary frequently is not synonymous with easy, we will see many beautiful proofs and "a-ha" moments in the course of our investigations. Students will be encouraged to explore these topics at levels compatible with their backgrounds.[ more ]
Game theory is the study of interacting decision makers involved in a conflict of interest. We investigate outcomes, dynamics, and strategies as players rationally pursue objective goals and interact according to specific rules. Game theory has been used to illuminate political, ethical, economical, social, psychological, and evolutionary phenomenon. We will examine concepts of equilibrium, stable strategies, imperfect information, repetition, cooperation, utility, and decisionOrigami is the art and study of folding and unfolding. Although ancient in origin, there has been a tremendous resurgence of interest recently, resulting in stunning sculptures and marvelously intricate pop-up books. The applications of origami have grown as well, from NASA's James Webb space telescope to cutting-edge protein folding models. This is a beautiful subject with a tremendous amount of active research, relating powerful ideas from studio art, computer science, and mathematics.
This tutorial is designed to introduce the foundations of origami design from a mathematical viewpoint: 1D linkages, 2D crease patterns and cut-theorems, 3D unfolding polyhedra. No experience in paper folding is necessary.[ more ]
Real analysis is the theory behind calculus. It is based on a precise understanding of the real numbers, elementary topology, and limits. Topologically, nice sets are either closed (contain their limit points) or open (complement closed). You also need limits to define continuity, derivatives, integrals, and to understand sequences of functions. [ more ]
Real analysis or the theory of calculus--derivatives, integrals, continuity, convergence--starts with a deeper understanding of real numbers and limits. Applications in the calculus of variations or "infinite-dimensional calculus" include geodesics, harmonic functions, minimal surfaces, Hamilton's action and Lagrange's equations, optimal economic strategies, nonEuclidean geometry, and general relativity. [ more ]
Investigation of the structure and properties of graphs with emphasis both on certain classes of graphs such as multi-partite, planar, and perfect graphs and on application to various optimization problems such as minimum colorings of graphs, maximum matchings in graphs, network flows, etc.[ more ]
Algebra gives us the tools to solve equations. Sets such as the integers or real numbers have special properties which make algebra work or not work according to the circumstances. In this course, we generalize algebraic processes and the sets upon which they operate in order to better understand, theoretically, when equations can and cannot be solved. We define and study the abstract algebraic structures called groups, rings and fields, as well as the concepts of factor group, quotient ring, homomorphism, isomorphism, and various types of field extensions. [ more ]
Phylogenetics is the analysis and construction of information trees based on shared characteristics. The foundational problem asks, given some data from objects, how can a tree be constructed which shows the proper relationships between the objects? This is a beautiful subject with a tremendous amount of cutting-edge research, relating powerful ideas from statistics, computer science, biology, and mathematics, having a wide range of applications, from literature, to linguistics, to visual graphics. This course is designed to introduce fundamental ideas of this subject from a mathematical viewpoint, touching and expanding upon the interests of the enrolled students.[ more ]
This course introduces a formal framework for investigating both the computability and complexity of problems. We study several models of computation including finite automata, regular languages, context-free grammars, and Turing machines. These models provide a mathematical basis for the study of computability theory--the examination of what problems can be solved and what problems cannot be solved--and the study of complexity theory--the examination of how efficiently problems can be solved. Topics include the halting problem and the P versus NP problem.[ more ]
The calculus of complex-valued functions turns out to have unexpected simplicity and power. As an example of simplicity, every complex-differentiable function is automatically infinitely differentiable. As examples of power, the so-called "residue calculus" permits the computation of "impossible" integrals, and "conformal mapping" reduces physical problems on very general domains to problems on the round disc. The easiest proof of the Fundamental Theorem of Algebra, not to mention the first proof of the Prime Number Theorem, used complex analysis. [ more ]
Over the years financial instruments have grown from stocks and bonds to numerous derivatives, such as options to buy and sell at future dates under certain conditions. The 1997 Nobel Prize in Economics was awarded to Robert Merton and Myron Schloles for their Black-Scholes model of the value of financial instruments. This course will study deterministic and random models, futures, options, the Black-Scholes Equation, and additional topics.[ more ]
Topology is the study of when one geometric object can be continuously deformed and twisted into another object. Determining when two objects are topologically the same is incredibly difficult and is still the subject of a tremendous amount of research, including recent work on the Poincare Conjecture, one of the million-dollar millennium-prize problems. The first part of the course on point-set topology establishes a framework based on "open sets" for studying continuity and compactness in very general spaces. The second part on homotopy theory develops refined methods for determining when objects are the same. We will prove for example that you cannot twist a basketball into a doughnut.[ more ]
Algebraic Geometry has been at the heart of mathematics for at least two hundred years. While starting with a humble study of circles, it has influenced a tremendous amount of modern mathematics, ranging from number theory to robotics. Algebraic Geometry uses tools from almost all areas of mathematics; key for this course will be abstract algebra and multivariable calculus. We will study conics, cubics (books are written about the geometry of cubics; the depth of ideas involved with these curves is amazing) and higher degree curves. In particular, we will study Bezout's Theorem and Riemann-Roch for curves. Simultaneously with learning about curves, we will also cover the more abstract ideas behind affine and projective varieties. Emphasis will be placed on both "big picture" concepts and the underlying technical details.[ more ]
This course further develops and explores topics and concepts from real analysis, with special emphasis on introducing students to subject matter and techniques that are useful for graduate study in mathematics or an allied field. Material will be drawn, based on student interest, from many areas, including analytic number theory, Fourier series and harmonic analysis, generating functions, differential equations and special functions, integral operators, equidistribution theory and probability, random matrix theory and probabilistic methods. This will be an intense, fast paced class which will give a flavor for graduate school. In addition to standard homework problems, students will also write reviews for MathSciNet, referee papers for journals, write programs in SAGE or Mathematica to investigate and conjecture, and read classic and current research papers.[ more ]
In the 1830's Evariste Galois developed a beautiful theory relating the structure of field extensions to the structure of a group. By understanding this relationship, one can often translate a problem about field extensions to a question about groups that is easier to answer. In this course, we will study Galois Theory and modules. A module is a generalization of vector spaces; in particular, a module can be thought of as a vector space with the weaker condition that the set of scalars are elements of a ring instead of a field. Possible topics covered will include field theory, galois theory, quotient modules, direct sums, free modules, and exact sequences.[ more ]
The study of measure theory arose from the study of stochastic (probabilistic) systems. Applications of measure theory lie in biology, chemistry, physics as well as in economics. In this course, we develop the abstract concepts of measure theory and ground them in probability spaces. Included will be Lebesgue and Borel measures, measurable functions (random variables). Lebesgue integration, distributions, independence, convergence and limit theorems. This material provides good preparation for graduate studies in mathematics, statistics and economics. [ more ]
Ergodic theory studies the probabilistic behavior of dynamical systems as they evolve through time. This course will be an introduction to the basic notions in ergodic theory. The course starts with an introduction to measure theory: (sigma-algebras, measurable sets and measurable transformations and Lebesgue integration). Then we will cover ergodic, weak mixing, mixing, and Bernoulli transformations, and transformations admitting and not admitting an invariant measure. There will be an emphasis on specific examples such as group rotations, the binary odometer transformations, and rank-one constructions. We will aslo cover some notions from topological dynamics. For the textbook: more ]
Commutative algebra has applications ranging from algebraic geometry to coding theory. For example, one can use commutative algebra to create error correcting codes. It is perhaps most often used, however, to study curves and surfaces in different spaces. To understand these structures, one must study polynomial rings over fields. This course will be an introduction to commutative algebra. Possible topics include polynomial rings, localizations, primary decomposition, completions, and modules.[ more ]
In the first N math classes of your career, it's possible to get an incomplete picture as to what the real world is truly like. How? You're often given exact problems and told to find exact solutions. The real world is sadly far more complicated. Frequently we cannot exactly solve problems; moreover, the problems we try to solve are themselves merely approximations to the world. We're forced to develop techniques to approximate not just solutions, but even the statement of the problem. In this course we discuss some powerful methods from advanced linear algebra and their applications to the real world, specifically linear programming (and, if time permits, random matrix theory). Linear programming is used to attack a variety of problems, from applied ones such as the traveling salesman problem, determining schedules for major league sports (or a movie theater, or an airline) to designing efficient diets to feed the world, to pure ones such as Hales' proof of the Kepler conjecture.[ more ]
We all know that integers can be factored into prime numbers and that this factorization is essentially unique. In more general settings, it often still makes sense to factor numbers into "primes," but the factorization is not necessarily unique! This surprising fact was the downfall of Lame's attempted proof of Fermat's Last Theorem in 1847. Although a valid proof was not discovered until over 150 years later, this error gave rise to a new branch of mathematics: algebraic number theory. In this course, we will study factorization and other number-theoretic notions in more abstract algebraic settings, and we will see a beautiful interplay between groups, rings, and fields. [ more ]
A single round soap bubble is the least-area way to enclose a given volume of air, as ws proved in 1884 by Schwarz. A double soap bubble is the least-area way to enclose and separate two given volumes of air, as was proved in 2000 as the culmination of a decade of work by many, including Williams faculty and students. Because it is hard to control ahead of time the complicated ways ("singularities") in which pieces of soap film theoretically might come together, the study of such physical problems had to wait for the development of a more general and inclusive kind of geometry, now known as Geometric Measure Theory. (These same tools can be applied to all kinds of singularities from fractures in materials to black holes in the universe.[ more ]
Since humankind first utilized stones and bricks to tile the floors of their abodes, tiling has been an area of interest. Practitioners include artists, engineers, designers, architects, crystallographers, scientists and mathematicians. This course will be an investigation into the mathematical theory of tiling. The course will focus on tilings of the plane, including topics such as the symmetry groups of tilings, the topology of tilings, the ergodic theory of tilings, the classification of tilings and the aperiodic Penrose tilings. We will also look at tilings in higher dimensions, including "knotted tilings".[ more ]
A Lie algebra is a vector space endowed with a multiplication operation known as a bracket. They have applications to a wide variety of mathematical fields such as geometry, representation theory, combinatorics, and mathematical physics. This course will cover the basic theory of Lie algebras, including solvable and nilpotent Lie algebras, Cartan subalgebras, the Killing form, root systems, the Weyl group, Dynkin diagrams, and Cartan matrices. Special attention will be paid to examples that highlight the importance of Lie algebras in modern mathematics.[ more ]
Mathematical modeling is concerned with translating a natural phenomenon into a mathematical form. In this abstract form the underlying principles of the phenomenon can be carefully examined and real-world behavior can be interpreted in terms of mathematical shapes. The models we investigate include feedback phenomena, phase locked oscillators, multiple population dynamics, reaction-diffusion equations, shock waves, and the spread of pollution, forest fires, and diseases. We will employ tools from the fields of differential equations and dynamical systems. The course is intended for students in the mathematical, physical, and chemical sciences, as well as for students who are seriously interested in the mathematical aspects of physiology, economics, geology, biology, and environmental studies.[ more ]
This course is an introduction to chaotic dynamical systems. The topics will include bifurcations, the quadratic family, symbolic dynamics, chaos, dynamics of linear systems, and some complex dynamics. [ more ]
Maxwell's equations are four simple formulas, linking electricity and magnetism, that are among the most profound equations ever discovered. These equations led to the prediction of radio waves, to the realization that a description of light is also contained in these equations and to the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe are deep generalizations of Maxwell's equations. Perhaps even more surprising is that these equations and their generalizations have led to some of the most important mathematical discoveries (where there is no obvious physics) of the last 25 years. For example, much of the math world was shocked at how these physics generalizations became one of the main tools in geometry from the 1980s until today. It seems that the mathematics behind Maxwell is endless. This will be an introduction to Maxwell's equations, from the perspective of a mathematician.[ more ]
Partial differential equations are often used to model the most basic natural phenomena. Examples include the flow of liquids, the spread of heat and the radiation of electromagnetic waves. These type of equations have lead to advances such as the prediction of radio waves, the discovery of the special theory of relativity and are essential to the theory of quantum mechanics. In this course we will introduce the theory of partial differential equations. A special focus will be on three classical equations: the wave equation, the Laplace equation and the heat equation. Classical techniques and theorems will be covered such as the Method of Characteristics, the Cauchy-Kovalevski Theorem and Fourier Transform techniques.[ more ]
Lying at the interface of combinatorics, ergodic theory, harmonic analysis, number theory, and probability, Additive Combinatorics is an exciting field which has experienced tremendous growth in recent years. Very roughly, it is an attempt to classify subsets of a given field which are almost a subspace. We will discuss a variety of topics, including sum-product theorems, the structure of sets of small doubling (e.g. the Freiman-Ruzsa theorem), long arithmetic progressions (e.g. Roth's theorem), structured subsets of sumsets, and applications to computer science (e.g. to pseudorandomess). Depending on time and interest, we may also discuss higher-order Fourier analysis, the polynomial method, and the ergodic approach to Szemeredi's theorem.[ colloquium. Meets every week for two hours both fall and spring. Senior majors must participate at least one hour a week. This colloquium is in addition to the regular four semester-courses taken by all students.[ more ]
Statistics Courses
It is nearly impossible to live in the world today without being inundated with data. Even the most popular newspapers feature statistics to catch the eye of the passerby, and sports broadcasters overwhelm the listener with arcane statistics. How do we learn to recognize dishonest or even unintentionally distorted representations of quantitative information? How are we to reconcile two medical studies with seemingly contradictory conclusions? How many observations do we need in order to make a decision? It is the purpose of this course to develop an appreciation for and an understanding of the interpretation of data. We will become familiar with the standard tools of statistical inference including the t-test, the analysis of variance, and regression, as well as exploratory data techniques. Applications will come from the real world that we all live in.[ more ]
Statistics can be viewed as the art (science?) of turning data into information. Real world decision-making, whether in business or science is often based on data and the perceived information it contains. Sherlock Holmes, when prematurely asked the merits of a case by Dr. Watson, snapped back, "Data, data, data! I can't make bricks without clay." In this course, we will study the basic methods by which statisticians attempt to extract information from data. These will include many of the standard tools of statistical inference such as hypothesis testing, confidence intervals, and linear regression as well as exploratory and graphical data analysis techniques.[ more ]
Data come from a variety of sources sometimes from planned experiments or designed surveys, but also arise by much less organized means. In this course we'll explore the kinds of models and predictions that we can make from both kinds of data as well as design aspects of collecting data. We'll focus on model building, especially multiple regression, and talk about its potential as well as its limits to answer questions about the world. We\'ll emphasize applications over theory and analyze real data sets throughout the course.[ more ]
What does statistics have to do with designing and carrying out experiments? The answer is, surprisingly perhaps, a great deal. In this course, we will study how to design an experiment with the fewest number of observations possible to achieve a certain power. We will also learn how to analyze and present the resulting data and draw conclusions. After reviewing basic statistical theory and two sample comparisons, we cover one and two-way ANOVA and (fractional) factorial designs extensively. The culmination of the course will be a project where each student designs, carries out, analyzes, and presents an experiment of interest to him or her. Throughout the course, we will use the free statistical software program R to carry out the statistical analysis efficientlyThe probability of an event can be defined in two ways: (1) the long-run frequency of the event, or (2) the belief that the event will occur. Classical statistical inference is built on the first definition given above, while Bayesian statistical inference is built on the second.
This course will introduce the student to methods in Bayesian statistics.
Topics covered include: prior distributions, posterior distributions, conjugacy, and Bayesian inference in single-parameter, multi-parameter, and hierarchical models. The computational issues associated with each of these topics will also be discussed.[ more ]
This course focuses on the building of empirical models through data in order to predict, explain, and interpret scientific phenomena. The main focus will be on multiple regression as a technique for doing this. We will study both the mathematics of regression analysis and its applications, including a discussion of the limits to such analyses. The applications will range from a broad range of disciplines, such as predicting the waiting time between eruptions of the Old Faithful geyser, forecasting housing prices or modeling the probability of failure of a scientific experiment.[ more ]
In elementary statistics courses, one typically studies how to analyze data and make inferences when only one population variable is of interest. But what if one wanted to make inferences about more than one variable in the population? In such cases, elementary statistical methods might not apply. In this course, we study the tools and the intuition that are necessary to analyze and describe such data sets. Specific topics covered will include the multivariate normal distribution, multivariate analysis of variance, principal component analysis, factor analysis, canonical correlation, and clustering.[ more ]
This course will introduce students to advanced mathematical concepts and techniques for a deeper understanding of statistical inference.
Many topics from STAT 201 such as random variables, the central limit theorem or how to test and estimate unknown parameters will be revisited and put on a more rigorous footing. In addition, emphasis will be placed on simulation and resampling (e.g., permutation and bootstrap) approaches to statistical inference and implemented with the statistical software R.[ more ]
This course explores modern statistical methods for drawing scientific inferences from longitudinal data, i.e., data collected repeatedly on experimental units over time. The independence assumption made for most classical statistical methods does not hold with this data structure because we have multiple measurements on each individual. Topics will include linear and generalized linear models for correlated data, including marginal and random effect models, as well as computational issues and methods for fitting these models. We will consider many applications in the social and biological sciences.[ more ]
This course focuses on methods for analyzing categorical response data. In contrast to continuous data, categorical data consist of observations classified into two or more categories. Traditional tools of statistical data analysis are not designed to handle such data and pose inappropriate assumptions. We will develop methods specifically designed to address the discrete nature of the observations and consider many applications in the social and biological sciences as well as in medicine, engineering and economics. All methods can be viewed as extensions of traditional regression models and ANOVA.[ more ]
In both science and industry today, the ability to collect and store data can outpace our ability to analyze it. Traditional techniques in statistics are often unable to cope with the size and complexity of today's data bases and data warehouses. New methodologies in Statistics have recently been developed, designed to address these inadequacies, emphasizing visualization, exploration and empirical model building at the expense of traditional hypothesis testing. In this course we will examine these new techniques and apply them to a variety of real data sets.[ more ]
Many statistical procedures and tools are based on a set of assumptions, such as normality. But, what if some or all of these assumptions are not valid? This question leads to the consideration of distribution-free analysis, an active and fascinating field in modern statistics called nonparametric statistics. In this course we aim to make inference for population characteristics while making as few assumptions as possible. Besides the classical rank or randomization-based tests, this course especially focuses on various modern nonparametric inferential techniques, such as nonparametric density estimation, nonparametric regression, selection of smoothing parameter (cross validation and unbiased risk estimation), bootstrap and jackknife, and Minimax theory. Throughout the semester we will examine these new methodologies and apply them on simulated and real data sets using R.[ more ] |
Intermediate Algebra : Graphs and Models - 3rd edition
Summary: The Third Edition of the Bittinger Graphs and Models series helps students succeed in algebra by emphasizing a visual understanding of concepts. This latest edition incorporates a new Visualizing the Graph feature that helps students make intuitive connections between graphs and functions without the aid of a graphing calculator.
3.1 Systems of Equations in Two Variables 3.2 Solving by Substitution or Elimination 3.3 Solving Applications: Systems of Two Equations 3.4 Systems of Equations in Three Variables 3.5 Solving Applications: Systems of Three Equations 3.6 Elimination Using Matrices 3.7 Determinants and Cramer's Rule 3.8 Business and Economics Applications
0321416163 |
Join the Conversation
Mathworks Curriculum Samples
Mathworks Math Explorations
Mathworks' innovative school-year curriculum for the 6th, 7th, and 8th grades integrates learning from the laboratory of our summer math camps with objectives that cover the TEKS through Algebra I. The curriculum includes completion of Algebra I by the end of 8th grade.
Young students are engaged in using algebraic ideas, and these ideas are built upon throughout their middle school years. Math Explorations weaves algebra and algebraic ideas with hands-on, inquiry-based explorations for students working independently and in groups. The curriculum is presented in carefully developed textbooks and supporting materials that has been implemented with over 3,500 middle school students across Texas.
Textbook ordering: If you are interested in purchasing copies of any of the three textbooks, please submit a request online and we will contact you as soon as possible. |
COURSES
Burger Math
About Professor Ed Burger Edward Burger is Professor of Mathematics at Williams College. He is the author of over 30 research articles and 12 books. He is also the star of over 2000 entertaining mathematics videos for middle school and high school students.
Saturday April 19, 2014 S.O.S. MATHematics is your free resource for math review material from Algebra to Differential Equations! The perfect study site for high school, college students and adult learners.
S.O.S. Math
Revision material (GCSE Grades B and C) The following word documents can be downloaded. They provide comprehensive coverage of all grade B and C grade GCSE topics (the topics that are most crucial to understand well if you wish to obtain a good grade). Each document contains revision notes, examples and worked past paper questions.
GCSE maths revision
DEWIS Test Yourself questions in a range of topic such as complex numbers, matrices, partial differentiation, percentages, ratios, vectors and transposition of formulae available from mathcentre. Find out more..... Welsh language Fact & Formulae leaflets are available. Find out more.....
"Absolutely love it - can't say it enough. My three children use it all the time. These lessons are a great safety net because they cover everything that is taught at school."
Mathematics.com.au - Maths Help Online | Maths Worksheets | Maths Software | Maths Tutor
Mathsguru:RESOURCES FOR STUDENTS AND TEACHERS OF MATHEMATICS
Schools / Colleges Use the iOS and Android apps without the adverts and when my site is busy and slow. News Flash! : Version 2.4 out now More details ... Maths Revision Videos and Past Papers
Here is a complete listing of all the subjects that are currently available on this site as well as brief descriptions of each. Cheat Sheets & Tables Algebra Cheat Sheet - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. Currently the cheat sheet is four pages long. Algebra Cheat Sheet (Reduced) - This is the same cheat sheet as above except it has been reduced so that it will fit onto the front and back of a single piece of paper. |
Important Links
Saxon Publications
Saxon is the nation's most comprehensive and most thoroughly researched homeschool math program, with more than 30 years of proven success. Saxon mathematics for grades K–12 is based on the teaching principles of incremental development, continual practice and review, and cumulative assessment.
When John Saxon created his original math text in 1979, his vision was for a teaching method to help students better understand math. Since then, the program has been augmented with features to help you at every level.
Saxon's K-3 program is designed to teach basic arithmetic concepts as well as geometry, patterns, time, and more. Each lesson is scripted for the parent, which takes the guesswork out of teaching young learners. Manipulatives accelerate understanding of abstract math concepts, and worksheets provide cumulative review.
Saxon Math for middle grades transitions students from manipulatives and worksheets to a textbook approach. The emphasis in the middle grades is on developing algebraic reasoning as well as geometric concepts. Lessons include a new concept plus a review of previous concepts, and Investigations give students a more in-depth treatment of math concepts. Available for middle and upper grades, a Solutions Manual gives step-by-step solutions for all problems in the book.
Saxon's high school texts prepare students for college and beyond. Like the middle grades, the upper grades program offers a textbook, tests, and a Solutions Manual. Homeschool kits are available for Algebra 1, Algebra 2, Geometry, Advanced Math, and Calculus |
To see the detailed Instructor Class Description, click on the underlined instructor name following the course description.
STMATH 300 Foundations of Modern Math (5) QSR Introduces students to mathematical argument and to reading and writing proofs. Develops elementary set theory, examples of relations, functions and operations on functions, the principle of induction, counting techniques, elementary number theory, and combinatorics. Places strong emphasis on methods and practice of problem solving. Prerequisite: minimum grade of 2.0 in B CUSP 125.
STMATH 420 History of Mathematics (5) NW, QSR Surveys the historical development of mathematics from its earliest beginnings, through the emergence of calculus, and into the early 20th century. Prerequisite: minimum grade of 2.0 in either B CUSP 124 or MATH 124.
STMATH 425 Real Analysis II (5) The Riemann-Stieljes integral and the Fundamental Theorem of Calculus. Sequences and series of functions, uniform convergence and its relationship to continuity, differentiation, and integration, the Stone-Weierstrass Theorem. Continuity and differentiability of functions of several variables, the Inverse and Implicit Function Theorems, and Rank Theorem. Prerequisite: minimum grade of 2.0 in STMATH 424.
STMATH 493 Special Topics in Mathematics (1-5, max. 15) Covers special topics in advanced mathematics in a classroom setting not currently taught in the mathematics curriculum. Prerequisite: minimum grade of 2.0 in either STMATH 300 or MATH 300. |
0131874799
9780131874794
Precalculus:Gets Them Engaged. Keeps Them Engaged. Blitzer's philosophy: present the full scope of mathematics, while always (1) engaging the student by opening their minds to learning (2) keeping the student engaged on every page (3) explaining ideas directly, simply, and clearly so they don't get "lost" when studying and reviewing. First, he gets students engaged in the study of mathematics by highlighting truly relevant, unique, and engaging applications. He explores math the way it evolved: by describing real problems and how math explains them. In doing so, it answers the question "When will I ever use this?" Then, Blitzer keeps students engaged by ensuring they don't get lost when studying. Examples are easy to follow because of a three-step learning system "See it, Hear it, Try it" embedded into each and every one. He literally "walks" the student through each example by his liberal use of annotations the instructor's "voice" that appears throughout.
Back to top
Rent Precalculus 3rd edition today, or search our site for Robert F. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
The new edition features increased emphasis on the computing technologies commonly used in such coureses. New to This Edition
&q...show moreuot;Technology Step by Step" sections show how to solve basic problems using Minitab software, the TI-83 graphing calculator, or Excel.
More examples and exercises based on actual data.
Features
Statistics Today problems open every chapter. These real-life problems, accompanied by a photo or graphic and sometimes a news item, show students the relevance of the chapter's topic. The answer is provided at chapter end.
Procedure Tables embody the book's step by step approach. These boxes summarize methods for solving various types of common problems. Worked examples include EVERY step.
Critical Thinking Challenges at the end of each chapter extend chapter concepts into new areas, inviting students to think about and apply what they have learned.
Allan G. Bluman is Professor of Mathematics at Community College of Allegheny County, near Pittsburgh. For the McKeesport and New Kensington Campuses of Pennsylvania State University, he has taught teacher-certification and graduate education statistics courses. Prior to his college teaching, he taught mathematics at a junior high school.
Professor Bluman received his B.S. from California State College in California, Penn.; his M.Ed. from the University of Pittsburgh; and, in 1971, his Ed.D., also from the University of Pittsburgh. His major field of study was mathematics education.
In addition to Elementary Statistics: A Step by Step Approach, Third Edition, and Elementary Statistics: A Brief Version, the author has published several professional articles and the Modern Math Fun Book (Cuisenaire Publishing Company). He has spoken and presided at national and local mathematics conferences and has served as newsletter editor for the Pennsylvania State Mathematics Association of Two-Year Colleges. He is a member of the American Statistical Association, the National Council of Teachers of Mathematics, and the Mathematics Council of Western Pennsylvania.
Al Bluman is married and has two children. His hobbies include writing, bicycling, and swimming.4.00 +$3.99 s/h
Acceptable
Mini City Media Nc Raleigh, NC
2000 Hardcover Fair ***TOO LARGE for INTERNATIONAL SHIPPING! ! *** Ex-library. Moderate interior markings. Good reading copy. Moderate wear. All items shipped to US include delivery confirmation. T...show morehanks for looking! ...show less
$6.49 +$3.99 s/h
VeryGood
AlphaBookWorks Alpharetta, GA
007231694259 +$3.99 s/h
Good
E1J1 Orlando, FL
Some shelf and edge wear. Scrape to board. There are writing/highlighting marks in the book. Most of the Pages are clean.
$24.59 +$3.99 s/h
VeryGood
walker_bookstore tempe, AZ
0072316942 WE HAVE NUMEROUS COPIES, -HARDCOVER, mild wear to cover/edges/corners, most pages appear free of markings/writing, some have a sticker on cover |
Source Algebra to Go: Student Edition Handbook (Softcover)
A resource providing explanations, charts, graphs, and numerous examples to help students understand and retain algebraic concepts.A resource providing explanations, charts, graphs, and numerous examples to help students understand and retain algebraic concepts |
More About
This Textbook
Overview
The content and character of mathematics needed in applications are changing rapidly. Introduces students of engineering, physics, mathematics and computer science to those areas that are vital to address practical problems. The Seventh Edition offers a self-contained treatment of ordinary differential equations, linear algebra, vector calculus, fourier analysis and partial differential equations, complex analysis, numerical methods, optimization and graphs, probability and statistics. New in this edition are: many sections rewritten to increase readability; problems have been revised and more closely related to examples; instructors manual quadrupled in content; improved balance between applications, algorithmic ideas and theory; reorganized differential equations and linear algebra sections; added and improved examples 2001
Good as a reference but not as a learning tool
I used this book for a second year engineering course in differential equations. I found this book extremely difficult to use due to the lack of plain english examples and explanations. It is chock full of information though, it's good as a reference. The majority of my class felt the same way about this book.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
Introductory & Intermediate Algebra for College Students, 4th Edition
Description
The Blitzer Algebra Series combinesTable of Contents
1. Variables, Real Numbers, and Mathematical Models
1.1 Introduction to Algebra: Variables and Mathematical Models
1.2 Fractions in Algebra
1.3 The Real Numbers
1.4 Basic Rules of Algebra
Mid-Chapter Check Point Section 1.1–Section 1.4
1.5 Addition of Real Numbers
1.6 Subtraction of Real Numbers
1.7 Multiplication and Division of Real Numbers
1.8 Exponents and Order of Operations
Chapter 1 Group Project
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
2. Linear Equations and Inequalities in One Variable
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 Solving Linear Equations
2.4 Formulas and Percents
Mid-Chapter Check Point Section 2.1–Section 2.4
2.5 An Introduction to Problem Solving
2.6 Problem Solving in Geometry
2.7 Solving Linear Inequalities
Chapter 2 Group Project
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Exercises (Chapters 1–2)
3. Linear Equations in Two Variables
3.1 Graphing Linear Equations in Two Variables
3.2 Graphing Linear Equations Using Intercepts
3.3 Slope
3.4 The Slope-Intercept Form of the Equation of a Line
Mid-Chapter Check Point Section 3.1–Section 3.4
3.5 The Point-Slope Form of the Equation of a Line
Chapter 3 Group Project
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Cumulative Review Exercises (Chapters 1–3)
4. Systems of Linear Equations
4.1 Solving Systems of Linear Equations by Graphing
4.2 Solving Systems of Linear Equations by the Substitution Method
4.3 Solving Systems of Linear Equations by the Addition Method
Mid-Chapter Check Point Section 4.1–Section 4.3
4.4 Problem Solving Using Systems of Equations
4.5 Systems of Linear Equations in Three Variables
Chapter 4 Group Project
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Exercises (Chapters 1–4)
5. Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.2 Multiplying Polynomials
5.3 Special Products
5.4 Polynomials in Several Variables
Mid-Chapter Check Point Section 5.1–Section 5.4
5.5 Dividing Polynomials
5.6 Long Division of Polynomials; Synthetic Division
5.7 Negative Exponents and Scientific Notation
Chapter 5 Group Project
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Cumulative Review Exercises (Chapters 1–5)
6. Factoring Polynomials
6.1 The Greatest Common Factor and Factoring By Grouping
6.2 Factoring Trinomials Whose Leading Coefficient Is 1
6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1
Mid-Chapter Check Point Section 6.1–Section 6.3
6.4 Factoring Special Forms
6.5 A General Factoring Strategy
6.6 Solving Quadratic Equations By Factoring
Chapter 6 Group Project
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Cumulative Review Exercises (Chapters 1–6)
7. Rational Expressions
7.1 Rational Expressions and Their Simplification
7.2 Multiplying and Dividing Rational Expressions
7.3 Adding and Subtracting Rational Expressions with the Same Denominator
7.4 Adding and Subtracting Rational Expressions with Different Denominators
Mid-Chapter Check Point Section 7.1–Section 7.4
7.5 Complex Rational Expressions
7.6 Solving Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Modeling Using Variation
Chapter 7 Group Project
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
8. Basics of Functions
8.1 Introduction to Functions
8.2 Graphs of Functions
8.3 The Algebra of Functions
Mid-Chapter Check Point Section 8.1–Section 8.3
8.4 Composite and Inverse Functions
Chapter 8 Group Project
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
9. Inequalities and Problem Solving
9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications
9.2 Compound Inequalities
9.3 Equations and Inequalities Involving Absolute Value
Mid-Chapter Check Point Section 9.1–Section 9.3
9.4 Linear Inequalities in Two Variables
Chapter 9 Group Project
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises (Chapters 1–9)
10. Radicals, Radical Functions, and Rational Exponents
10.1 Radical Expressions and Functions
10.2 Rational Exponents
10.3 Multiplying and Simplifying Radical Expressions
10.4 Adding, Subtracting, and Dividing Radical Expressions
Mid-Chapter Check Point Section 10.1–Section 10.4
10.5 Multiplying with More Than One Term and Rationalizing Denominators
10.6 Radical Equations
10.7 Complex Numbers
Chapter 10 Group Project
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises (Chapters 1–10)
11. Quadratic Equations and Functions
11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formulas |
More About
This Textbook
Overview
NEW! Get a head-start. The Student Workbook contains all of the assessments, activities, and worksheets from the Instructor's Resource Binder for classroom discussions, in-class activities, and group work.
Product Details
ISBN-13: 9781111575090
Publisher: Cengage Learning
Publication date: 1/1/2011
Edition description: New Edition
Edition number: 4
Pages: 520
Product dimensions: 8.50 (w) x 10.80 (h) x 1.20 (d)
Meet the Author
Charles P. "Pat" McKeague earned his B.A. in Mathematics from California State University, Northridge, and his M.S. in Mathematics from Brigham Young University. A well-known author and respected educator, he is a full-time writer and a part-time instructor at Cuesta College. He has published twelve textbooks in mathematics covering a range of topics from basic mathematics to trigonometry. An active member of the mathematics community, Professor McKeague is a popular speaker at regional conferences, including the California Mathematics Council for Community Colleges, the American Mathematical Association of Two-Year Colleges, the National Council of Teachers of Mathematics, the Texas Mathematics Association of Two-Year Colleges, the New Mexico Mathematics Association of Two-Year Colleges, and the National Association for Developmental Education. He is a member of the American Mathematics Association for Two-Year Colleges, the Mathematics Association of America, the National Council of Teachers of Mathematics, and the California Mathematics Council for Community |
Business Math, Statistical data Analysis & Descriptive Statistics
Math shows up in all aspects of business. It is fundamental mathematical concepts that drive many business computations such as computing sales price, price discounts, volume discounts, cost of production, depreciation, valuing assets, etc. More advanced mathematical and statistical methods such as calculus, probability, decision trees, statistical data analysis, descriptive statistics and regression analysis are used for other aspects of business such as forecasting, modeling uncertainty, options pricing and investment analysis.
GraduateTutor.com provides tutoring for all your needs from basic math and statistical data analysis to tutoring in advanced math and statistical methods such as regression analysis, and multiple regression model building that show up in business school programs.
MBA students will have many courses that draw upon math concepts extensively. Our MBA tutors are well positioned to tutor MBA students on most of these courses from introductory data analysis to options modeling courses.
"I worked with a number of books and attended several case interview workshops, but there is no substitute for working with a seasoned consultant and interviewer on challenging case interviews." ~ Gabe, CA. |
About this product
Book Information
Spectrum Geometry helps students apply essential math skills to everyday life The lessons, perfect for students in grades 6-8, strengthen math skills by focusing on points, lines, rays, angles, triangles, polygons, circles, perimeter, area, and moreBook description
Spectrum Geometry helps students apply essential math skills to everyday life! The lessons, perfect for students in grades 6-8, strengthen math skills by focusing on points, lines, rays, angles, triangles, polygons, circles, perimeter, area, and more!
The |
Book summary
This is the newly revised and expanded edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangualtions, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but it reaches topics on the frontier of current research. Thus professional programmers will find it a useful tutorial. [via] |
Publisher's Description
Access all your instructional materials and digital content from one place. Demonstrate the possibilities. Using the built-in TI-SmartView emulator, present engaging problems and real-world concepts for the entire class to see, experience and easily follow along. The emulator works with interactive whiteboards, digital projectors and other technology you may already have in your classroom. Simplify class preparation. Browse a library of ready-to-use lessons. Modify existing activities or develop your own lessons. Create exciting connections. Color-code lines, curves and objects to match their algebraic equations on the software's full-color display. Assess their thinking. Choose from a menu of question types you want to ask your class: open response, true/false, yes/no |
pages: 10 size: 430.00 KB
2-1 Using Inductive Reasoning to Make ConjecturesInductive Reasoning Conjecture Exercise A Find the next item in each pattern, or make a conjecture. 1 ...
pages: 2 size: 56.00 KB
What are Reasoning/Aptitude Tests?Reasoning tests or aptitude tests as they are also called are tests designed to test the test takers abilities in certai ...
pages: 20 size: 489.00 KB
Title: Nutrition, Exercise, and Mathematics Brief Overview: Students will use algebraic formulas to gain an understanding of how the body stores and uses ene ... |
This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the...
see more
This is a free textbook offered by BookBoon.'The success of Group Theory is impressive and extraordinary. It is, perhaps, the most powerful and influential branch of all Mathematics. Its influence is strongly felt in almost all scientific and artistic disciplines (in Music, in particular) and in Mathematics itself. Group Theory extracts the essential characteristics of diverse situations in which some type of symmetry or transformation appears. Given a non-empty set, a binary operation is defined on it such that certain axioms hold, that is, it possesses a structure (the group structure). The concept of structure, and the concepts related to structure such as isomorphism, play a decisive role in modern Mathematics.The general theory of structures is a powerful tool. Whenever someone proves that his objects of study satisfy the axioms of a certain structure, he immediately obtains all the valid results of the theory for his objects. There is no need to prove each one of the results in particular. Indeed, it can be said that the structures allow the classification of the different branches of Mathematics (or even the different objects in Music (! )).The present text is based on the book in Spanish "Teoría de Grupos: un primer curso" by Emilio Lluis-Puebla, published by the Sociedad Matemática Mexicana This new text contains the material that corresponds to a course on the subject that is offered in the Mathematics Department of the Facultad de Ciencias of the Universidad Nacional Autónoma de México plus optional introductory material for a basic course on Mathematical Music Theory.This text follows the approach of other texts by Emilio Lluis-Puebla on Linear Algebra and Homological Algebra. A modern presentation is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, among other disciplines, is introduced.This work consists of four chapters. Each section contains a series of problems that can be solved with creativity by using the content that is presented there; these problems form a fundamental part of the text. They also are designed with the objective of reinforcing students' mathematical writing. Throughout the first three chapters, representative examples (that are not numbered) of applications of Group Theory to Mathematical Music Theory are included for students who already have some knowledge of Music Theory.In chapter 4, elaborated by Mariana Montiel, the application of Group Theory to Music Theory is presented in detail. Some basic aspects of Mathematical Music Theory are explained and, in the process, some essential elements of both areas are given to readers with different backgrounds. For this reason, the examples follow from some of the outstanding theoretical aspects of the previous chapters; the musical terms are introduced as they are needed so that a reader without musical background can understand the essence of how Group Theory is used to explain certain pre-established musical relations. On the other hand, for the reader with knowledge of Music Theory only, this chapter provides concrete elements, as well as motivation, to begin to understand Group Theory.'
In four voices fugues there are 24 possible combinations in the order of voice entries in the exposition. This system of...
see more
In four voices fugues there are 24 possible combinations in the order of voice entries in the exposition. This system of classification according to the order of voice entries in the expositions summarizes all possible combinations using a few simple circles.
An interactive music theory quiz that helps students improve their ability to identify errors in pitch or time. A piece of...
see more
An interactive music theory quiz that helps students improve their ability to identify errors in pitch or time. A piece of music is displayed and students must press the play button to hear the correct way it is played. They must select the measure number in which the written error occurs. A 'Show Answer' button can help themWe have created a computer program that simulates a vibrating string, and allows the user to perform experiments similar to...
see more
We have created a computer program that simulates a vibrating string, and allows the user to perform experiments similar to those performed with an actual vibrating string apparatus used in physics lab experiments. Our simulation is unique in several respects: it produces the sound due to the vibrating string, it has a high-quality 3d display, it runs on multiple platforms (Linux, MacOS, and Windows), and it computes and displays the frequency spectrum of the sound. It allows for interactive control of the string parameters, which can be set to mimic the conditions seen by students in the real-world lab experimentThe Music Animation Machine provides visual reference for musical lines, from very simple to complex. The developer of this...
see more
The Music Animation Machine provides visual reference for musical lines, from very simple to complex. The developer of this system states that the program was developed from his own personal interest in being able to visualize multiple musical lines at one time, hearing and seeing together the progression of musical material. There are many offerings on this YouTube channel, and one can see the development of the program as well, as visualizations have become more granular. Some include bar lines, some show impingment of notes, and decay of sound. Colors indicate individual voices within multiple lines, and the viewer/listener is able to practice following one line, move out to view the overall musical fabric and to gain skill in micro and macro viewing/listening. I use these visualization videos in Introduction to Music, and find students fascinated by the visual display. I have also shared many of these with my professional musician colleagues who are equally fascinated.Selections include a wide range of musical repertory from piano solo, chamber, and orchestral literature.For an interesting YouTube video from the author of these many musical visualizations, that outlines his development of this musical tool, see: |
More About
This Textbook
Overview
Following a unique approach, this innovative book integrates the learning of numerical methods with practicing computer programming and using software tools in applications. It covers the fundamentals while emphasizing the most essential methods throughout the pages. Readers are also given the opportunity to enhance their programming skills using MATLAB to implement algorithms. They'll discover how to use this tool to solve problems in science and engineering.
Related Subjects
Meet the Author
Amos Gilat, Ph.D., is Professor of Mechanical Engineering at The Ohio State University. Dr. Gilat's main research interests are in plasticity, specifically, in developing experimental techniques for testing materials over a wide range of strain rates and temperatures and in investigating constitutive relations for viscoplasticity. Dr. Gilat's research has been supported by the National Science Foundation, NASA, Department of Energy, Department of Defense, and various industries.
Vish Subramaniam, Ph.D., is Professor of Mechanical Engineering & Chemical Physics at The Ohio State University. Dr. Subramaniam's main research interests are in plasma and laser physics and processes, particularly those that involve non-equilibrium phenomena. Dr. Subramaniam's research is both experimental and computational, and has been supported by the Department of Defense, National Science Foundation, and numerous |
This algebra lesson from Illuminations involves slope as a rate of change. Distance-time graphs for three bicyclists climbing a mountain are compared and contrasted. The material will help students understand how to...
This algebra lesson helps students connect how logarithms work to the real world example of financing a car. Students will use a formula to calculate the number of months it will take them to pay off a car loan based on...
How financial institutions use the monthly mortgage payment and mortgage amortization formulas can be a confusing concept to grasp. This lesson asks students to find a current interest mortgage rate for their city and... |
- Mechanics and Probability
Many students who embark on a GCE A-level course in mathematics choose the combination of pure mathematics with applications to mechanics. The pure ...Show synopsisMany students who embark on a GCE A-level course in mathematics choose the combination of pure mathematics with applications to mechanics. The pure mathematics content of most such syllabuses is covered in "Mathematics - The Core Course for A-Level", while this book provides the companion mechanics course. It also contains a section on probability, a topic included in many A-level mathematics syllabuses. An appreciation of the properties of vectors is introduced at an early stage and, wherever appropriate, problems are solved using vector methods. Worked examples are incorporated in the text to illustrate each main development of a topic, and a set of straightforward problems follows each section. A selection of more challenging questions is given in a miscellaneous exercise at the end of most chapters. Multiple-choice exercise are also included on many topics 672 p 672 p.
Description:Good. Wear and tear on the main cover. Pages inside are intact....Good. Wear and tear on the main cover. Pages inside are intact. Does not have name, stamps, highlighting or notes written inside. Overall a good used copy. Trade paperback (US). Glued binding. 672 |
Otto Bretscher
This book contains the standard material usually found in an introduction to linear algebra course in U.S. colleges and universities. It does have some novel features, but it does not overdo it. This is a textbook where an instructor might be able to cover all of the material.
The author does not start out with an overview of vectors and vector algebra (this is relegated to an appendix) and I did not miss it. Dot and cross products are introduced as needed. The book begins with linear systems and their solutions. Chapter 1 also includes the first taste of historical comments that are liberally placed throughout the text. Many sections of the text also include exercises either with an historical bent or from actual original sources. This is one of the novel and very welcome features of this book.
The author considers matrix multiplication Ax as linear combinations of the columns of A, in keeping with current pedagogical practice. I did miss Gaussian elimination as LU factorization and back substitution, but that is a personal preference, I suppose.
Linear transformations are introduced early in Chapter 2, but strictly as matrix operations on the Euclidean spaces \(\mathbb{R}^n\). By using transformations the author can take an early look at geometry (rotations, reflections) and projections (although only on \(\mathbb{R}^2\) and \(\mathbb{R}^3\) for now). This is a nice compromise between the "linear algebra as the study of linear transformations" adherents and the "linear algebra as the study of matrices" followers. We all know that in finite dimensions these are one and the same but the choice of perspective can very much change the nature of an introductory linear algebra course.
The author saves the general notion of vector space (which he calls "linear space" to avoid confusion with ways in which "vector" is used) until Chapter 4. A matrix-only course could skip this chapter with no loss in continuity in the course.
Continuing this compromise approach, kernel and image are introduced for matrices in Chapter 3 and the general notions for linear transformations are also saved until Chapter 4. The properties of the kernel and image serve as prototypes for the definition of subspace that comes later. Linear independence and basis are nicely done through the notion of "redundant" vectors. In addition, orthogonality is introduced in \(\mathbb{R}^n\) first and then in general inner product spaces, allowing Fourier series to make an appearance. The author links orthogonality to least squares and curve fitting and also links Gram-Schmidt to QR factorization, again keeping with more modern approaches in textbooks. While the orthogonality of the subspaces of a matrix and its transpose is mentioned, the idea does not receive the prominence it deserves; it is just as important as the dimension theorem.
The author handles the difficult idea of determinants with a nice approach using "pattern" instead of the difficult (at this level) notion of permutations. This pattern approach works well for sparse matrices, as the author shows, but for less sparse matrices he resorts to using elimination. It is interesting to note that minors and cofactor expansion are listed in an optional section, given their association with Laplace and this author's nice use of history throughout the text.
As is typical in an introductory text, determinants are used only as a test for invertibility and for finding eigenvalues. This book does not use a determinant free approach to eigenvalues. The main use of eigenvalues and eigenvectors in the book is in differential equations/dynamical systems. Dynamical systems are used as examples and motivation for eigenvalues and eigenvectors, and an additional chapter is devoted to further study of these applications.
Finally, the author covers symmetric matrices and quadratic forms. There are nice applications to conic sections, but many other applications of symmetric matrices are left out. I was pleased, however, to see singular values and the singular value decomposition included, although again applications were wanting.
Each section contains a very nice list of exercises, and these exercises range from basic to challenging. There are typically some easy (but realistic) applications, particularly early on in the book. These early application exercises can be used to help motivate the study of linear algebra beyond solving systems of linear equations.
The author uses a combination of the "definition/theorem/proof" style with a more "conversational" style. Some theorems summarize what was found in earlier examples, some are in the "theorem/proof" style. As is the nature of the subject matter, however, many proofs are merely computational. While there are definitions, theorems, and proofs, they do not appear from nowhere. Each definition or theorem follows after a few motivating examples. Students should have little difficulty reading this text. The author includes historical commentary and problems. These are not an afterthought; history is included at various places throughout the book and I found the author's historical comments a nice jumping off point for further study. It is by no means an historical text, but the historical material is a very nice addition to a solid introduction to linear algebra.
In summary, this book covers the typical introduction to linear algebra course. It does not suffer from "textbook bloat," but then again a few of an instructor's pet topics might be omitted. There is no reliance on technology, so an instructor will need to supply his/her own technology-related material.
Gary Stoudt (gsstoudt@iup.edu) has been in the Mathematics Department at Indiana University of Pennsylvania since 1991. |
Browse Results
Modify Your Results
The unifying theme of this text is the development of the skills necessary for solving equations and inequalities, followed by the application of those skills to solving applied problems. Every section ending in the text begins with six simple writing exercises. These exercises are designed to get students to review the definitions and rules of the section before doing more traditional exercises |
MERLOT Search - materialType=Collection&keywords=mathematics
A search of MERLOT materialsCopyright 1997-2014 MERLOT. All rights reserved.Thu, 24 Apr 2014 00:33:33 PDTThu, 24 Apr 2014 00:33:33 PDTMERLOT Search - materialType=Collection&keywords=mathematics
4434Cut-the-Knot!
This site is the parent site of an extensive collection of interactive mathematics authored by Alexander Bogomolny and includes an interactive monthly column . The content is accessible to the casual reader but offers much depth along with links to other high-quality resources. Altogether, this site is a mathematician's delight.Exploring Multivariable Calculus
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and "play" with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly "see" how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.Demos with Positive Impact
Demos with Positive Impact is a collection of quick classroom demos that enhance the learning of mathematics content through animations, experiments etc. Each demo comes with stated objective, prerequisites, instructor notes and platform info, plus the level of the demo and credits. This setup appears conducive to quick inclusion into a class. To view a video of the award winning author, go to target=״_blank״>Demos with Positive Impact - the Mathematics Award Winner 2008 videoThe author also participated in the MERLOT Classics Series on Elluminate: " target=״_blank״> National Library of Virtual Manipulatives
Large collection of platform independent, interactive, java applets and activities for K-12 mathematics and teacher education.Interactive Mathematics--Games and Puzzles
This site contains an extensive collection of games and puzzles in the form of java applets including Nim, the Tower of Hanoi, Cryptarithms, Latin Squares, and much more. Written by Alexander Bogomolny, these applets are designed to engage the reader in interactive investigations. Background material is provided and the site serves as an excellent educational resource.Interactive Mathematics--Arithmetic/Algebra
This site contains an extensive collection of java applets involving arithmetic and algebra miscellany and puzzles. Written by Alexander Bogomolny, these applets are designed to engage the reader in interactive investigations. Background material is provided and the site serves as an excellent educational resource.nrich maths
This is a website that is designed for use in extending more able pupils in maths. It includes investigations, interactive resources as well as printable resources. This resource can be used to extend children at difeerent stages. I found it to be really useful, not only are there resources for children there is also information to improve your own subject knowledge.Nick's Mathematical Puzzles
A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided, along with fully worked solutions, and links to related mathematical topics.Probability/Statistics Object Library
The Probability/Statistics Object Library is a virtual library of objects for use by teachers and students of probability and statistics. The library contains objects of two basic types, applets and components.An applet is a small, self-contained program that runs in a web page. Applets are intended to illustrate concepts and techniques in an interactive, dynamic way. A teacher or student can download an applet, drop it in a web page, and then add other elements of her own choice (such as expository text, data sets, and graphics). The applets in the library contain essentially no mathematical theory and thus can be used by students at various levels. The applets are intended to be small "micro worlds" where students can run virtual versions of random experiments and play virtual versions of statistical games.Components are the building blocks of applets and of other components. The Java objects are of three basic types: virtual versions of physical objects, such as coins, dice, cards, and sampling objects; virtual versions of mathematical objects, such as probability distributions, data structures, and random variables; user-interface objects such as custom graphs and tables. The Java objects can be used by teachers and students with some programming experience to create custom applets or components without having to program every detail from scratch, and thus in a fraction of the usual time. In addition, the components are extensively documented through a formal object model that specifies how the components relate to each other.Each object can be downloaded as a Java "bean" that includes all class and resource files needed for the object. An object in the form of a Java bean can be dropped into a builder tool (such as JBuilder or Visual Cafe) to expose the properties and methods of the object. Each object can also be downloaded in the form of a zip file that includes the source files and resource files for the object.Xah's Home Page
Link to math graphic images and programs. |
More About
This Textbook
Overview
Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.
Editorial Reviews
From the Publisher
From the reviews:
"The book is a study about the formation of Descartes's mathematical thought and its philosophical significance. … The book is well documented as one can see also looking at the footnotes and the bibliography. There are also some interesting digressions as that concerning Jesuit mathematical education." (Raffaella Franci, Zentralblatt MATH, Vol. 1045 (20), 2004)
"This magnificent volume originates in a 1989 Ph.D. thesis from Princeton University. … The author aims at a reconstruction of R. Descartes' early mathematical career, studying the formation of his mathematical thought and relating it to his methodological and philosophical ideas. … The volume, containing a wealth of material, is made accessible by indexes of names, subjects and treatises." (Volker Peckhaus, Mathematical Reviews, 2005 d)
Related Subjects
Table of Contents
Preface. List of Abbreviations and a Note on the Quotation and Translation.
Introduction. René Descartes and Modern European Mathematics.
1: The Formation of Descartes's Mathematical Thought. 1. Descartes and Jesuit Mathematical Education. 1. Descartes and the Jesuit College of La Flèche. 2. The Curriculum at La Flèche. 3. Mathematical Studies in the Ratio Studiorum 4. Motives for the Teaching of Mathematics in the Jesuit Colleges.
2: The Mathematical Thought of Christoph Clavius. 1. Descartes and Clavius. 2. The Philosophy of Mathematics of Clavius. 3. Pappus in the Works of Clavius. 4. Diophantus in the Works of Clavius. 5. Descartes's Mathematical Background before the Encounter with Beeckman.
3: The First Attempt at Reforming Mathematics. 1. 'An Entirely New Science': The Idea for the Unification of Arithmetic and Geometry. 2. The Mathematics in the Cogitationes privatae. 3. The De Solidorum Elementis. 4. Descartes's Mathematical and Philosophical Dream of 1619.
4: The Mathematical Background of the Regulae Ad Directionem Ingenii. 1. The Old Algebra: The First Fruit of 'An Entirely New Science'. 2. The Mathematics in the Regulae ad Directionem Ingenii. 3. Mathesis Universalis. 5. The Géométrieof 1637. 1. The Pappus Problem. 2. The Composition of the Géométrie. 3. Descartes's Place in the Formative Period of the Modern Analytic Tradition. 4. Beyond Cartesian Mathematics. Interim Consideration. Descartes and the Beginnings ofMathematicism in Modern Thought.
II: The Concept of 'Mathesis Universalis' in Historical Perspective. 6. 'Universal Mathematics' In Aristotle. 1. Aristotle's Metaphysics and Posterior Analytics. 2. Greek Commentators: Alexander of Aphrodisias and Asclepius of Tralles. 3. Medieval Commentators: Ibn Rushd (Averroës), Albertus Magnus, Thomas Aquinas, and the Scotist Antonius Andreae. 4. Renaissance Commentators: Agostino Nifo and Pedro da Fonseca. 5. The Status of Mathematics in the Aristotelian Scheme of Learning.
7: 'Mathesis Universalis' in the Sixteenth Century. 1. Proclus Diadochus and Francesco Barozzi. 2. Adriaan van Roomen.
8: 'Mathesis Universalis' in the Seventeenth Century. 1. Reviewing Descartes's Concept of 'Mathesis Universalis' from His Philosophy of Mathematics. 2. The Leibnizian Synthesis.
Conclusion: Descartes and the Modern Scheme of Learning. Bibliography.
Indices. Name Index. Subject Index. Treatise |
Glendale, CA ACTLinear Algebra works great for modeling static situations, but more interesting phenomena in the real world include changing variables such as temperature, volume, population, etc. To understand these more interesting physical situations, one needs to find the differential equation describing th |
Transformation Geometry : An Introduction to Symmetry - 82 edition
Summary: Transformation Geometry: An Introduction to Symmetryis a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers60 +$3.99 s/h
VeryGood
Bookbyte-OR Salem, OR
Has minor wear and/or markings. SKU:9780387906362-3-0
$18.690560.63 +$3.99 s/h
New
indoo Avenel, NJ
BRAND NEW
$63.00 +$3.99 s/h
New
surplus computer books fallbrook, CA
0387906363 BRAND NEW NEVER USED IN STOCK 125,000+ HAPPY CUSTOMERS SHIP EVERY DAY WITH FREE TRACKING NUMBER
$64.66 +$3.99 s/h
VeryGood
PsychoBabel Books Abingdon,
USA 1997 hardcover Very Good. No Dust Jacket Ex-Library Minor Edgewear. Minimal stamping, sticker on spine. Good clean copy, pages clean bright and tight. *****PLEASE NOTE: This item is shipping fro...show morem |
illustrates how Mathematica can be used in chemical engineering. The notebooks were written to augment various chemical engineering classes (junior, senior and graduate) at UCDavis. Topics include applied mathematics, nonlinear dynamics, separation processes,thermodynamics, fluid mechanics, heat transfer, and bioinformatics. There is also a section on the use of webMathematica for interactive calculations. |
Math in pen makes since, you will waste more paper BUT you also strike through your bad work once and you can still understand WHERE you went wrong while looking at notes. Plus pen is a fuckton easier to read.
I learned calc better because I did everything in pen, it helped me noticed problems I would constantly screw up on and what I was going wrong. Granted everything was easier once we were allowed to use the derivative shortcut versus the algebraic way.
After you hit a certain point you need a pencil to keep everything legible. My second boundary value problems class (partial differential eqns) yielded so many mistakes you couldn't simply cross things out effectively.
Are you talking about a theorem-proof math class or a learn-the-steps intro class? I think most modern graphing calculators will do many equivalent operations, as long as you know the theory. For the ones that don't, if it's programmable, you can do a lot of it yourself.
It's entirely possible for a linear algebra exam to be crafted in a way that a calculator is not necessary. I took my linear algebra exam today (strangely enough) and I didn't have a calculator either.
My thoughts exactly, this shouldn't be buried in the comments, but I guess it goes to show how many people actually take linear algebra on Reddit versus the number of people who think they took linear algebra.
We just weren't allowed graphing or programmable calculators in my Calculus classes. We were usually allowed scientific calculators though. In linear algebra, we actually had a class set of ti-83 calculators that the teacher taught us how to do everything on.
My school don't either. It made me train my ability to do calculations in my head (and on paper, mind you, but there's still a significant amount of headwork). I'm grateful for that, it has proven very useful.
It's probably not exclusive to here, but in the UK (the bit I'm from at least) everybody over the age of ~10 does everything in pen, with the exception of graphs. Just cross things out and move on, or if you really must, buy an erasable pen. |
The Calculus 2 Advanced Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers L'Hospital's Rule in Calculus, including what L'Hospital's Rule is, how it is used to take derivatives, and why it is a central topic in Calculus. Grades 9-12. 70 minutes on DVD. |
208384 / ISBN-13: 9781429208383
Calculus: Early Transcendentals
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of ...Show synopsis synopsis
...Show more 1429208384 INSTRUCTOR'S REVIEW COPY. Same as student but...New. 1429208384 Calculus: Early Transcendentals
This is a great book and it is very easy to understand. But the only downfall of it is I wish the answers to the selected answers showed each step to finding the solution because even though the problems are based on the same concept, some questions are harder. But it's an overall good back and totally |
Elementary Algebra - 8th edition
Algebra is accessible and engaging with this popular text from Charles ?Pat? McKeague! ELEMENTARY ALGEBRA is infused with McKeague?s passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague?s attention to detail and exceptionally clear writing style help yo...show moreu to move through each new concept with ease. Real-world applications in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book?s multimedia learning resources, including ThomsonNOW for ELEMENTARY ALGEBRA, a personalized online learning companionSellBackYourBook Aurora, IL
04951083912007 Hardcover Good |
Quick Reference Guide: Table of Standards and Expectations
Product Details
Stock #
12493
ISBN #
Published
1/1/2002
Pages
Folded to 9" x 11"
Grades
_Pre-K-2, Grades 3-5, Grades 6-8, Grades 9-12,
See What's Inside
Product Description
This easy-to-use format presents the goals and expectations for the six Principles and ten Standards. Produced from the Table of Standards and Expectations of the appendix of the Principles and Standards, this practical guide includes three 11" x 17" sheets to display the expectations across the four grade bands for each of the five Content Standards: Number and Operations, Algebra, Geometry, Data Analysis and Probability, and Measurement. Allowing readers to see how the same mathematical idea grows and develops from one grade band to the next, this document also summarizes the Principles and Process Standards. The guide can be used as a checklist or tool for teachers or administrators, a resource for professional development workshops, or as supplementary material for college methods courses.
This CD contains a variety of presentations, handouts, and video clips
designed to enable you to speak to teachers, parents, administrators, and the
wider community about the messages of Principles and Standards.
This CD contains a variety of presentations, handouts, and video clips
designed to enable you to speak to teachers, parents, administrators, and the
wider community about the messages of Principles and Standards.
This book examines the study of geometry in the middle grades as a pivotal point in the mathematical learning of students and emphasizes the geometric thinking that can develop in grades 6–8 as a result of hands-on exploration.
This book focuses on algebra as a language of process, expands the notion
of variable, develops ideas about the representation of functions, and extends
students' understanding of algebraic equivalence and change.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. |
Math Worksheets for CAHSEE
All about CAHSEE Math Worksheets
Students preparing for the California High School Exit Examination
(CAHSEE) are usually worried about the Mathematics section. This is
primarily because; statistics show that the passing rate in the
Mathematics segment is less than that of the English-Language-Arts
(ELA) section.
Moreover, it has been identified that students are more prone to
simplistic mistakes when it comes to Mathematics. This is where the math worksheets
come in handy, because they not only provide the questions but also an
extensive answer key. The following section of this article will help
you understand the use and nature ofthe worksheets:
What are the Mathematics Worksheets for CAHSEE?
The primary job of any worksheet is to provide ample description and
practice questions on the subject that the worksheet is regarding.
However, these math worksheets have a number of other unique features some of which are as follows:
Discussion of formulas: The Mathematics segment of
the CAHSEE will evaluate your school as well as high school knowledge
of Arithmetic, Algebra, Geometry and Statistics. Thus, typicalworksheets
will begin with a list (sometimes short discussions alongside) of the
formulas that you will need to apply in order to solve the problems.
For example, when you begin solving the questions on Algebra, some of
the common formulas that you will have to apply are: (a+b)2 = a2 + 2ab + b2 and (a+b)3 = a3 + b3 + 3a2b + 3ab2 etc. You will have to memorize many more such formulas in order to solve the questions and hence, yourworksheets must have a list of them.
Good number of questions: The primary objective of the worksheets is
to give you sufficient practice. Thus, these worksheets consist of a
large number of questions, covering all the topics on which you will be
tested in this segment of the examination. You must solve these
questions, as per the instructions given, so that you get acquainted
with the type of questions you are likely to face in the actual
examination. Since the CAHSEE consists of multiple-choice questions,
ensure that the worksheet that you choose also comprises such
questions. Usually, in the CAHSEE, each question is followed by 4
answer options and your worksheet should also follow the same format.
Extensive answer key: The final section of the worksheet
is the answer key. Some worksheets merely provide the correct answer,
whereas others provide elaborate explanations. There are even some
which will solve the entire problem, so that you can understand how to
work out the question. These worksheets sometimes even come with
strategies that will help you identify the particular areas of
Mathematics that you are weak in. You can then put in extra effort on
these topics, so that you are able to answer the questions competently.
The above-mentioned list will help you understand the features of a typical worksheet.
However, you must now be wondering from where you can access such
worksheets. The following section of this article will help you with
this.
Review of a Math Worksheet for CAHSEE
Good worksheets must consist of a large number of questions, so that
you get sufficient practice. The official website for the California
Department of Education (CDE) consists of one such worksheet for
Mathematics. The unique features of this worksheet are as follows:
Original CAHSEE questions: Most of the questions
that you will come across in this worksheet are problems that have
appeared in past CAHSEE question papers. Hence, the questions are
authentic and will give you an idea of the exact nature of the
questions.
Answer key: The answer key is not exhaustive, but
it comes with a reference as to which year the particular question
featured in the CAHSEE. This will give you an idea as to difficulty
level of the question papers.
Once you have mastered the nature of the worksheets, you will
find it easier to understand the question paper format of the test. You
should then study the link and start solving the questions in it, at
the earliest. This will familiarize you with the type of problems that
you have to answer during |
Saxon Math 7/6
Saxon Math for Middle Grades provides a structured series of levels to guide your child successfully from lower grades to high school algebra and advanced math.
Math 7/6 helps improve preparation for high school math by introducing concepts your child will need for upper-level algebra and geometry, including circumference and pi, angles, coordinate graphing, and prime factorization.
Math 7/6 introduces new concepts your child will need for upper-level algebra and geometry. After every tenth lesson is an investigation - an extensive examination of a specific math topic, discussed at length to ensure solid understanding. |
Representations
and
Translations among
Representations in Mathematics
Learning and Problem Solving
Richard
Lesh WICA T & Northwestern University
Tom Post University of Minnesota
Merlyn Behr Northern Illinois University
This chapter briefly
describes several roles that representations, and translations among representations,
play in mathematical learning and problem solving. The term representations
here is interpreted in a naive and restricted sense as external (and therefore
observable) embodiments of students' internal conceptualizations-although
this external/internal dichotomy is artificial.
Comments in this chapter
are based on three recent or current National Science Foundation funded
projects on Applied Mathematical Problem Solving (AMPS), Proportional
Reasoning (PR), and Rational Number (RN) concept formation. Past PN, PR,
and AMPS publications (e.g., Behr, Lesh, Post, & Silver, 1983; Lesh,
1981; Lesh, Landau, & Hamilton, 1983) have identified five distinct
types of representation systems that occur in mathematics learning and
problem solving (see Fig. 4.1); they are: (1) experience?based
"scripts"-in which knowledge is organized around "real
world" events that serve as general contexts for interpreting and
solving other kinds of problem situations; (2) manipulatable models-like
Cuisenaire rods, arithmetic blocks, fraction bars, number lines, etc.,
in which the "elements" in the system have little meaning per
se, but the "built in" relationships and operations fit many
everyday situations; (3) pictures or diagrams-static figural models that,
like manipulatable models, can be internalized as "images";
(4) spoken languages-including specialized sub languages related to domains
like logic, etc.; (5) written symbols-which, like spoken languages, can
involve specialized sentences and phrases (X + 3 = 7, A'UB' = (AnB)')
as well as normal English sentences and phrases.
This chapter emphasizes
that, not only are these distinct types of representation systems important
in their own rights, but translations among them, and transformations
within them, also are important.
Item 31 (Fig.
4.2), taken from a written test on "rational number relations
and proportions'' from our RN/PR projects, illustrates a "written
symbol to picture" translation. The aim is to require students to
answer the item correctly by establishing a relationship (or mapping)
from one representational system to another, preserving structural characteristics
and meaning in much the same way as in translating from one written language
to another.
Item 29 (Fig.
4.3) is from the same ''relations and proportions" test as Item
31, but it was adapted from a recent "National Assessment'' examination
(Carpenter et al., 1981). To answer item 29 correctly, the student's primary
task is to perform a (computational) transformation within the domain
of written symbols.
We have found it useful
to sort out ''between-system mappings" (i.e., translations) from
''within-system operations" (i.e., transformations) even though transformations
and translations tend to be interdependent in reality. For example, RN/PR
research suggests that students' solutions to item 29 (preceding) typically
involve the use of spoken language (together with accompanying translations
and transformations) in addition to pure written symbol manipulations
(i.e. transformations). On the other hand, our studies also show that
repeated drill on problems like 29 does not necessarily provide needed
instruction related to underlying translations. For example, consider
the following results.
Educators familiar
with results from recent ''National Assessments" (Carpenter et al.,
1981) may not be surprised that our students' success rates for item 29
were only 11% for 4th graders, 13% for 5th graders, 30% for 6th graders,
29% for 7th graders, and 51% for 8th graders. Such performances by American
students led to "Nation at Risk" reports from a number of federal
agencies and professional organizations. However, success rates on the
seemingly simpler
Item
29. The ratio of boys to girls in a class is 3 to 8. How many girls
were in the class if there were 9 boys?
One major conclusion
from our research is apparent from the preceding examples; not only do
most fourth - through eight-grade students have seriously deficient understandings
in the context of "word problems'' and "pencil and paper computations,"
many have equally deficient understandings about the models and language(s)
needed to represent (describe and illustrate) and manipulate these ideas.
Furthermore, we have found that these ''translation (dis)abilities"
are significant factors influencing both mathematical learning and problem-solving
performance, and that strengthening or remediating these abilities facilitates
the acquisition and use of elementary mathematical ideas (Behr, Lesh,
Post, & Wachsmuth, 1985; Post, 1986).
Part of what we mean
when we say that a student ''understands" an idea like "1/3''
is that: (1) he or she can recognize the idea embedded in a variety of
qualitatively different representational systems, (2) he or she can flexibly
manipulate the idea within given representational systems, and (3) he
or she can accurately translate the idea from one system to another. As
a student's concept of a given idea evolves, the related underlying transformation/translation
networks become more complex; and teachers who are successful at teaching
these ideas often do so by reversing this evolutionary process; that is,
teachers simplify, concretize, particularize, illustrate, and paraphrase
these ideas, and inbed them in familiar situations (i.e., scripts).
To diagnose a student's
learning difficulties, or to identify instructional opportunities, teachers
can generate a variety of useful kinds of questions by presenting an idea
in one representational mode and asking the student to illustrate, describe,
or represent the same idea in another mode. Then, if diagnostic questions
indicate unusual difficulties with one of the processes in Fig.
4.1, other processes in the diagram can be used to strengthen or bypass
it. For example, a child who has difficulty translating from real situations
to written symbols may find it helpful to begin by translating from real
situations to spoken words and then translate from spoken words to written
symbols; or it may be useful to practice the inverse of the troublesome
translation, i.e., identifying familiar situations that fit given equations.
Not only are the translation
processes depicted in Fig. 4.1 important components
of what it means to understand a given idea, they also correspond to some
of the most important "modeling'' processes that are needed to use
these ideas in everyday situations. Essential features of modeling include:
(1) simplifying the original situation by ignoring "irrelevant''
(or ''less relevant") characteristics in order to focus on other
''more relevant" factors; (2) establishing a mapping between the
original situation and the ''model"; (3) investigating the properties
of the model in order to generate predictions about the original situation;
(4) translating (or mapping) the predictions back into the original situation;
and (5) checking to see whether the translated prediction is useful and
sensible.
Translation processes
are implicit in a variety of techniques commonly used t investigate whether
a student "understands" a given textbook word problem e.g.,
''Restate it in your own words." ''Draw a diagram to illustrate what
it's about." "Act it out with real objects.'' ''Describe a similar
problem in a familiar situation." Or, techniques for improving performance
on word problems' include: (1) using several different kinds of concrete
materials to "act out" given problem situation; (2) describing
several different kinds of everyday problem situations that are similar
to a given prototype concrete model; or (3) writing equations to describe
a series of word problems-delaying the actual solution until the student
becomes proficient at this descriptive phase.
Even though representation
(or modeling) often tends to be portrayed a involving only a single simple
mapping from the modeled situation to the mode (or to their underlying
concepts, which might be characterized as the skeletons of external structural
metaphors), our AMPS, RN, and PR research suggests that the act of representation
tends to be plural, unstable, and evolving; and these
three attributes play important roles to make it possible for concepts
and representations to evolve during the course of problem-solving sessions.
Here are some examples.
In RN and PR research
involving concrete/realistic versions of typical text book word problems,
we have found that students seldom work through solution in a single representational
mode (Lesh, Landau, & Hamilton, 1983). Instead students frequently
use several representational systems, in series and/or in parallel, with
each depicting only a portion of the given situation. In fact, man realistic
problem-solving situations are inherently multimodal from the outset
The following two pizza problems illustrate this point.
Show a 6th grader
one-fourth of a real pizza, and then ask, ''If I eat this much pizza,
and then one-third of another pizza, how much will I have eaten altogether?''
Show a 6th grader
one-third of a real pizza, and then ask, ''If I already ate one-fourth
of a pizza, and now eat this much, how much will I have eater altogether?"
Neither of the preceding
problems is a "symbol-symbol" or "word-word' problem. Instead,
the "givens'' in both problems include a real object (i.e., piece
of pizza), and a spoken word (to represent a past or future situation).
Like many realistic problems in which mathematics is used, the situation
in these two pizza problems is inherently multimodal. Each of the problems
is a ''pizza word'' problem in which one of the student's difficulties
is to translate the two givens into a homogeneous representation mode
so that combining is sensible
Not only may problems
of the preceding type occur naturally in a multimodal form but solution
paths also often weave back and forth among several representational systems,
each of which typically is well suited for representing some parts of
the situation but is ill suited for representing others. For example,
in the two problems just given, a student may think about the static quantities
(e.g., the two pieces of pizza) in a concrete way (perhaps using pictures)
but may switch to spoken language (or to written symbols) to carry out
the dynamic "combining" actions (Lesh, Landau, & Hamilton,
1983).
Good problem solvers
tend to be sufficiently flexible in their use of a variety of relevant
representational systems that they instinctively switch to the most convenient
representation to emphasize at any given point in the solution process.
Figure
4.4 suggests one way that the act of representation tends to be plural;
that is, solutions often are characterized by several partial mappings
from parts of the given situation to parts of several (often partly incompatible)
representational systems. Each partial mapping represents a ''slice"
of the problem situation, using only part of the available representational
system. It is not a mapping from the whole ''given" situation to
only a single representational system.
The act of representation
also may be plural in a second sense; that is, a student may begin a solution
by translating to one representational system and may then map from this
system to yet another system, as illustrated in Fig. 4.5.
In fact, for concrete
or realistic versions of textbook word problems the actual solutions our
students have tended to use often combine features depicted in both Fig.
4.4 and 4.5 preceding, as well as a third aspect
of representational plurality; that is, a given representational system
often appears to be related (in a given student's mind) to several distinct
clusters of mathematical ideas. An example to illustrate this point occurred
in the AMPS project when several of our students worked on the following
"million dollar" problem.
The Million Dollar
Problem: Imagine that you are watching "The A Team" on
television. In the first scene, you see a crook running out of a bank
carrying a bag over his shoulder, and you are told that he has stolen
one million dollars in small bills. Could this really have been the
case'?
One student who solved
this problem began by using sheets of typewriter paper to represent several
dollar bills. Then, he used a box of typewriter paper to find how many
$1 bills such a box would hold-thinking about how large (i.e., volume)
a box would be needed to hold one million $1 bills. Next, however, holding
the box of typewriter paper reminded him to think about weight
rather than volume. So, he switched his representation from using
a box of typewriter paper to using a book of about the same weight. By
lifting a stack of books, he soon concluded that, if each bill was worth
no more than $10, then such a bag would be far too large and heavy for
a single person to carry.
For the preceding
solution, the first representation involved a sheet of paper, which was
quickly subsumed into a second representation based on the size of boxes
(i.e., volume), which played a role in switching from conceptualizations
based on volume to a conceptualization focused on weight. Clearly, the
meaning(s) associated with each of these representations were plural in
nature; and they evolved during the solution process. The unstable
nature of the representations was reflected in the fact that when attention
was focused on ''the whole situation" (or representation), details
that previously were noticed frequently were neglected. Or, when attention
was focused on one detail (or one interpretation), the student often temporarily
lost cognizance of others.
We have addressed
the topic of conceptual and representational instability in other RN,
PR, and AMPS publications (e.g., Behr, Lesh, Post, & Silver, 1983;
Lesh, 1985), so we do not attempt to deal with this rather complex topic
here. Instead, we want to stress the inherent plural and evolving nature
the act of ''representation," because both of these characteristics
are linked to the importance of translations in mathematical learning
and problem solving.
ACKNOWLEDGMENTS
The research of the
RN, PR, and AMPS projects was supported in part by the National Science
Foundation under grants SED 79?20591, SED 80-17771, and SED 82-20591.
Any opinions, findings, and conclusions expressed in this report are those
of the authors and do not necessarily reflect the views of the National
Science Foundation.
Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R.
(1981). Results from the Second Mathematical Assessment of the National
Association of Educational Progress. Reston, VA: National Council
of Teachers of Mathematics.
Post, T. (1986). Research
based methods for teachers of elementary and junior high mathematics:
Boston: Allyn & Bacon.
Post, T. R., Lesh,
R., Behr, M. J., Wachsmuth, 1. (1985). Selected results from the rational
number project. In L. Streefland (Ed.)., Proceedings of the Ninth International
Conference of Psychology of
Mathematics Education: Vol 1. Individual contributions (pp. 342-351).
Stat University of Utrecht, The Netherlands: International Group for the
Psychology of Mathematics Education. |
Find a ClintonIt is helpful to know the characteristics of polynomial and transcendental functions. These characteristics include the zeros, possible asymptotes, and global behavior. Reviewing your equation - solving skills is useful, as wellMy primary focus is building the student's confidence, through thorough explanation of the basic concepts involved, by interactive practice and feedback. I love to work with computers! I see it as an exercise in logical thinking: computers are, basically, stupid; you must be very clear and expl... |
grew from the authors' conviction that both prospective school teachers and college teachers of maths need a background in history to be more effective as instructors in the classroom. Prospective instructors gain an appreciation of the contributions of all cultures, and this text explains how mathematics developed over the centuries. Also suitable for those studying maths and science at degree level. |
#5 Reading Time 3 [Only Audio]
#6 Elementary Topology
3-08-2010, 04:58
Elementary Topology 2007 | 400 pages | ISBN:0821845063 | PDF | 8 Mb
The.
#10 Elementary Concepts of Topology
Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.
#18 Reading Time 3 [Only Audio]
Reading Time is a three-level reading series designed for young, beginner EFL students. Throughout the series, students will expand their basic reading ability, acquire useful and relevant vocabulary, and develop their writing skills |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
Find a Pearland Statistics also study linear, quadratic, exponential, and inverse functions. Methods for graphing, analyzing, and solving systems of equations and inequalities can also be covered. As needed, we can reinforce pre-algebra concepts such as negative numbers, fractions, and calculator and computational skills |
Find a Woodacre PrecalculusClasses such as quantum mechanics or even classical mechanics make extensive use of the mathematical tools and concepts studied in linear algebra, and I have taken many of those! The fact that I use the tools of linear algebra on a regular basis, instead of just studying the theory, means that m... |
and Trigonometry
Bob Blitzer,s unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus ...Show synopsisBob Blitzer,s unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets students engaged and keeps them engaged. Presenting the full scope of the mathematics is just the first step. Blitzer draws students in with vivid applications that use math to solve real-life problems. These applications help answer the question "When will I ever use this?" Students stay engaged because the book helps them remain focused as they study. The three-step learning system-See It, Hear It, Try It-makes examples easy to follow, while frequent annotations offer the support and guidance of an instructor,s voice. Every page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!Hide synopsis321837Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321837240240.
Description:Good. Looseleaf. May include moderately worn cover, writing,...Good. Looseleaf. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321837Fine. Looseleaf. Almost new condition. SKU: 9780321837653-2-0-3...Fine. Looseleaf. Almost new condition. SKU: 9780321837653Looseleaf. New Condition. SKU: 9780321837653-1-0-3 Orders ship...Looseleaf. New Condition. SKU: 97803218376532254X Brand new book. International Edition. Ship...New. 129202254XReviews of Algebra and Trigonometry
I got this book to finish my algebra requirement and it has really helped me...plus I have a talented instructor. Although I find the book a great asset, I think the author has tried too hard to explain things with too many details. All the labels and arrows are hard to follow and do more to confuse |
Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey1111578494 Instructors edition! Item has some cover wear but otherwise in good condition!!Used texts may not include supplemental matieral. All day low prices, buy from us sell to us we do it all!!
$50.00 +$3.99 s/h
Good
Oakwood_EMB Kernersville, NC
2012 Hardcover Good Covers show moderate wear. Pages show little or no marking/ highlighting. THIS ITEM IS OVERSIZED. PLEASE, NO INTERNATIONAL ORDERS.
$50.00 +$3.99 s/h
Good
Oakwood_EMB Kernersville, NC
2012 Hardcover Good BOOK ONLY-no supplemental materials included. Covers show moderate wear. Pages show some marking/ highlighting. THIS ITEM IS OVERSIZED. PLEASE, NO INTERNATIONAL ORDERS.52.45 +$3.99 s/h
VeryGood
Magus Books WA Seattle, WA
2012 Hardcover Very Good 1111578494. THIS ITEM IS LARGE/HEAVY AND MAY REQUIRE EXTRA SHIPPING FOR INTERNATIONAL OR EXPEDITED DELIVERY; used hardcover with no dust jacket. light shelfwear; corners/edg...show morees are lightly bumped and rubbed. binding and pages remain straight and solid. no marks to text. boards and page edges are lightly scuffed but clean.; 10.90 X 8.50 X 1.40 inches; 1008 pages. ...show less
$58.91 +$3.99 s/h
New
Textbook Charlie Nashville, TN
Brand new instructors edition. May contain answers and/or notes in margins. Ships same day or next business day. Free USPS Tracking Number. Excellent Customer Service. Ships from TN
$59.95 +$3.99 s/h
VeryGood
Bookbyte-OR Salem, OR
Has minor wear and/or markings. SKU:9781111578497-3-0
$60.77 +$3.99 s/h
Good
newrecycleabook centerville, OH
1111578494 used book - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back
$61.63 +$3.99 s/h
New
JUGGERNAUTZ Troy, MI
1111578494 |
High School Pre-Calculus Tutor
9780878919109
ISBN:
0878919104
Publisher: Research & Education Assn
Summary: Algebra * Biology * Chemistry * Earth Science Geometry * Physics * Pre-Algebra * Pre-Calculus * Probability Trigonometry * Math Skills for SAT * Verbal Skills for SAT "With the Tutor Books, it's Easy to learn difficult subjects." The best help in preparing for homework and exams Includes every type of problem that may be assigned by your teacher or given on a test Guides you by working out problems in step-by-step de...tail Each "Tutor" helps you understand the subject fully, no matter which textbook you use.
Fogiel, M. is the author of High School Pre-Calculus Tutor, published under ISBN 9780878919109 and 0878919104. Two hundred sixteen High School Pre-Calculus Tutor textbooks are available for sale on ValoreBooks.com, one hundred eight used from the cheapest price of $0.01, or buy new starting at $12.46 |
...
More
Discussion for Finite Math for Windows
charlie sam
(Student)
finite math for windows is a site that helps students by giving them the tools of the software, so students can solve problems and checks it after that answers will be provided. which is effective.The software is made only for window users. The software makes it easier to search for topics related to the finite mathematic books.The site makes it so that you can print out the problems to take it on the go. The software also has demos which you can download for free. This sites allows students to freshen up on their math skills.
Time spent reviewing site:
45 mins spent reviewed,and the site provides interactive demos for students to use.
5 years ago
Claudia Ayerdis
(Student)
Found that this site interesting, as a first time user I have know been on this site for almost 2 hours. there is a lot of information to cover. This would be a could companion program to run while in a finite math class.
Technical Remarks:
I found it very difficult to follow. I downloaded the demo and felt lost to try to figure out how to use it. I is possible that because I don't have the full version I do not have access to some of the material that would make the site user friendly.
6 years ago
Christine DeRouin
(Student)
This site is a good resource for the classroom and home use, and I spent an hour exploring the different areas in this interactive website. It's a 30-day free trial download that does a good job of presenting concepts and models that are educationally significant to any Finite Math class. I believe that students and faculty can benefit by using this resource. For example, you can enter a problem from your textbook and this site will help you do it! Even though the downloading process and familiarizing yourself with the program takes time, once that's done, first time users will find it very useful and helpful. |
Essay | The Mathematical Part of Me
The Mathematical Part of Me
Summary: The following is a personal essay entitled "The Mathematical Part of Me", which discusses math classes I have taken.
Back in the days of elementary and middle school, math was different and was not as complex as high school math. It came quicker than high school math and every since then it has stuck with me. Math is so much more enjoyable as a subject in school then any other to me.
In my previous math courses these past years, they were pretty basic and just help add to the information I already knew. I felt like math comes natural to me and I just get carried away in it and could do it for hours. Even though it can be frustrating everything just takes time to settle in. I don't really have any major issues or weakness I'm bringing with me. I try to stop right when something happens and try to figure it out there instead of wasting time not knowing how to do it and get behind in the other information I should be learning. However, if I feel like I know something it might seem like I'm not paying attention but I'm and so that might be considered a weakness. Staying focus and making sure that my work gets done on time and correctly is my strengths. Studying did not really have to be too much of a bother to me in the pervious years.
Due to my success in previous math classes I was accepted into Mu Alpha Theta last year and really hope I enjoy being in it. I signed up for precalculus for one I needed another class to fill in my slot and two because I realized that I should get some more help before I go off to college. My plans for after highschool involve me getting a major in accounting and minoring in business. So yea math courses make an importance to me because I'll be using a lot of it in college so I can succeed in my later years successfully. |
Mathematics for Elementary Teachers II: Basic Principles of Algebra
Course Details
Min Credits
3
Max Credits
3
Course ID
2556
Status
Active
The course examines the topics related to ratio and proportion, slope, the notion of function, absolute value, linear and non linear functions, sets, equations, inequalities, simultaneous equations, reading and creating graphs of functions, formulas (in closed and recursive forms), and tables; studying characteristics of particular classes of functions on integers. It will also investigate some topics related to statistical analysis and probability. |
8th grade (U.S.)
8th grade is all about tackling the meat of algebra and getting exposure to some of the foundational concepts in geometry. If you get this stuff (and you should because you're incredibly persistent), the rest of your life will be easy. Okay, maybe not your whole life (no way to avoid the miseries of wedding planning), but at least your mathematical life. Seriously, we're not kidding. If you get the equations and functions and systems that we cover here, most of high school will feel intuitive (even relaxing). If you don't, well.. at least you have high school to catch up. :)
On top of that, we will sharpen many of the skills that you last saw in 6th and 7th grades. This includes extending our knowledge of exponents to negative exponents and exponent properties and our knowledge of the number system to irrational numbers!
(Content was selected for this grade level based on a typical curriculum in the United States.)
In proportional relationships, the ratio between one variable and the other is always constant. In the context of rate problems, this constant ratio can also be considered a rate of change. This tutorial allows you dig deeper into this idea.
Common Core Standard: 8.EE.B.5
There are many ways to graph a line and this tutorial covers one of the simpler ones. Since you only need two points for a line, let's find what value an equation takes on when x = 0 (essentially the y-intercept) and what value it takes on when y = 0 (the x-intercept). Then we can graph the line by going through those two points.
If you've ever struggled to tell someone just how steep something is, you'll find the answer here. In this tutorial, we cover the idea of the slope of a line. We also think about how slope relates to the equation of a line and how you can determine the slope or y-intercept given some clues.
Common Core Standard: 8.F.B.4
In this tutorial, we use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. We'll connect this idea to the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Common Core Standard: 8.EE.B.6
f(x), g(x), etc. What does this mean? Well they are ways of referring to "functions of x". This is an idea that will show up throughout more advanced mathematics and computer science so it is a good idea to understand them now!
Relationships can be any association between sets of numbers while functions have only one output for a given input. This tutorial works through a bunch of examples of testing whether something is a valid function. As always, we really encourage you to pause the videos and try the problems before Sal does!
Common Core Standard: 8.F.A.1
Linear functions show up throughout life (even though you might not realize it). This tutorial will have you thinking much deeper about what a linear function means and various ways to interpret one. Like always, pause the video and try the problem before Sal does. Then test your understanding by practicing the problems at the end of the tutorial.
Common Core Standards: 8.F.A.2, 8.F.A.4, 8.F.A.5
Not every relationship in the universe can be represented by a line (in fact, most can't be). We call these "nonlinear". In this tutorial, you'll learn to tell the difference between a linear and nonlinear function!
Have fun!
Common Core Standare: 8.F.A.3 |
Related Directories
Learn or re-learn the algebra you need to know to solve math problems found on your certification exam or during your daily work. This 8 lecture course will show you how to solve problems and give you plenty of guided practice to master the techniques |
'Chemistry Maths 1 teaches Maths from a "chemical" perspective and is the first of a three part series of texts taken during...
see more
'Chemistry Maths 1 teaches Maths from a "chemical" perspective and is the first
PC-based software and interactive tutorial to learn how to write mathematical proofs. Makes use of innovative proof-checking...
see more
PC-based software and interactive tutorial to learn how to write mathematical proofs. Makes use of innovative proof-checking technology to provide instant feedback to students/users. Free, full-version download available at website.
'Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum...
see more
'Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the pro-cesses of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are as follows:To help students learn how to read and understand mathematical definitions and proofs;To help students learn how to construct mathematical proofs;To help students learn how to write mathematical proofs according to ac-cepted guidelines so that their work and reasoning can be understood by others; andTo provide students with material that will be needed for their further study of mathematics.'
Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs...
see more
Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs and solutions to various mathematical equations. Material is crucial for the teaching of secondary school mathamatics.Compulsory Readings for Mathematics II: Number Theory (PDF)
3 KS3 and KS4 mathematic lesson plans covering the following topics:KS3 - MEAN, MEDIAN, AND MODAL AVERAGES - Learners will be...
see more
3 KS3 and KS4 mathematic lesson plans covering the following topics:KS3 - MEAN, MEDIAN, AND MODAL AVERAGES - Learners will be able to recognise the difference between different types of average, i.e. mean, median, and mode, and know how to calculate each variant accurately. They will be able to understand the statistical implications of the different types of average, and assess their usefulness/appropriateness in different situations.KS3 - PERCENTAGES - Learners will be able to calculate percentage decreases and increases.KS4 - AREA, PERIMETER AND VOLUME - Learners will be able to estimate/calculate the Area and Perimeter of 2D shapes and Volume of 3D shapes.Each 1 hour with a range of activities and national cirriculum level descriptors.
This power point presentation, in kiosk mode, allows the user to explore rows, columns, and cells of a 4x4...
see more
This power point presentation, in kiosk mode, allows the user to explore rows, columns, and cells of a 4x4 matrix. Images, speech, and text guide users through the presentation and concludes with a short 5 question independent assessment. Learners are provided feedback as the questions increase in difficulty. |
Preface.- Introduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- Exercises.- Bibliography and Cited References.- Index. |
Categories
Get Newsletter
Homeschool Math Curriculum for the College Bound!
Complete college prep homeschool math curriculum for the high school math subjects of Algebra, Geometry, Algebra 2 with Trigonometry, and Calculus.
Homeschool mom friendly - Does teaching homeschool math at the high school level concern you? Do you think you just do not have the time or energy to deal with homeschool math at the high school level? We support our homeschool math courses and your homeschool students because we know that as homeschooling parents you have a few other things going on! We homeschool too!
ACT and SAT Prep - Many homeschool math programs teach a "cookbook" style of math that leaves homeschool students weak in math concepts. Our homeschool math curriculum teaches an understanding of the math concepts, which is of critical importance for the SAT and ACT exams.
College accepted - Be ready to step from homeschool to college math and science classes with ease.
Homeschool math at the college level - These may be homeschool math courses, but we teach at the college level. As a college engineering professor, I know how unprepared most college students are in math. And, a lot of homeschool math teaches BELOW the typical high school path. We teach our homeschool math courses at the college level, but change the pace so that your homeschool student can handle the load and be prepared at the same time.
Free Stuff
Free shipping---we offer Free Shipping every day to homeschool parents on all of our math curriculum bundles and DVDs and most orders over $100.
Free Support --- We support our products by helping homeschool parents and homeschool students! We work daily with homeschool students and parents to help them understand math concepts.
Recent Updates
Why AskDrCallahan for your homeschool math curriculum?
We know as homeschool parents and educators you ask the question "Why this product instead of that product?" So allow us to provide three reasons we think you will like our homeschool math products over some of the others being sold in the homeschool market.
1) Homeschool math for ACT / SAT Prep
The math sections of the ACT and SAT exams do not focus on the student's ability to use math - instead the exams focus on an understanding of the math concepts! Most math courses will drill your homeschooler into being able to do math - using brute force to cram through formulas. This approach is similar to your homeschooler being trained to use individual tools in a toolbox without teaching them what each tool actually accomplishes on its own. They can use each one, but it is also important that they understand when hanging a picture why, or when, a hammer might be a better option as opposed to a screwdriver.
We seek to have your homeschooler understand the concepts in our homeschool math curriculum. Math formulas and theorems are useful tools that homeschoolers need to know. But owning a toolbox full of tools doesn't matter unless you understand what each tool is designed to do. In other words, your homeschool math course needs to teach the WHY before the how. In other words, you need to learn the concepts. Our homeschool math curriculum explains the why before the what - why we need to use math tools before we get into what the specific tool does.
It is only with this level of understanding that your homeschool student can perform 60 math problems within 60 minutes on the ACT and SAT. (These tests are designed to weed out the "memorizers" by doing the whole "timed test" approach. Learn the mathematical concepts!)
2) Homeschool Math that is REAL
Too many homeschoolers just bring school home - doing the same boring stuff without understanding. We also focus on real world applications of math. The history of math has not been about the study of numbers - it has been about the study of nature, of the life around us every day. The AskDrCallahan homeschool math courses use lots of real world problems in explaining the techniques of math. We introduce areas such as biology, engineering, economics, astronomy, physics, construction, and chemistry. Math is a set of tools to understand and subdue the world around us- not simply repetitious exercises in academics. So we hope to keep our homeschool math curriculum REAL and applied to real life.
3 ) Help for the Homeschooling Parent.
We homeschool! We understand that even if you do remember the subject matter, your time between normal duties of being CEO of the household and raising and homeschooling children of multiple ages on multiple subjects limits your ability to develop teaching and testing material. We do not leave that out - in fact we consider it critical that you have the tools to teach and evaluate your homeschool students. We include |
Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective.
Scheinerman, Edward R. is the author of Mathematics A Discrete Introduction, published 2005... under ISBN 9780534398989 and 0534398987. Ninety five Mathematics A Discrete Introduction textbooks are available for sale on ValoreBooks.com, seventeen used from the cheapest price of $4.85, or buy new starting at $60.00.[read more |
(Available: )
Mathematics Vocabulary for Algebra
Algebra Vocabulary
abscissa
Definition and illustration (if applicable):
the x-value of an ordered pair that describes the vertical distance from the x-axis.
It is always written as the first element in the ordered pair.
3 is the abscissa of the ordered pair (3, 5).
Associated terms:
Algebra Vocabulary
absolute value
Definition and illustration (if applicable):
The absolute value of a real number, x, is the distance from x to the origin on the
real number line. Because absolute value represents distance, absolute value is
never less than zero.
Associated terms:
Algebra Vocabulary
algorithm
Definition and illustration (if applicable):
a sequence of steps that produce a desired outcome
In mathematics, an algorithm is often a step-by-step procedure.
Associated terms:
Algebra Vocabulary
argument
Definition and illustration (if applicable):
numeric or algebraic input into an algorithm, nth function, or other defined
function
Associated terms:
Algebra Vocabulary
arithmetic sequence
Definition and illustration (if applicable):
a sequence in which successive terms have a common difference
All arithmetic sequences can be written as an=a1+(n-1)d where an is the nth term
of the sequence, a1 is the first term and d is the common difference.
3, 7, 11, 15, 19 … is an arithmetic sequence and can be represented by
an=3 + (n-1) 4.
Associated terms:
Algebra Vocabulary
arithmetic series
Definition and illustration (if applicable):
the sum of the terms of an arithmetic sequence
Associated terms:
Algebra Vocabulary
asymptote
Definition and illustration (if applicable):
a line or curve that approaches a given curve arbitrarily closely
Associated terms:
Algebra Vocabulary
binary operation
Definition and illustration (if applicable):
an action performed on two quantities
Addition, subtraction, multiplication, division and exponentiation are binary
operations.
Associated terms:
Algebra Vocabulary
binomial
Definition and illustration (if applicable):
the sum or difference of two monomials
Associated terms:
Algebra Vocabulary
circle
Definition and illustration (if applicable):
the locus of all points that are a fixed distance from a given point
Associated terms:
Algebra Vocabulary
Closure Property
Definition and illustration (if applicable):
A set is said to be closed under some operation if the operation on members of the
set produces a member of the set. A set that is closed under an operation or
collection of operations is said to satisfy a closure property. For example, the real
numbers are closed under subtraction, where the subset of natural numbers is
not.
Associated terms:
Algebra Vocabulary
complex fraction
Definition and illustration (if applicable):
a fraction with one or more fractions embedded in the numerator and/or
denominator
Associated terms:
Algebra Vocabulary
complex number
Definition and illustration (if applicable):
any number that can be written in the form a + bi where a and b are real
numbers and i is 1 (the square root of -1).
Note that the set of real numbers is a subset of the set of complex numbers.
Associated terms:
Algebra Vocabulary
composition of functions
Definition and illustration (if applicable):
combining two functions by taking the output of one and
using it as the input of another
If the output of g is used as the input of f, then the composition is referred to as "f
of g of x" and is denoted f(g(x)) or f ○ g(x)
Associated terms:
Algebra Vocabulary
consistent system (of equations)
Definition and illustration (if applicable):
a system of equations that has at least one solution
Associated terms: systems of equations
Algebra Vocabulary
constant of variation
Definition and illustration (if applicable):
the non-zero (usually denoted k) in a direct variation (y=kx), an indirect
variation (y= k ) or a joint variation (z=kxy)
x
Associated terms: direct variation, joint variation, inverse variation
Algebra Vocabulary
continuous function
Definition and illustration (if applicable):
A function f is continuous at a point (x, y) if it is defined at that point and passes
through that point without a break.
Associated terms:
Algebra Vocabulary
decreasing function
Definition and illustration (if applicable):
A function f is decreasing on an interval if and only if for every a and b in the
interval, f(a) > f(b) whenever a < b.
Associated terms:
Algebra Vocabulary
degree (of a polynomial)
Definition and illustration (if applicable):
the degree of the term with greatest sum of powers.
Associated terms:
Algebra Vocabulary
dependent system of equations
Definition and illustration (if applicable):
system of linear equations where one linear equation is a multiple of the other
and, therefore, has an infinite number of solutions
Associated terms: consistent system, dependent system
Algebra Vocabulary
direct variation
Definition and illustration (if applicable):
a relationship between two variables, x and y, that can be expressed as y=kx
where k is the constant of variation
Associated terms: joint variation, constant of variation, inverse variation
Algebra Vocabulary
discriminant
Definition and illustration (if applicable):
an algebraic expression related to the coefficients of a quadratic equation that
can be used to determine the number and type of solutions to the equation
Associated terms:
Algebra Vocabulary
domain
Definition and illustration (if applicable):
the set of independent values in a function; the set of first elements in ordered
pairs in a function
Associated terms:
Algebra Vocabulary
ellipse
Definition and illustration (if applicable):
For two given points (the foci), an ellipse is the locus of points such that the sum of the
distances to each focus is constant.
Associated terms:
Algebra Vocabulary
function
Definition and illustration (if applicable):
a rule that pairs elements from one set, called the domain, to elements from
another set, called the range, in such a way that no first element is repeated
The result is a set of ordered pairs, (x, y) where each x value is unique.
Representations of functions include graphs, tables, function notation, mapping
diagrams and words.
Functional notation: A way to represent a function where a functional name,
often f, is used and the function is written where an independent variable, x, is the
input of the function and f(x) is the output.
Associated terms: increasing function, decreasing function, constant function
Algebra Vocabulary
Fundamental Theorem of Algebra
Definition and illustration (if applicable):
Every polynomial equation with degree greater than zero has at least one root in
the set of complex numbers.
Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the
product of a constant k (k ≠ 0) and n linear factors
P(x) = k (x – r1) (x – r2 ) (x – r3 )…(x – rn)
Thus a polynomial equation of degree n has exactly n complex roots,
namely r1, r2, r3,…, rn.
Associated terms:
Algebra Vocabulary
Fundamental Theorem of Arithmetic
Definition and illustration (if applicable):
In number theory, the Fundamental Theorem of Arithmetic (or unique
factorization theorem) states that every natural number greater than 1 can be
written as a unique product of prime numbers.
Associated terms:
Algebra Vocabulary
geometric sequence
Definition and illustration (if applicable):
a sequence in which consecutive terms have a common ratio
All geometric sequences can be written as an=a1rn-1 where an is the nth term of the
sequence, a1 is the first term and r is the common ratio.
Associated terms:
Algebra Vocabulary
geometric series
Definition and illustration (if applicable):
the sum of the terms of a geometric sequence
The sum of the first n terms of a geometric series is given by
a1 a1r n
Sn = .
1 r
Associated terms:
Algebra Vocabulary
hyperbola
Definition and illustration (if applicable):
For two given points (the foci), a hyperbola is the locus of points such that the
difference between the distances to each focus is constant
Associated terms:
Algebra Vocabulary
inconsistent system of equations
Definition and illustration (if applicable):
system of linear equations that has no solutions; parallel lines
Associated terms:
Algebra Vocabulary
increasing function
Definition and illustration (if applicable):
A function f is increasing on an interval if and only if f(a) > f(b) for every a > b in
the interval.
Associated terms:
Algebra Vocabulary
independent system of equations
Definition and illustration (if applicable):
a consistent system of linear equations with only one solution
Associated terms:
Algebra Vocabulary
index
Definition and illustration (if applicable):
number indicating what root is being taken
4
981 the index is 4.
Associated terms:
Algebra Vocabulary
indirect (inverse) variation
Definition and illustration (if applicable):
k
A relationship between two variables, x and y, that can be expressed as y
x
where k is the constant of variation
Associated terms:
Algebra Vocabulary
x-intercept
y-intercept
Definition and illustration (if applicable):
point where a curve crosses the x- or y-axis.
Associated terms:
Algebra Vocabulary
joint variation
Definition and illustration (if applicable):
a relationship that exists when a quantity varies directly with the product of two
or more quantities
y = kxy
Associated terms: direct variation, inverse variation
Algebra Vocabulary
leading coefficient
Definition and illustration (if applicable):
In a polynomial function of degree n, the leading coefficient is an and the leading
term is anxn
Associated terms:
Algebra Vocabulary
linear function
Definition and illustration (if applicable):
a function in the form y = mx+b where m and b are constants
The graph of a linear function is a line.
A linear equation has degree 1.
Associated terms:
Algebra Vocabulary
literal equations
Definition and illustration (if applicable):
an equation that contains more than one variable; an implicit equation; often
mathematical formulae
Associated terms:
Algebra Vocabulary
matrix
Definition and illustration (if applicable):
a rectangular table of elements which may be numbers or any abstract quantities that
can be added and multiplied; used to describe linear equations, keep track of the
coefficients of linear transformations, and to record data that depend on multiple
parameters; a key component of linear algebra; dimensions of a matrix--number of
rows and the number of columns of a matrix, written r x c
Associated terms:
Algebra Vocabulary
monomial
Definition and illustration (if applicable):
a monomial is a product of constants and variables; a polynomial with one term
Associated terms:
Algebra Vocabulary
one-to-one function
Definition and illustration (if applicable):
a function where every value of y has a unique value for x
If a given function passes the horizontal line test then it is a one-to-one function.
One-to-one functions have inverses that are also functions.
Associated terms: function, increasing function, decreasing function
Algebra Vocabulary
outlier
Definition and illustration (if applicable):
a value in a data set that is much higher or lower than the rest; a point which
falls more than 1.5 times the interquartile range above the third quartile or below
the first quartile
Associated terms:
Algebra Vocabulary
parabola
Definition and illustration (if applicable):
a locus of points whose perpendicular distances to a line, called the directrix, and
to a fixed point, called the focus, are equal
The graph of any quadratic function is a parabola.
Associated terms:
Algebra Vocabulary
piecewise function
Definition and illustration (if applicable):
a function that consists of one or more functions, each with a limited or specified
domain; when the pieces are graphed, on the same coordinate plane, the graph
may or may not be continuous.
Associated terms: continuous function
Algebra Vocabulary
polynomial function
Definition and illustration (if applicable):
a function that can be written as
Associated terms:
Algebra Vocabulary
prime polynomial
Definition and illustration (if applicable):
a polynomial that cannot be factored over the real numbers further;
i. e. x2 + 4
Associated terms:
Algebra Vocabulary
quadratic formula
Definition and illustration (if applicable):
Associated terms:
Algebra Vocabulary
quadratic function
Definition and illustration (if applicable):
a function that may be written f(x)=ax2 + bx + c
Associated terms:
Algebra Vocabulary
radical (nth root)
Definition and illustration (if applicable):
an expression of the form r or n
r where r is a number or expression
r
n
n
r
The radicand is the argument for a radical expression.
Associated terms:
Algebra Vocabulary
range (of a function)
Definition and illustration (if applicable):
the possible values for the dependent variable in a function or relation
Associated terms:
Algebra Vocabulary
range (of a set of data)
Definition and illustration (if applicable):
the difference between the maximum value and the minimum value in a data set
The range of {5, 7, 9, 2, 4, 7, 1, 7} is 8 because the maximum value is 9 and the
minimum value is 1.
Associated terms:
Algebra Vocabulary
rational functions
Definition and illustration (if applicable):
a function that can be written as R(x) = P(x) / Q(x) where P(x) and Q(x) are
polynomials and Q(x) ≠ 0.
Associated terms: function
Algebra Vocabulary
regression
Definition and illustration (if applicable):
Linear regression is the process of obtaining the line of best fit. The relationship
between two sets of data may be described with a line using some goodness-of-fit
criterion. The regression line obtained may be used to describe data and make
predictions.
Associated terms:
Algebra Vocabulary
roots (of a polynomial)
Definition and illustration (if applicable):
A root of a polynomial is a number x such that P(x)=0. A polynomial of degree n
has n roots.
Associated terms: Fundamental Theorem of Algebra
Algebra Vocabulary
slope
Definition and illustration (if applicable):
the steepness of a line going from left to right; rise over run; a constant rate of change
If the line rises from left to right on the graph, then the line has a positive slope; if the line
falls from left to right, then it has a negative slope. A horizontal line has a slope of zero. A
vertical line has no slope; i. e. the slope is undefined. Slope is calculated using two points on
the line. The difference of the y-values is divided by the difference in the x-values (rise
divided by run). The symbol for slope is m.
y2 y1
m
x2 x1
Associated terms:
Algebra Vocabulary
trinomial
Definition and illustration (if applicable):
a polynomial expression with three terms
Associated terms:
Algebra Vocabulary
zeros (of a function)
Definition and illustration (if applicable):
a value of x for which f(x) = 0
Associated |
This page offers a clear explanation of the equations that can be used to describe the one-dimensional, constant acceleration motion of an object in terms of its three kinematic variables: velocity, displacement, and...
The dedicated folks at the Mathematical Association of America (MAA) have created this handy compendium of learning capsules as part of their online digital library. This compendium contains fifteen different areas,...
Created by staff members at the University of Arizona's Center for Recruitment & Retention of Mathematics Teachers (CRR), Do the Math is a weekly cable television show that features mathematics teachers explaining key...
This series of lectures, created by Salman Khan of the Khan Academy, features topics covered in the first two or three semesters of college calculus; Everything from limits to derivatives to integrals to vector...
Bates College in Maine has worked diligently to bring together this set of mathematical resources to the public, and it's a nice find. The materials here are drawn from four courses at the school: Math 105, Math 106,... |
5 Student Support Edition of Intermediate Algebra: An Applied Approach, 7/e, brings comprehensive study skills support to students and the latest technology tools to instructors. In addition, the program now includes concept and vocabulary review material, assignment tracking and time management resources, and practice exercises and online homework to enhance student learning and instruction. With its interactive, objective-based approach, Intermediate Algebra provides comprehensive, mathematically sound coverage of topics essential to the intermediate algebra course. The Seventh Edition features chapter-opening Prep Tests, real-world applications, and a fresh design--all of which engage students and help them succeed in the course. The Aufmann Interactive Method (AIM) is incorporated throughout the text, ensuring that students interact with and master concepts as they are presented.
Table of Contents
Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, Review Exercises, and a Chapter Test
Inequalities in Two Variables Focus on Problem Solving: Find a Pattern Projects and Group Activities: Evaluating a Function with a Graphing Calculator; Introduction to Graphing Calculators; Wind-Chill Index
Application Problems
Solving Systems of Linear Inequalities Focus on Problem Solving: Solve an Easier Problem Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations
Polynomials
Exponential Expressions
Introduction to Polynomial Functions
Multiplication of Polynomials
Division of Polynomials
Factoring Polynomials
Special Factoring
Solving Equations by Factoring Focus on Problem Solving: Find a Counterexample Projects and Group Activities: Astronomical Distances and Scientific Notation
Complex Numbers Focus on Problem Solving: Another Look at Polya's Four-Step Process Projects and Group Activities: Solving Radical Equations with a Graphing Calculator; The Golden Rectangle
Quadratic Equations
Solving Quadratic Equations by Factoring or by Taking Square Roots
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by using the Quadratic Formula
Solving Equations That Are Reducible to Quadratic Equations
Quadratic Inequalities and Rational Inequalities
Applications of Quadratic Equations Focus on Problem Solving: Inductive and Deductive Reasoning Projects and Group Activities: Using a Graphing Calculator to Solve a Quadratic Equation
Functions and Relations
Properties of Quadratic Functions
Graphs of Functions
Algebra of Functions
One-to-One and Inverse Functions Focus on Problem Solving: Proof in Mathematics Projects and Group Activities: Finding the Maximum or Minimum of a Function Using a Graphing Calculator; Business Applications of Maximum and Minimum Values of Quadratic Functions
Exponential and Logarithmic Functions
Exponential Functions
Introduction to Logarithms
Graphs of Logarithmic Functions
Solving Exponential and Logarithmic Equations
Applications of Exponential and Logarithmic Functions Focus on Problem Solving: Proof by Contradiction Projects and Group Activities: Solving Exponential and Logarithmic Equations Using a Graphing Calculator; Credit Reports and FICO Scores
Conic Sections
The Parabola
The Circle
The Ellipse and the Hyperbola
Solving Non-linear Systems of Equations
Quadratic Inequalities and Systems of Inequalities Focus on Problem Solving: Using a Variety of Problem-Solving Techniques Projects and Group Activities: The Eccentricity and Foci of an Ellipse; Graphing Conic Sections Using a Graphing Calculator
Proofs of Logarithmic Properties Proof of the Formula for the Sum of n Terms of an Geometric Series Proof of the Formula for the Sum of n Terms of an Arithmetic Series Table of Symbols Table of Properties Table of Algebraic and Geometric Formulas Solutions to You Try Its Answers to Selected Exercises |
Short Description
Study & Master Mathematics Grade 8 covers and integrates all LOs as stated in the NCS.
Long description
Study & Master Mathematics Grade 8 is an exciting new course that covers and integrates all the Learning Outcomes for Mathematics stated in the National Curriculum Statement. The material is presented in a user-friendly way that will not only boost learners' confidence, but will also show them how to enjoy Mathematics |
Introductory Algebra for College Students (Pearson) – Hardcover (2011)
by
Robert F. Blitzer
Hardcover, Pearson 2011
6th edition.
768 pages
ISBN: 0321758951 ISBN-13: 9780321758958
Hide
Description:New. No dust jacket. 100% BRAND NEW ORIGINAL US HARDCOVER...New. No dust jacket. 100% BRAND NEW ORIGINAL US HARDCOVER STUDENT 6th Edition / Mint condition / Never been read / ISBN-13: 9780321758958 / Shipped out in one business day with free tracking.
Reviews of Introductory Algebra for College Students
tHIS IS NOT THE COVER Of the book. Its orange and has a bottle cap on the cover. BUUT this book is great. It clearly lists the steps and reasons for the math eq. and such. Although I DESPISE the ANSWER KEY in the back because it only lists the answers for ODD NUMBERS. Other than that, the condition ...
More
Unfortunately, this text was required for my class. I got to use the Lial series for PreAlgebra, and I will get to for Intermediate as well. They are much better for those who need more examples, description, worked problems, etc. This one assumes you know a lot |
Course Materials
Site Feedback
More Information
Site owners
Robert Hoar
Mark Mathison
Intermediate Algebra Home
Welcome to UW-L's Math 051 Site
The UW System Institute for Innovation in Undergraduate Research and Learning (IIURL) has developed this site to share a collection of digital learning objects (LOs). These materials are designed to support the study of mathematics and is appropriate for use by students enrolled in Math 051: Intermediate Algebra course.
This course is designed to enhance ones skills in selected areas of intermediate algebra; areas covered include polynomials, rational expressions, exponents, equations, and inequalities.
In this collection, you will find digital materials clustered into seven chapters: |
This is a free, online textbook that is also part of an online course. According to the author, "Analysis is the study of...
see more
This is a free, online textbook that is also part of an online course. According to the author, "Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. Some of the examples which will be important in this course are sequences, infinite series, derivatives of functions, and integrals. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know.״
According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY...
see more
According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.'
'This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my...
see more
'This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.'
This is a free, online textbook for an introductory course in complex analysis. General topics include Complex Numbers,...
see more
This is a free online course offered by the Saylor Foundation.'This course is an introduction to complex analysis, or the...
see more
This is a free online course offered by the Saylor Foundation.'This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable. Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable. Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing. Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear. Simply put, you will be working with lines and sets and very specific functions on the complex plane—drawing pictures of them and teasing out all of their idiosyncrasies. You will again find yourself calculating line integrals, just as in multivariable calculus. However, the techniques you learn in this course will help you get past many of the seeming dead-ends you ran up against in calculus. Indeed, most of the definite integrals you will learn to evaluate in Unit 7 come directly from problems in physics and cannot be solved except through techniques from complex variables.We will begin by studying the minimal algebraically closed extension of real numbers: the complex numbers. The Fundamental Theorem of Algebra states that any non-constant polynomial with complex coefficients has a zero in the complex numbers. This makes life in the complex plane very interesting. We will also review a bit of the geometry of the complex plane and relevant topological concepts, such as connectedness.In Unit 2, we will study differential calculus in the complex domain. The concept of analytic or holomorphic function will be introduced as complex differentiability in an open subset of the complex numbers. The Cauchy-Riemann equations will establish a connection between analytic functions and differentiable functions depending on two real variables. In Unit 3, we will review power series, which will be the link between holomorphic and analytic functions. In Unit 4, we will introduce certain special functions, including exponentials and trigonometric and logarithmic functions. We will consider the Möbius Transformation in some detail.In Units 5, 6, and 7 we will study Cauchy Theory, as well as its most important applications, including the Residue Theorem. We will compute Laurent series, and we will use the Residue Theorem to evaluate certain integrals on the real line which cannot be dealt with through methods from real variables alone. Our final unit, Unit 8, will discuss harmonic functions of two real variables, which are functions with continuous second partial derivatives that satisfy the Laplace equation, conformal mappings, and the Open Mapping Theorem.'
This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning...
see more
This is a free, online textbook offered by Bookboon.com. Topics include: 1. Some simple theoretical results concerning power series, 2. Simple Fourier series in the Theory of Complex Functions, 3. Power series, 4. Analytic functions described as power series, 5. Linear differential equations and the power series method, 6. The classical differential equations, 7. Some more difficult differential equations, 8. Zeros of analytic functions, 9. Fourier series, and 10. The maximum principle.
This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing...
see more
This is a free, online textbook offered by Bookboon.com. "This is the fifth textbook you can download for free containing examples from the Theory of Complex Functions. In this volume we shall consider the Laurent series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of Laurent series.״ |
Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions... more...
The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations.... |
Aristotle Problem Solver
Summary
The Aristotle Problem Solver is an application that solves linear programming problems. An example of a linear programming problem is the optimization of a factory production with limited raw supplies so as to maximize the profits of selling the produced goods in specific prices.
1. Program Description
The program uses the Simplex Method to solve linear programming problems (see next section of the article for description of that method).
The main loop in the program's code that actually solves the problems is presented below:
2. Algorithm Analysis
That text is distributed under the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
2.1 Linear Programming Problems
In mathematics, linear programming (LP) is a technique for optimization of a linear objective function, subject to linear equality and linear inequality constraints. Informally, linear programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model and given a list of requirements represented as linear equations.
More formally, given a polytope (for example, a polygon or a polyhedron), and a real-valued affine function
defined on this polytope, a linear programming method will find a point in the polytope where this function has the smallest (or largest) value. Such points may not exist, but if they do, searching through the polytope vertices is guaranteed to find at least one of them.
Linear programs are problems that can be expressed in canonical form:
Maximize
Subject to
represents the vector of variables (to be determined), while and are vectors of (known) coefficients and is a (known) matrix of coefficients. The expression to be maximized or minimized is called the objective function ( in this case). The equations are the constraints which specify a convex polyhedron over which the objective function is to be optimized.
Linear programming can be applied to various fields of study. Most extensively it is used in business and economic situations, but can also be utilized for some engineering problems. Some industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proved useful in modeling diverse types of problems in planning, routing, scheduling, assignment, and design.
2.2 Standard form LP models
If a LP model satisfies the following two conditions it is said to be in standard form:
All the constraints with the exception of the non-negativity restrictions are equations with non-negative right hand side.
All the variables are non-negative.
For example,is an LP model in standard form.
How do we convert a given model into a standard model while retaining its sense? This is done as follows:
If there is a constraint of the type then the right hand side usually represents some limit on the resource (for example the amount of the raw material available) and the left hand side the usage of that resource (i.e. how much raw material is actually used) and so their difference represents the 'slack' or unused amount of the resource. So to convert into an equality we must add a variable representing the slack amount on the left hand side. This variable is known as the 'slack variable' and is obviously also non-negative. If we represent it by s1 our constraint is converted into the equation 6x1 + 4x2 + s1 = 24. A similar thing is done in case of a constraint of the type . Here the left hand side has a 'surplus' or extra amount then the right hand side and so a non-negative 'surplus variable' say s2 must be subtracted to get the equation 6x1 + 4x2 − s2 = 24.
If the given variable xi is given to be non-positive then its negative yi = − xi is obviously non-negative and can be substituted in the problem. The real problem comes in the case when the variable is allowed to take on any sign. Then it is called an 'unrestricted variable.' This is overcome by using the substitution where are both non-negative. Intuitively if the variable xi is positive then is positive and is zero, while if the variable xi is negative then is zero and is positive. If xi is zero then obviously are both zero.
A point to note is that the objective function in the original LP model and the standard model is the same.
2.3 Algebraic Solution of a LP
Let us now try to analyze a LP model algebraically. A solution of the standard LP model will be a solution for the original model (since the slack and surplus variables once removed would make the equations regain their old imbalance) and due to a similar reasoning a solution for the original model will also correspond to a solution for the standard model. Since the objective function is the same for both models so an optimal solution for the standard model will be optimal for the original model as well. Therefore we need to bother only about the standard model.
Now what are the candidates for the optimal solution? They are the solutions of the equality constraints. All we need to do is to find out the solutions and check which of those give the optimal value when put in the objective function. Now usually in the LP model the number of constraints, say m, is outnumbered by the number of variables, say n, and so there are infinitely many solutions to the system of constraints. We can't possibly examine the complete set of infinite solutions. However due to a mathematical result our work is shortened. The result is that if out of the n variables, n-m variables are put to zero, and then if the constraint system can be solved then the solution will correspond to a corner point in the n-space. Such a solution is called a 'basic solution.' If in addition to being basic it happens to be feasible to the original problem, then it is called a 'basic feasible solution' (often abbreviated as BFS). Since the optimal solution is obtained on a corner point (as we observed graphically) so all we need to do is to examine all the basic feasible solutions (which are at most in number, reflective of the number of ways n-m variables can be chosen among the total n to be zero) and then decide which one gives the maximum value for the objective function.
Let us consider an example:
Consider the following LP model:
Maximize z = 2x1 + 3x2
subject to,
,
,
.
We first convert it into standard form:
Maximize z = 2x1 + 3x2
subject to,
2x1 + x2 + s1 = 4,
x1 + 2x2 + s2 = 5,
.
The constraint system has m=2 constraints and n=4 variables. Thus we need to set 4-2=2 variables equal to zero to get a basic solution. For example putting x1 = 0 and x2 = 0 we get a solution s1 = 4 and s2 = 5. This is also clearly feasible and so is a basic feasible solution. The variables being put to zero, that are x1,x2 are called 'nonbasic variables' and s1,s2 are called 'basic variables.' The 'objective value' (the value that is obtained by putting the solution in the objective function) that these solutions (both basic and non basic) give on substitution in the objective function is zero.
The following table summarizes all the basic solutions to the problem:
Nonbasic variables
Basic variables
Basic solution
Feasible
Objective value
(x1,x2)
(s1,s2)
(4,5)
Yes
0
(x1,s1)
(x2,s2)
(4,-3)
No
-
(x1,s2)
(x2,s1)
(2.5,1.5)
Yes
7.5
(x2,s1)
(x1,s2)
(2,3)
Yes
4
(x2,s2)
(x1,s1)
(5,-6)
No
-
(s1,s2)
(x1,x2)
(1,2)
Yes
8
Note that we have not bothered to calculate the objective value for infeasible solutions. The optimal solution is the one which yields the highest objective value i.e. x1 = 1,x2 = 2. Hence we have solved the LP model algebraically.
This procedure of solving LP models works for any number of variables but is very difficult to employ when there are a large number of constraints and variables. For example, for m = 10 and n = 20 it is necessary to solve sets of equations, which is clearly a staggering task. With the simplex method, you need only solve a few of these sets of equations, concentrating on those which give improving objective values.
2.4 The Simplex Method
The method in a nutshell is this. You start with a basic feasible solution of an LP in standard form (usually the one where all the slack variables are equal to the corresponding right hand sides and all other variables are zero) and replace one basic variable with one which is currently non-basic to get a new basic solution (since n-m variables remain zero). This is done in a fashion which ensures that the new basic solution is feasible and its objective value is at least as much as that of the previous BFS. This is repeated until it is clear that the current BFS can't be improved for a better objective value. In this way the optimal solution is achieved.
It is clear that one factor is crucial to the method: which variable should replace which. The variable which is replaced is called the 'leaving variable' and the variable which replaces it is known as the 'entering variable.' The design of the simplex method is such so that the process of choosing these two variables allows two things to happen. Firstly, the new objective value is an improvement (or at least equals) on the current one and secondly the new solution is feasible.
Let us now explain the method through an example. Consider our old chemical company problem in standard form:.
Now an immediate BFS is obtained by putting all the xi equal to zero. (Clearly the solution thus obtained will be feasible to the original problem as the right hand sides are all non-negative which is precisely our solution.) If we consider our objective function z = 5x1 + 4x2 then it is evident that an increase in x1 or x2 will increase our objective value. (Note that currently both are zero being non-basic). A unit increase in x1 will give a 5-fold increase in the objective value while a unit increase in x2 will give a 4-fold increase. It is logical that we elect to make the entering variable x1 in the next iteration.
In the tabular form of the simplex method the objective function is usually represented as z − 5x1 − 4x2 = 0. Also the table contains the system of constraints along with the BFS that is obtained. Only the coefficients are written as is usual when handling linear systems.
Basic
z
x1
x2
s1
s2
s3
s4
BFS
z
1
-5
-4
0
0
0
0
0
s1
0
6
4
1
0
0
0
24
s2
0
1
2
0
1
0
0
6
s3
0
-1
1
0
0
1
0
1
s4
0
0
1
0
0
0
1
2
Now for the next iteration we have to decide the entering and the leaving variables. The entering variable is x1 as we discussed. In fact, due to our realignment of the objective function, the most negative value in the z-row of the simplex table will always be the entering variable for the next iteration. This is known as the 'optimality condition.' What about the leaving variable? We have to account for the fact that our next basic solution is feasible. So our leaving variable must be chosen with this thought in mind.
To decide the leaving variable we apply what is sometimes called as the 'feasibility condition.' That is as follows: we compute the quotient of the solution coordinates (that are 24, 6, 1 and 2) with the constraint coefficients of the entering variable x1 (that are 6, 1, -1 and 0). The following ratios are obtained: 24/6 = 4, 6/1 = 6, 1/-1 = -1 and 2/0 = undefined. Ignoring the negative and the undefined ratio we now proceed to select the minimum of the other two ratios which is 4, obtained from dividing 24(the value of s1) by 6. Since the minimum involved the division by s1's current value we take the leaving variable as s1.
What is the justification behind this procedure? It is this. The minimum ratios actually represent the intercepts made by the constraints on the x1 axis. To see this look at the following graph:
Since currently all xi are 0 we are considering the BFS corresponding to the origin. Now, in the next iteration according to the simplex method we should get a new BFS i.e move to a new corner point on the graph. We can induce an increase in the value of only one variable at a time by making it an entering variable, and since x1 is our entering variable our plan is to increase the value of x1. From the graph we can see that the value of x1 must be increased to 4 at the point (4,0), which is the smallest non-negative intercept with the x1 axis. An increase beyond that point is infeasible. Also at (4,0) the slack variable s1 assumes a zero value as the first constraint is satisfied as an equality there and so s1 becomes the leaving variable.
Now the problem is to determine the new solution. Although any procedure of solving a linear system can be applied at this stage, usually Gauss Jordan elimination is applied. It is based on a result in linear algebra that the elementary row transformations on a system [A|b] to [H|c] do not alter the solutions of the system. According to it the columns corresponding to the basic-variables in the table are given the shape of an identity matrix. (Readers familiar with linear algebra will recognize that it means that the matrix formed with the basis variable columns is transformed into reduced row echelon form.) The solution can then be simply read off from the right most solution column (as n-m of the variables are put to zero and the rest including z have coefficient 1 in one constraint each). Since z is also a variable it's row is treated as one among the constraints comprising the linear system.
The entering variable column is called the 'pivot column' and the leaving variable row is called the 'pivot row.' The intersection of the pivot column and the leaving variable column is called the 'pivot element.' In our example the second row (of s1) is the pivot row and the second column(of x1) is the pivot column.
The computations needed to produce the new basic solution are:
Replace the leaving variable in the 'Basic' column with the entering variable.
The optimality condition now shows that x2 is the entering variable. The feasiblity condition produces the ratios: 4/(2/3) = 6, 2/(4/3) = 1.5, 5/(5/3) = 3 and 2/1 = 2 of which the minimum is 1.5 produced by dividing the coefficient in the s2 row (i.e. the row in which the basic variable s2 has coefficient 1). So s2 becomes the leaving variable. The Gauss Jordan elimination process is applied again to get the following table:
Basic
z
x1
x2
s1
s2
s3
s4
BFS
z
1
0
0
0
0
21
x1
0
1
0
0
0
3
x2
0
0
1
0
0
s3
0
0
0
1
0
s4
0
0
0
0
1
Based on the optimality condition none of the z-row coefficients associated with the non-basic variables s1 and s2 are negative. Hence the last table is optimal. The optimal solution can thus be read off as and and the optimal value as z = 21. Obviously the variables s1 and s2 are zero. Our original problem involving only x1 and x2 also clearly has the same solution (just disregard the slacks).
We have dealt with a maximization problem. If the minimization case, since min z = max (-z) (if z is a linear function, which it is) so we can either convert the problem into a maximization one or reverse the optimality condition. Instead of selecting the entering variable as the one with the most negative coefficient in the z row we can select the one with the most positive coefficient. The rest of the steps are the same.
3. How to Use the Program
The program is fairly easy to use. First, you must select the category of problem you want the program to solve, by clicking on the proper menu choice.
Then, you should enter all the data of the problem: the constraints and the equation parameters. In the case of the production optimization problem you must enter the following data: The price of the goods produced (necessary for the program to find the solution that results to highest profit), the quantity of each raw material required for each good produced, the quantity of each raw material that is available for goods production.
Press the button "Enter constraints" to enter the quantity of each raw material available and the quantity required for the production of each good.
Then press the button "Enter function to minimize / maximize" so as to enter the price of the goods produced (that function is what the program actually optimized: the total profit).
After everything is set, you press the Solve button and the program provides you with the optimal solution! Simple isn't it? Simplex to be exact…!
Please use the message board below for any comments, reporting or suggestions for future versions.
License
About the Author
Spiros [Spyridon or Spyros are also used] Kakos (huo) lives in Athens, Greece. He is currently working as an IT consultant in a large firm. Begun programming during the Commodore era in MS Basic and is still trying to learn (mostly in C++ and C#)...
He likes chess and has recently bought a new (old) modem for one of his Commodores 128 (yes, he has two of them!) to set up a server based on 8-bit technology. He thinks that when the World Wide Web crashes completely by an alien cyber attack, he will be the only one capable of surfing with his Commodore computer and will eventually save the day...
He likes reading and writting philosophy and is a fond admirer of Aristotle and Alfred Russel Wallace. His main heritage is Harmonia Philosophica.
At his free time he is researching the application of polypyrrole (PPy) in the PCB manufacturing process (through-hole plating) at the National Technical University of Athens - Advanced Materials section.
You have attached the code to use some DLL to solve the simplex method. Therefore, the code you provided does not reflect the good article you have written. Therefore, this is just a plug to promote the DLL.
Dear sisira, as a stated in the answer belowThat dataset will be used in future versions for additional program enhancements. The code of the dataset can be found in the program (HuCoMa dataset). However that does not play any role whatsoever at this initital version. Thanks for your comments.
Dear sisira,
Thanks very much for the vote and the feedback. I will be more carefull in the future not to take things for granted and I will add more comments in the code so as to make everything more clear. I could use your feedback again for the next version I will upload. Keep coding!_ |
Book Description:Hardcover. Book Condition: New. Hardcover. Advanced Mathematical Concepts, 2006 in the Teacher Wraparound Edition. Advanced Mathematical Concepts lessons develop mathematics using numerous examples, real-world applications, and an engaging narrative. Graphs, diagrams, and illustrations are used throughout to help students visualize concepts. Directions clearly indicate which problems may require the use of a graphing calculator. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN, Momence,IL, Commerce,GA. book. Bookseller Inventory # 97800786822 |
Product Description
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students the concept of the slope of a line. The slope of a line is defined in terms of the rise and the run of the points on the line and students are taught how to calculate this slope. In addition, students are taught how to read the slope directly from an equation of a line. Grades 8-12. 25 |
The MathWorks interactive, video-based MATLAB? tutorial gets students up to speed in using MATLAB for homework and course projects.
MATLAB On-Ramp Tutorial (30 minutes)
Learn the basics of MATLAB in the context of using it as a powerful graphical calculator.
Tutorial 1 - Navigating the MATLAB Desktop (6:10)
Tutorial 2 - Using MATLAB as a Graphical Calculator (22:55)
This course reviews the basics of MATLAB and additional advanced topics: object-oriented programming, Handle graphics and GUIs, and MATLAB/C interface (MEX functions). It also covers basics of Simulink. Material created by Prof. Andrew Packard.
This site contains a number of different MATLAB tutorials collected from universities across the United States. These tutorials are intended for the new MATLAB user and provide a quick introduction to programming in MATLAB.
This course uses MATLAB to introduce the elements of procedural and object-oriented programming. Topics include: MATLAB functions, relational operators and control flow, recursion, debugging, data structures, object-oriented programming, and use of Handle graphics. The course also covers basic numerical analysis and numerical methods for calculus, with examples drawn from science and engineering. Material created by Prof. Andrew Packard.
The objective of this tutorial is to provide the basics of using MATLAB. Topics covered include math functions, plot curves, optimizations, manipulation of vectors and matrices, linear systems, data analysis, loops and conditions, and logical operators. Examples using real world applications, such as the deformation of a system of springs, are provided.
Material created by Professor Marc Buffat.
This course material is in French.
The goal of the tutorials here is to provide a simple overview and introduction to matlab. The tutorials are broken up into some of the basic topics. The first includes a few examples of how Matlab makes it easy to create and manipulate vectors. Submitted: Sep 03, 2008
A group of 6 MATLAB tutorials which cover, in addition to the basics of MATLAB, using MATLAB in linear algebra, numerical linear algebra, numerical analysis with MATLAB, and linear programming with MATLAB.
Material created by Edward Neuman.
Purdue University teaches a MATLAB based introductory computing class, ENGR 106: Engineering Problem Solving and Computer Tools, to more than 1,600 first year students in order to help them develop a logical problem solving process for fundamental engineering problems. Students are introduced to the problem solving method in the lecture component of the course, while in lab they practice using MATLAB syntax by solving simple problems. Homework and projects allow students to use MATLAB to solve more complex, open-ended problems. The flexibility of the software allows professors to create interesting, authentic engineering problems. By using MATLAB, students can focus on problem solving rather than coding, a skill that proves useful in upper-level classes and industry.
Georgia Tech has developed a practical introductory course to computer science for engineers (CS1371-Computing for Engineers) which uses the MATLAB programming language. Over 1,000 students take this class per semester as it is a requirement for all engineering students and a prerequisite for many upper-level courses. The course covers three broad topics: basic procedural programming, writing applications, and dynamic data structures. MATLAB provides an ideal environment for engineering computation because it allows students to focus on the big picture rather than wasting time writing low-level functions. Using MATLAB allows the course to combine computer science theory and concepts with problem solving in engineering.
This is a brief tutorial that focuses on basic computer science principles. Topics covered include debugging programs and optimization. Executable files in MATLAB are included.
Material created by Michel Bercovier and Olivier Ricou.
This material is in French.
Northeastern University's computer-based discovery lab, which teaches computer programming and engineering concepts to freshmen by providing hands-on experience with test and measurement instrumentation, uses MATLAB as its programming environment. Using MATLAB as the programming language allows professors to introduce programming and engineering concepts in simple, observable, and sequential steps. MATLAB and various MathWorks toolboxes allow students to use a single, efficient software tool to control their instruments and analyze their data. |
0321385233
9780321385239
Essentials of College Algebra:Focused on helping students develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, the authors present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. The book addresses the diverse needs of today's students through an open design, current figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids.
Back to top
Rent Essentials of College Algebra 1st edition today, or search our site for Margaret L. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Addison Wesley. |
Transformations and Projections in Computer Graphics
Transformations and Projections in Computer Graphics provides a thorough background, discussing the mathematics of perspective in a detailed, yet accessible style. It also reviews nonlinear projections in depth, including fisheye, panorama, and map projections frequently used to enhance digital images.
This book provides a thorough background in these two important topics in graphics. The book introduces perspective in an original way and discusses the mathematics of perspective in detail, in an accessible way. It treats nonlinear projections in depth, including the popular fisheye, panorama, and map projections. Only a basic knowledge of linear algebra, vectors, and matrices is required, as key ideas are introduced slowly, examined and illustrated by figures and examples, and enforced through solved exercises. Topics and Features: - Provides a complete and self-contained presentation of the topic's core concepts, principles, and methods - Features a 12-page color section - Includes a wealth of exercises - Integrates a complementary website that supplies additional auxiliary material Written for computer professionals both within and outside the field of Computer Graphics, this succinct text/reference will prove an essential resource for readers. Also suitable for graduates studying in Computer Graphics and CAD courses. |
their official computer science curriculum (Denning et al., 1989).
Meanwhile, scientists from other disciplines had been examining effects that the usage of computers had on people. Cognitive psychologists studied the impacts of computer on perception, memory, learning, and problemsolving; and...
system will be able to achieve the above mentioned task and any other that it will be carrying out. It is a complementary problemsolvingmethod that is focused on systems specifications and it is based on the system's requirement. It is a description of the needs or desires, functions and features of...
Computer Science. The book contains derivation of algorithms for solving engineering and science problems and also deals with
error analysis. It has numerical examples suitable for solving through computers. The special features are comparative efficiency and accuracy
of various algorithms due to finite...
all relevant constraints. (2) Solving the problem. Simple two-variable problems can be solved graphically. The graphicalmethod is very good for understanding the LP concept and gaining an insight into what is involved in the solution procedure. Whenever there are more than two decision variables...
is called the simplex method.1 Computer programs based on this method can routinely solve linear programming problems with thousands of variables and constraints. The Management Science in Action, Fleet Assignment at Delta Air Lines, describes solving a linear program involving 60,000 variables and...
much easier to obtain with a new transportation table than a new simplex tableau. After practice, a relatively large transportation problem can be solved by hand. This is not true when solving large LPproblems using the simplex method. Finally, some LPcomputer programs are set up to solve both...
Problem 4.1 Isoprofit Line Solution Method 4.2 Corner Point Solution Method 5. Solving Minimization Problems 6. Four Special Cases in LP
Dual Degree – Management UNP
Introduction
The easiest way to solve a small LPproblems is with the graphical solution approach The graphicalmethod only works...
Europe) devised what is now known as "Alhazen's problem", which leads to an equation of the fourth degree, in his Book of Optics. While solving this problem, he performed an integration in order to find the volume of a paraboloid. Using mathematical induction, he was able to generalize his result for...
written report.Upon completion of the Additional Mathematics Project Work,we are to gain valuable experiences and able to: y Apply and adapt a variety of problemsolving strategies to solve routine and non-routine problems; y Experience classroom environments which are challenging, interesting and...
10A: THE BASIC LINEAR PROGRAMMING (LP) PROBLEM SOLUTION TECHNIQUES: GRAPHICALMETHOD AND ENUMERATING THE CORNER POINTS
Class Plan:
We begin the last module which is integrative in nature. It deals with the use of linear programming for planning and optimizing systems. We shall discuss several...
40 pounds of sewage. Each pound of compost costs Sweet Smell 5 cents and each pound of sewage costs 4 cents. Use a graphicalLPmethod to determine the least cost blend of compost and sewage in each bag.
This is a minimization. We do it in a similar fashion as optimization.
Objective Equation... |
Graham, WA GeometryThe use of numbers and symbols, which may be frightening to students, has already begun in the use of numerals, for example, 1, 2, 3, etc., in arithmetic. Algebra uses additional symbols, which can easily learned by using the basic rules of arithmetic, such as addition, subtraction, multiplication, and division. Algebra has these same rules and also others to be learned. |
Web Resources
Lesson Plans
Title: Growth Rate (Slope)
Description:Standard(s): 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]
Growth Rate (Slope)
Title: Pedal Power
Description:
In this lesson, students investigate slope as a rate of change. Students compare, contrast, and make conjectures based on distance-time graphs for three bicyclists climbing to the top of a mountain (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5] [MA2013] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]
Pedal Power
In this lesson, students investigate slope as a rate of change. Students compare, contrast, and make conjectures based on distance-time graphs for three bicyclists climbing to the top of a mountain.
Podcasts
Title: Math in Video Games
Description:
The teams use algebra to save their spaceship in the Asteroids game 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3] [MA2013] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7] |
Buy Used
$52.49 used this book to teach gifted high school students about the following topics: the implicit function theorem, manifolds, and differential forms. With the Hubbards' approach, even students without a course in linear algebra actually get it! Not only do they understand the material, but they also become amazingly enthusiastic when they begin to see the unifying effect of understanding differential forms. This is the only text that I have seen that really makes forms clear. It does so by taking the time to carefully, but rigorously, explain them in a "classical" setting. One of the reasons forms are so difficult to grasp is that while some things, such as the exterior derivative and the work form of a function, can be seen as natural objects (when explained well), the connection between these objects and calculating with forms using coordinates is not so easy to make clear. The Hubbards' do make these ideas clear - even when presenting topics as hard as orientation. Unfortunately, most of us had to wait till graduate school to see forms - usually, in a more abstract setting. By then, we probably didn't have time to sit, calculate, and make clear connections. This text makes that later transition, for those in math, much easier. It also makes physics easier. The Hubbards' make that point by showing that the electric field shouldn't really be a field, but a two form. Any book that lets one explain that - and much more - to high school students, which I do, should be a part of every multivariable calculus course. Finally, I should note that this book contains much, much more than manifolds, the implicit function theorem and differential forms. But, even if that were all it contained, it would fully be worth the price. In summary, this book opens the door to new worlds that most students never get to see clearly. What a present to us all.
This is the textbook used for the math 223/224 Theoretical Calculus and Linear Algebra sequence in Cornell University. The book is designed for prospective math students. Although the book mainly follows a rigorous development of the theories of multi-dimensional calculus, the mathematical machinery used in developing the theories is immensely broad, especially in linear algebra. The book covers most of the standard topics in a first semester linear algebra course and touches on many other areas of mathematics such as, real and complex analysis, set theory, differential geometry, integration theory, measure theory, numerical analysis, probability theory, topology, etc. The highlight of the book is its introduction of differential forms to generalize the fundamental theorems of vector calculus. The author is not the first one who follows this path. There are many other books written before this one that have similar approach, such as Calculus On Manifolds by Spivak, which was written 40 years ago and was too old to suit modern students.
The author tries hard to retain rigor and present to the readers as many examples and applications as possible. Often he tries to cover a broad range of mathematics and digresses a little. The book more or less touches on most of the areas of undergraduate mathematics curriculum and does not go into depth. It sometimes gives me the impression that the book is almost like a survey of undergradute math. The book is also not error-free. There are many typos and some technical errors. If you buy this book, make sure to get the errata from the author's website.
This book is unique in several ways: it covers an immense amount of material, much of which is never presented in books aimed at this level. The underlying idea of the authors is to present constructive proofs, which has the great benefit of providing the reader with the ability to actually compute quantities appearing in the theorems. As an example, the Inverse Function Theorem is proved using Newton's method, which relies on Kantorovich's Theorem, and thus actually gives an explicit size of the domain on which the inverse exists. The book also contains a very nice section on Lebesgue integrals, a topic which is usually reserved for graduate level courses. The construction is to my knowledge completely new, and does not rely on sigma-algebras, but utilizes only elementary mathematics. Another nice feature is that the book considers abstract spaces at an early stage. Thus the reader is presented with the idea of computing derivatives of functions acting on e.g. matrix-spaces, as opposed to the usual Euclidian spaces. The concluding treatment on differential forms brings a lot of the introduced ideas together and completes the picture by a thorough treatment on integration over manifolds. This book can be studied at several levels. For a first year honours course, one may skip the trickiest proofs, which appear in the appendix. More advanced readers may choose to study constructions and details of selected theorems and proofs. Anyone who buys this book will have a solid companion for many years ahead.
I've read sections of both the first & second editions and the second has numerous minor changes that make it a much better book. The changes are not major--the content and order are almost identical. However, places where the explanations were unclear or difficult frequently have new diagrams or helpful comments in the margins. A few topics that were too difficult or digressions have been moved to appendices or omitted. It remains a challenging book, intended for honors students, but is now a reasonable alternative to Apostol or a sequel to Spivak. |
More About
This Textbook
Overview
This text presents a comprehensive introduction to the topics in intermediate- and college-level algebra. It provides students with the basic skills they'll need to succeed in their next mathematics course. As the book progresses, the mathematical language matures, examples grow less structured, and exercises grow more varied, thus improving students problem solving skills.
Editorial Reviews
Booknews
A textbook for a one-semester four- or five-hour course, or a two- semester sequence in algebra. Revisions in the fifth edition reflect the NCTM standards, the AMATYC Crossroads, and current trends in mathematics reform, such as more emphasis on graphing and problem solving. An appendix contains answers to odd-numbered exercises |
Mathematics With Infotrac A Good Beginning
9780534529055
ISBN:
0534529054
Publisher: Thomson Learning
Summary: More than just a textbook, this is a complete instructional program that serves a multitude of curriculum needs. This edition is solidly grounded in the latest research on how children learn mathematics and how teachers develop attitudes, beliefs, and knowledge that promote successful teaching.
Troutman, Andria P. is the author of Mathematics With Infotrac A Good Beginning, published under ISBN 9780534529055... and 0534529054. Twenty two Mathematics With Infotrac A Good Beginning textbooks are available for sale on ValoreBooks.com, twenty one used from the cheapest price of $5.35, or buy new starting at $114.51.[read more]
Missing components. May include moderately worn cover, writing, markings or slight discoloration. SKU:9780534529055-4-1-3 Orders ship the same or next business day. Expedited [more]
Missing components. May include moderately worn cover, writing, markings or slight discoloration. SKU:9780534529055 Hassle free 14 day return policy. Contact Customer Service for questions.[less] |
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
Lesson Plan
Instr COS Date
Course of Study Objective Suggested Lesson Resources/Activities (description,
Seq # Implemented
number, etc.)
Explain how the definition of the meaning of rational A1133
exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals
3 1
in terms of rational exponents. [N-RN1]
Example: We define 51/3 to be the cube root of 5 because we
want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Rewrite expressions involving radicals and rational exponents A1133
3 2
using the properties of exponents. [N-RN2]
Explain why the sum or product of two rational numbers is A1121, A1125, A1131
rational; that the sum of a rational number and an irrational
1 3 number is irrational; and that the product of a nonzero
rational number and an irrational number is irrational. [N-
RN3]
Use units as a way to understand problems and to guide the (graphs) A1316, A1615, A1617; (area/surface
solution of multistep problems; choose and interpret units area) GE711, GE721, GE723, GE725, GE727,
1,2,
4 consistently in formulas; choose and interpret the scale and GE1011, GE1013, GE1015, GE1017, GE1031,
3,4
the origin in graphs and data displays. [N-Q1] ge1428 (WS); (volume) GE1021, GE1023, GE1025,
GE1027, GE1033
Define appropriate quantities for the purpose of descriptive
1,2,4 5
modeling. [N-Q2]
Choose a level of accuracy appropriate to limitations on
1 6
measurement when reporting quantities. [N-Q3]
Interpret expressions that represent a quantity in terms of its
1 7
context.* [A-SSE1]
a. Interpret parts of an expression such as terms, factors, and A1211, A1231, a11612 (WS)
coefficients. [A-SSE1a]
1 7a
Example: Interpret P(1+r)n as the product of P and a factor not
depending on P.
b. Interpret complicated expressions by viewing one or more of A11431, a11612 (WS)
their parts as a single entity. [A-SSE1b]
1 7b
Example: Interpret P(1+r)n as the product of P and a factor not
depending on P.
2010 Alabama Course of Study Mathematics 1
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
Use the structure of an expression to identify ways to rewrite Same as A-SSE1a and A-SSE1b
it. [A-SSE2]
4 8
Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 - y2)(x2 + y2).
Choose and produce an equivalent form of an expression to
4 9 reveal and explain properties of the quantity represented by
the expression.* [A-SSE3]
a. Factor a quadratic expression to reveal the zeros of the A11011, A11021, A11031, a11628
function it defines. [A-SSE3a]
4 9a Example: The expression 1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
b. Complete the square in a quadratic expression to reveal the A11151, A11153
4 9b maximum or minimum value of the function it defines. [A-
SSE3b]
c. Determine a quadratic equation when given its graph or
4 9c
roots.
d. Use the properties of exponents to transform expressions A1911, A1913, A1915, a2270
4 9d
for exponential functions. [A-SSE3c]
Understand that polynomials form a system analogous to the A1921, A1923, A1931, a2180, a2190, a11627
integers; namely, they are closed under the operations of (WS)
4 10
addition, subtraction, and multiplication; add, subtract, and
multiply polynomials. [A-APR1]
Create equations and inequalities in one variable, and use (solving equations) A1311, A1313, A1321, A1331;
them to solve problems. Include equations arising from linear (writing equations) A1341, a11614 (WS);
and quadratic functions, and simple rational and exponential (ratios/proportions) A1411, a11615 (WS);
1,2 11
functions. [A-CED1] (inequalities) A1511, A1521, A1523, A1531,
A1541, A1551, a11618 (WS); (exponential)
A11211, A11213
Create equations in two or more variables to represent (arithmetic) A1661; (graphing) A1751, A1761;
relationships between quantities; graph equations on (functions) A1851, A11111, A11321, A11421,
1,2 12 coordinate axes with labels and scales. [A-CED2] a2060, a2170, a2320, a2360, a2370, a2380,
a11632 (WS), a2810 (WS), a2850 (WS), a2870
(WS), a2890 (WS)
Represent constraints by equations or inequalities, and by (solving systems of equations) A1341, A1811,
1,2,3 13
systems of equations and/or inequalities and interpret A1821, A1831, A1841, a11614 (WS), a11624
2010 Alabama Course of Study Mathematics 2
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
solutions as viable or non-viable options in a modeling (WS); (solving systems of inequalities) A1843,
context. [A-CED3] a11625 (WS); A11411, a2310, a2490, a2500,
Example: Represent inequalities describing nutritional and cost a2900 (WS)
constraints on combinations of different foods.
Rearrange formulas to highlight a quantity of interest, using A2040
the same reasoning as in solving equations. [A-CED4]
1 14
Example: Rearrange Ohm's law V = IR to highlight resistance
R.
Explain each step in solving a simple equation as following
from the equality of numbers asserted at the previous step,
1 15 starting from the assumption that the original equation has a
solution. Construct a viable argument to justify a solution
method. [A-REI1]
Solve linear equations and inequalities in one variable, (solving equations) A1311, A1313, A1321, A1331;
including equations with coefficients represented by letters. (solving inequalities) A1511, A1521, A1523,
1,2 16
[A-REI3] A1531, A1541, A1551, a11618 (WS); (literal
equations) a2040
4 17 Solve quadratic equations in one variable. [A-REI4]
a. Use the method of completing the square to transform any A11151, A11153, A11161, A11163, a11630 (WS)
quadratic equation in x into an equation of the form (x - p)2 = q
4 17a
that has the same solutions. Derive the quadratic formula from
this form. [A-REI4a]
b. Solve quadratic equations by inspection (e.g., for x2 = 49), A11021, A11031, A11111, A11121, A11131,
taking square roots, completing the square and the quadratic A11141, A11151, A11153, A11161, A11163,
formula, and factoring as appropriate to the initial form of the a11628 (WS), a11629 (WS), a11630 (WS)
4 17b
equation. Recognize when the quadratic formula gives
complex solutions, and write them as a ± bi for real numbers a
and b. [A-REI4b]
Prove that, given a system of two equations in two variables, A1831, a11624 (WS)
replacing one equation by the sum of that equation and a
3 18
multiple of the other produces a system with the same
solutions. [A-REI5]
Solve systems of linear equations exactly and approximately A1811, A1821, A1831, A2480, A11624 (WS)
3,4 19 (e.g., with graphs), focusing on pairs of linear equations in
two variables. [A-REI6]
4 20 Solve a simple system consisting of a linear equation and a A2030, A2480, A2490
2010 Alabama Course of Study Mathematics 3
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
quadratic equation in two variables algebraically and
graphically. [A-REI7] Example: Find the points of intersection
between the line y = –3x and the circle x2 + y2 = 3.
Understand that the graph of an equation in two variables is A1751, A1761, A1851, A11111, A11321, A11421,
the set of all its solutions plotted in the coordinate plane, A2060, A2170, A2320, A2360, A2370, A2380,
1 21
often forming a curve (which could be a line). [A-REI10] A11632 (WS), A2810 (WS), A2820 (WS), A2870
(WS), A2880 (WS), A2890 (WS)
Explain why the x-coordinates of the points where the graphs A1821, A1831, A2480, A2490, A11624 (WS)
of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph the functions,
1,4 22
make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic
functions.* [A-REI11]
Graph the solutions to a linear inequality in two variables as a A2500, A2510, A2900 (WS)
half-plane (excluding the boundary in the case of a strict
3,4 23 inequality), and graph the solution set to a system of linear
inequalities in two variables as the intersection of the
corresponding half-planes. [A-REI12]
Understand that a function from one set (called the domain) A1631, A2010, A2020
to another set (called the range) assigns to each element of
the domain exactly one element of the range. If f is a function
1 24
and x is an element of its domain, then f(x) denotes the
output of f corresponding to the input x. The graph of f is the
graph of the equation y = f(x). [F-IF1]
Use function notation, evaluate functions for inputs in their A2010
1,2 25 domains, and interpret statements that use function notation
in terms of a context. [F-IF2]
Recognize that sequences are functions, sometimes defined A1661, A11231, A2590, A2600
recursively, whose domain is a subset of the integers. [F-IF3]
2,3 26
Example: The Fibonacci sequence is defined recursively by
f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥1.
For a function that models a relationship between two A1751, A1761
1,2,4 27 quantities, interpret key features of graphs and tables in A11111, A11321
terms of the quantities, and sketch graphs showing key A11421, tr080, tr090, tr100, tr130, tr140
2010 Alabama Course of Study Mathematics 4
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
features given a verbal description of the relationship. Key
features include intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and
periodicity.* [F-IF4]
Relate the domain of a function to its graph and, where A2020
applicable, to the quantitative relationship it describes.* [F- A2080
IF5] A2090
1,2,4 28
Example: If the function h(n) gives the number of person-hours A2320
it takes to assemble n engines in a factory, then the positive A2360
integers would be an appropriate domain for the function.
Calculate and interpret the average rate of change of a A1711
function (presented symbolically or as a table) over a
1,2 29
specified interval. Estimate the rate of change from a graph.*
[F-IF6]
Graph functions expressed symbolically and show key
1,2
30 features of the graph, by hand in simple cases and using
3,4
technology for more complicated cases.* [F-IF7]
1,2 a. Graph linear and quadratic functions, and show intercepts, A1641, A1751,A1761
30a
3,4 maxima, and minima. [F-IF7a] A11111
b. Graph square root, cube root, and piecewise-defined A11321
1,2
30b functions, including step functions and absolute value
3,4
functions. [F-IF7b]
c. Graph exponential and logarithmic functions, showing a2370, a2380, tr080, tr090, tr100, tr130, tr140
1,2
30c intercepts and end behavior, and trigonometric functions,
3,4
showing period, midline, and amplitude. [F-IF7e]
Write a function defined by an expression in different but
1,2
31 equivalent forms to reveal and explain different properties of
3,4
the function. [F-IF8]
a. Use the process of factoring and completing the square in a Aa11011, A11021, A11031, A11151, A11153
1,2 quadratic function to show zeros, extreme values, and
31a
3,4 symmetry of the graph, and interpret these in terms of a
context. [F-IF8a]
b. Use the properties of exponents to interpret expressions for A1911, A1913, A1915, A11211, A11213
1,2
31b exponential functions. [F-IF8b]
3,4
Example: Identify percent rate of change in functions such as y
2010 Alabama Course of Study Mathematics 5
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
= (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t/10, and
classify them as representing exponential growth and decay.
Compare properties of two functions each represented in a A1761, A11111, A11321, A11421, tr080, tr090,
different way (algebraically, graphically, numerically in tables, tr100, tr130, tr140
or by verbal descriptions). [F-IF9]
2,3,4 32
Example: Given a graph of one quadratic function and an
algebraic expression for another, say which has the larger
maximum.
1,2 Write a function that describes a relationship between two
33
3,4 quantities.* [F-BF1]
1,2 a. Determine an explicit expression, a recursive process, or A1651, A1771, a2070
33a
3,4 steps for calculation from a context. [F-BF1a]
b. Combine standard function types using arithmetic A1921, A1923, A1931, A11462, A1661
operations. [F-BF1b]
1,2
33b Example: Build a function that models the temperature of a
3,4
cooling body by adding a constant function to a decaying
exponential, and relate these functions to the model.
Write arithmetic and geometric sequences both recursively A1661, A11231, a2590, aqa2600
2,3 34 and with an explicit formula, use them to model situations,
and translate between the two forms.* [F-BF2]
Identify the effect on the graph of replacing f(x) by f(x) + k, k a2100, a2110, tr110, tr120
f(x), f(kx), and f(x + k) for specific values of k (both positive
and negative); find the value of k given the graphs.
2,3,4 35 Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them. [F-BF3]
1 36 Find inverse functions. [F-BF4]
a. Solve an equation of the form f(x) = c for a simple function f a2130
that has an inverse, and write an expression for the inverse. [F-
1 36a
BF4a]
Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
Distinguish between situations that can be modeled with
3,4 37
linear functions and with exponential functions. [F-LE1]
a. Prove that linear functions grow by equal differences over A1711, A1715, A11211, A11213
3,4 37a
equal intervals, and that exponential functions grow by equal
2010 Alabama Course of Study Mathematics 6
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
factors over equal intervals. [F-LE1a]
b. Recognize situations in which one quantity changes at a A1711, A1715, A1716
3,4 37b
constant rate per unit interval relative to another. [F-LE1b]
c. Recognize situations in which a quantity grows or decays by A11211, A11213
3,4 37c a constant percent rate per unit interval relative to another. [F-
LE1c]
Construct linear and exponential functions, including A1341, A1661, A1771, A11231
arithmetic and geometric sequences, given a graph, a
1,2,3 38
description of a relationship, or two input-output pairs
(include reading these from a table). [F-LE2]
Observe, using graphs and tables, that a quantity increasing A1761, A11111, A11211, A11213
exponentially eventually exceeds a quantity increasing
4 39
linearly, quadratically, or (more generally) as a polynomial
function. [F-LE3]
Interpret the parameters in a linear or exponential function in A1761, A11211, A11213, A11221
2,3 40
terms of a context. [F-LE5]
Represent data with plots on the real number line (dot plots, A1613, A1615
4 41
histograms, and box plots). [S-ID1]
Use statistics appropriate to the shape of the data a2420, a2430
distribution to compare center (median, mean) and spread
4 42
(interquartile range, standard deviation) of two or more
different data sets. [S-ID2]
Interpret differences in shape, center, and spread in the a2420, a2430
4 43 context of the data sets, accounting for possible effects of
extreme data points (outliers). [S-ID3]
Summarize categorical data for two categories in two-way
frequency tables. Interpret relative frequencies in the context
4 44 of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in
the data. [S-ID5]
Represent data on two quantitative variables on a scatter
2 45
plot, and describe how the variables are related. [S-ID6]
a. Fit a function to the data; use functions fitted to data to A1791, a2440, a2450
solve problems in the context of the data. Use given functions
2 45a
or choose a function suggested by the context. Emphasize
linear, quadratic, and exponential models. [S-ID6a]
2010 Alabama Course of Study Mathematics 7
Algebra 1A and 1B
(Instructional Sequence 1 & 2 are Algebra 1A; 3 & 4 are Algebra 1B)
b. Informally assess the fit of a function by plotting and a2440, a2450
2 45b
analyzing residuals. [S-ID6b]
c. Fit a linear function for a scatter plot that suggests a linear A1791
2 45c
association. [S-ID6c]
Interpret the slope (rate of change) and the intercept A1791
1,2 46 (constant term) of a linear model in the context of the data.
[S-ID7]
Compute (using technology) and interpret the correlation
2 47
coefficient of a linear fit. [S-ID8]
2 48 Distinguish between correlation and causation. [S-ID9]
Describe events as subsets of a sample space (the set of
outcomes), using characteristics (or categories) of the
4 49
outcomes, or as unions, intersections, or complements of
other events (―or,‖ ―and,‖ ―not‖). [S-CP1]
Understand that two events A and B are independent if the
probability of A and B occurring together is the product of
4 50
their probabilities, and use this characterization to determine
if they are independent. [S-CP2]
2010 Alabama Course of Study Mathematics |
Summary: Demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. Focuses on repeating and growing patterns, introducing the concepts of variable and equality, and examining relations and functions. Features activities with questions that stimulate students to think more deeply about the mathematical ideas. Discusses expectations for students' accomplishment and provides helpful margin notes and blackline masters.
Edition/Copyright:01 Cover: Paperback Publisher:National Council of Teachers of Mathematics Published: 01/28/2001 International: No4.40 +$3.99 s/h
LikeNew
walker_bookstore tempe, AZ
0873534999 WE HAVE NUMEROUS COPIES. -PAPERBACK -MARKS FREE CD INCLUDED mild shelf wear to cover/edges/corners, school writing on front cover
$4.99 +$3.99 s/h
Good
Booksavers MD Hagerstown, MD
2001 Paperback 2001 |
MAD 2502 (sec 13301): Introduction to Computational Mathematics
The course provides an introduction to the use of computers for solving mathematical problems. The course explains the basics of the Python Programming Language and demonstrates how a programming language can enable and support the solution of mathematical problems. The course does not assume prior programming experience and does not aim at an in-depth understanding of the details of Python. Rather the focus is on understanding concepts and techniques of how programming can help to expand the spectrum of tractable mathematical problems.
04/20/10: implementing polynomial division in Python
04/22/10: exercise for the final exam: printing terms of a polynomial with free choice of variable names
The final exam will take place on Thursday, April 29, 1:15-3:45 pm in room SE 271 (computer lab).
You can bring any books, manuscripts, and printouts you like. Internet access will be restricted to the domain python.org. Windows versions of IDLE with Python 2.6 are available in the lab, but you can work with your own laptop as well.
For questions or comments, please feel free to contact me anytime
(see my homepage for email, phone number, etc.).
Apr 28, 2010 |
The Matrix Algebra Tutor: Learning by Example DVD Series teaches students about matrices and explains why they're useful in mathematics. This episode teaches students about inconsistent and dependent systems in matrix math. Sometimes, a system of equations does not have a well-defined solution. For example, if we have two equations that represent two lines and these lines are exactly parallel and never intersect, then these equations do not have a solution. In this program, these ideas are explored. Grades 9-College. 54 minutes on DVD.
Customer Reviews for Inconsistent & Dependent Systems DVD
This product has not yet been reviewed. Click here to continue to the product details page. |
978007066 With Applications
This text is designed for the one-term calculus course taken by students in business, economics, management and the social, biological and environmental sciences. Some knowledge of intermediate algebra is assumed. In courses where college algebra is the prerequisite, much of Chapter One may be omitted. For students that need additional work in algebra, an algebra review is provided in Appendix A. Since the students this book addresses aspire to become users of mathematics rather than makers of mathematics, this text includes few mathematical proofs. The author introduces a deducible statement through a concrete situation that either illustrates the statement or involves steps that parallel those in a general proof. The focus is on problem-solving and the author includes exercise sets so that the student can practise these skills. Exercise sets include problems that ask the student to discuss, write, explore and use technology. Many sections include graphing calculator problems and a few of these sections contain subsections that serve as a basis for the problems. These problems are clearly identified with an icon. In addition, this book integrates nine BASIC computer language programs. The sections where these programs appear also include problems that take advantage of the computer |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.