This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.
Author: I.M. Gelfand,Alexander Shen
Publisher: Springer Science & Business Media
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
A Real and Imaginary History of Algebra
Author: John Derbyshire
Publisher: National Academies Press
"The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. While the breadth of topics may go beyond what an instructor would cover, the modular approach and the richness of content ensures that the book meets the needs of a variety of programs."--Page 1.
Author: Jay P. Abramson,Valeree Falduto,Rachael Gross (Mathematics teacher),David Lippman,Rick Norwood,Melonie Rasmussen,Nicholas Belloit,Jean-Marie Magnier,Harold Whipple,Christina Fernandez
Introduces readers to algebra by using simple addition, subtraction, multiplication, and division to solve equations.
A First Book of Algebra
Author: David A. Adler
Category: Juvenile Nonfiction
Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, the book uses a visually rich format designed for the way your brain works, not a text-heavy approach that puts you to sleep.--Publisher's note.
A Learner's Guide to Algebra I
Author: Tracey Pilone,Dan Pilone
Publisher: "O'Reilly Media, Inc."
Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
Author: Alfred S. Posamentier,Charles T. Salkind
Publisher: Courier Corporation
Practical Algebra If you studied algebra years ago and now need a refresher course in order to use algebraic principles on the job, or if you're a student who needs an introduction to the subject, here's the perfect book for you. Practical Algebra is an easy and fun-to-use workout program that quickly puts you in command of all the basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you'll learn: * The basic approach and application of algebra to problem solving * The number system (in a much broader way than you have known it from arithmetic) * Monomials and polynomials; factoring algebraic expressions; how to handle algebraic fractions; exponents, roots, and radicals; linear and fractional equations * Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, and more Authors Peter Selby and Steve Slavin emphasize practical algebra throughout by providing you with techniques for solving problems in a wide range of disciplines--from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology and business administration. Step by step, Practical Algebra shows you how to solve algebraic problems in each of these areas, then allows you to tackle similar problems on your own, at your own pace. Self-tests are provided at the end of each chapter so you can measure your mastery.
A Self-Teaching Guide
Author: Peter H. Selby,Steve Slavin
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author: Paolo Aluffi
Publisher: American Mathematical Soc.
For Colleges, Schools, and Private Students
Author: Joseph Ray
Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. A variety of factors set this text apart. Its clear exposition, with each chapter building upon the previous ones, provides greater clarity for the reader. The author first introduces permutation groups, then linear groups, before finally tackling abstract groups. He carefully motivates Galois theory by introducing Galois groups as symmetry groups. He includes many computations, both as examples and as exercises. All of this works to better prepare readers for understanding the more abstract concepts. By carefully integrating the use of Mathematica® throughout the book in examples and exercises, the author helps readers develop a deeper understanding and appreciation of the material. The numerous exercises and examples along with downloads available from the Internet help establish a valuable working knowledge of Mathematica and provide a good reference for complex problems encountered in the field.
A Computational Introduction
Author: John Scherk
Publisher: CRC Press
A Process Approach (Student Text)
Covers a wide variety of topics including understanding patterns; using algebraic symbols; solving problems with graphs, tables, and equations; and more. Works as an end-of-class activity, extra-credit, or at-home assignment. Includes teaching suggestions, skills matrix, and answer section.
Author: Hope Martin
Publisher: Walch Publishing
This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."
Author: Serge Lang
Publisher: Springer Science & Business Media
Algebra is fundamental in the learning of mathematics. In Singapore, students begin the learning of formal algebra in primary six (Singapore Ministry of Education, 2006a). In secondary school, algebra features prominently in the curriculum (Singapore Ministry of Education, 2006b). Prior to learning formal algebra, primary school students use the model method as one of the methods to solve word problems. The model method is one of the most recognised features of the Singapore mathematics curriculum (Singapore Ministry of Education, 2009). It has been found that the model method has allowed primary school students without access to formal algebra a means to represent and solve algebraic word problems (Ng & Lee, 2009). Research has indicated that students encounter a variety of difficulties in formal algebra. These include understanding the meaning of letters used in formal algebra (Kuchemann, 1981) and translating information in text into algebraic equations (e.g. Stacey & MacGregor, 2000). The use of concrete and pictorial representations has been found to help students in solving word problems (e.g. Lewis, 1989; Willis & Fuson, 1988). While the model method has helped students solve word problems using pictorial representations, such representations are seldom harnessed for beginning students in formal algebra to acquire skills in algebraic manipulation. This book aims to do the latter. There has been much evidence that the model method can be integrated with the algebraic method (Kho, 1987, 2005, 2007; Beckmann, 2004). Secondary school teachers have been trained to show the relationship between the model method and the algebraic method (Kho, 2007). This book fleshes out this approach using topics in lower secondary algebra. This book focuses on helping students develop a strong foundation in algebraic manipulation. Basic algebraic manipulations including writing, evaluating, expanding, simplifying, and factorising algebraic expressions and solving algebraic equations are introduced pictorially. While it is not the intention that students to always rely on pictorial representations when doing algebra, the model method serves as a good starting point for students to learn algebraic manipulation meaningfully. It is hoped that this book will provide teachers with a resource to help students make the transition from the model method to formal algebra. As for students who find formal algebra daunting, this book serves as a bridge.
Focus in Maths
Author: Dr Yeap Ban Har
Publisher: Shing Lee Publishers Pte Ltd
Finally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.
Author: Thomas W. Hungerford
Publisher: Springer Science & Business Media
as a student." --Book Jacket.
A Graduate Course
Author: I. Martin Isaacs
Publisher: American Mathematical Soc.