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Book Reviews

Review of Intermediate Algebra (The Learning Equation)

Editorial review
This workbook/CD-ROM package is almost identical to the package published in mid-2001 under ISBN 0-534-39013-7, except for the addition of an updated introductory pamphlet, to be used instead of pages ix to xxxiv in the bound book. Intended for students in computer-based college courses, the workbook contains problems and exercises; the three CD-ROMs run on all Windows and Macinstosh platforms, on stand-alone computers, over a LAN, and over the internet.Book News, Inc.®, Portland, OR

Review of Prealgebra (The Learning Equation)

Editorial review
This workbook/CD-ROM package is almost identical to the package published in mid-2001 under ISBN 0-534-39011-0, except for the addition of an updated introductory pamphlet, to be used instead of pages ix to xxxiv in the bound book. Designed for interactive, student-directed learning, coverage includes the vocabulary of mathematics, key concepts, and skills in reasoning, modeling, and analysis, with application problems from business, entertainment, science and technology, and history. The progression is from whole numbers and fractions through the language of algebra, polynomials, measurement, and polygons and circles. The CD-ROMs run on Windows and Macintosh platforms, and can be used on a stand-alone computer, over a LAN, and over the Internet.Book News, Inc.®, Portland, OR

Review of Algebra: A Graduate Course

Editorial review
The author encourages students to develop an appreciation of how basic algebra is put together. The text is in two sections: noncommutative algebra, including homomorphisms, Sylow theorems, and rings; and commutative algebra, with polynomial rings, Galois theory, finite fields, Noetherian rings, and Dedekind domains. Discussion of such topic as the factorization algorithm of polynomials over finite fields gives students insight into the types of algorithms that underlie computer algebra software. Problems follow each chapter. Annotation copyright Book News, Inc. Portland, Or.

Reviewed by a reader, from Texas, United States
Isaacs' algebra text is probably the best math book I've encountered so far as an undergraduate student for several reasons. First, the structure of the book is unique- most introductory algebra books tend to cover groups, rings, and fields in that order. More mathematically mature students, though, can gain a greater appreciation for rings by first understanding modules. Most texts tend to introduce rings first, because the classic examples of rings are easy to understand, and then generalize to modules. Isaacs instead builds upon the composition structures of groups to introduce the topic of X-groups (this is the only introductory graduate text that covers this extensively), so that modules and rings are not only presented at the same time, but in such a way that the reader can see the interplay between the two. This presentation also makes it easier to discuss the Jacobson radical and by the time the Wedderburn-Artin theorems are presented, the reader is familiar enough with the necessary elements of the proof that it actually becomes easy.Another reason this book is good is because Isaacs includes difficult topics not generally covered in an introductory text, but in a way that they seem to be just a simple extension of the more basic material. For example, at the end of the noncommutative section (the first half of the book), Isaacs proves the algebraic foundation of character theory using the Wedderburn-Artin theorems, showing the module presentation of a representation as well as the classic homomorphism presentation. He then proves the basic results about characters, giving a very powerful tool to analyze the structure of a group.In a more applied vein, Isaacs proves the steps used in the Berlekamp algorithm in the finite fields chapter, which not only allows the reader to gain experience using the generalized Chinese Remainder Theorem but also to apply it to the study of fields. After covering integrality, Isaacs explains the role of rational integers in character theory and applies it to prove Burnside's celebrated solvability proof, whose statement about groups seems to have nothing to do with integrality, or even noetherian rings for that matter.While Isaacs covers other advanced topics (for example, Transfer theory in the study of groups, or the Schraier-Artin theorem), the text is excellent because he proves the basic results so clearly. While he doesn't talk about the geometric significance of groups that much, he does talk about groups from a stabilizer-orbit perspective that makes further study of symmetries a lot easier. The proofs of the Fundamental Theorem of Galois Theory, Galois' proof of solvability, the Principal Ideal Theorem, and a stronger form of Sylow's theorem are particularly elegant, along with the chapter on solvable and nilpotent groups. What makes the book far superior to others, though, is the problems. If you can understand the hard proofs of this book, you should be able to do the problems in easier books (Dummit and Foote, Hungerford) pretty easily. Be warned- the problems are not there to have you "fill in the details" Isaacs left out (because his proofs generally don't leave even minute details out) or to get practice, but to actually prove new results. For example, important topics such as metabelian groups, supersolvability, and the structure of a field with an abelian Galois group are presented as problems.In sum, anyone who wants to appreciate the beauty of algebra and understand more than just the basic concepts should learn it from Isaacs' book. While it is self-contained, one may want to study Herstein's book first and do some problems so that this book doesn't seem as intimidating. After studying this, you should be prepared to answer any basic algebra question on any prelim exam in the country and be sufficiently prepared to tackle more advanced branches of algebra.

Reviewed by Neils Schoenfelder, from Alaska
If you are looking for a great first book on abstract algebra, this is it! Dr. Isaacs has written a self-contained work that covers the basics of the subject in an easy to read manner. This book assumes that the reader has no previous knowledge of modern [abstract] algebra, though some mathematical maturity is required. It also avoids the twin pitfalls of mathematical writing: "Theorem, proof, theorem, proof,...", and "The details are left to the reader."

Review of Intermediate Algebra: A Worktext

Editorial review
Unlike many college-level algebra texts, Smith's begins with polynomials and emphasizes graphing. (Graphing calculators, while recommended, are not necessary to use the book.) Includes sections on practicalities such as the mathematics of finance and algebraic word problems to help students develop general mathematical skills and literacy. Annotation copyright Book News, Inc. Portland, Or.

Review of Algebra Facts: Survival Guide to Basic Algebra

Editorial review
This booklet is a stand-alone supplement listing basic algebra facts. It corresponds to topics learned in basic algebra, but can be used to supplement a number of courses, as a quick reference, including statistics, life sciences and technical mathematics. Students taking algebra and other developmental math courses have a great deal of math anxiety, and are often desperate for any help they can get. Students in these courses are also weak in reading skills. ALGEBRA FACTS gives them easy access to the most crucial concepts and formulas in basic mathematics, without having to dig through their textbook. The booklet has the same effect as flash cards, but in a bound form.

Reviewed by txj2522@dcccd.edu, from Dallas, TX
I wish I had upper level Math books just like this one! I wrote many formulas and examples on index cards for many years and I have my students do the same. The Survival guide is well organized and will be a wonderful reference for my college algebra students.

Reviewed by a reader, from Botswana
If you want help with Algebra ask your teacher because this book has information that even a 5 yearold child would know.

Review of Prealgebra

Editorial review
In preparation for an introductory algebra course, this book aims to develop students' basic mathematical skills in the context of solving meaningful application problems. This package of the second edition includes a CD-ROM with an "interactive video skillbuilder" (the second edition is also available under a different ISBN, without the CD-ROM).Book News, Inc.®, Portland, OR --This text refers to the Paperback edition.

Review of Beginning Algebra 3rd

Editorial review
By providing a continuous flow from elementary to intermediate algebra, this text eliminates the overlap found when these topics are covered in separate courses. Kaufmann's organizational format allows for frequent reinforcement of concepts, but eliminates the need to reintroduce topics (as is necessary when two separate texts are used). Kaufmann develops basic algebraic concepts in a logical sequence, allowing them to develop from their arithmetic counterparts whenever possible.

Reviewed by a reader, from Dubai, U.A.E.
The plot is intricate, and the mystery deepens until the last few pages of the text. The authors richly deserve the highest praise for their tireless efforts.

Review of College Algebra: A Contemporary Approach

Editorial review
A text with emphasis on applying algebra to socially relevant and popular issues. Learning features include historical notes, tips and warnings, key terms and topics, worked examples, and motivating questions designed to pique students' curiosity. Exercise sets include standard and application exercises, discussion and essay questions, critical thinking exercises, and projects. The graphing calculator is integrated throughout. This second edition includes new learning aids and exercises. The authors are affiliated with the University of Evansville. -- Copyright © 2000 Book News, Inc., Portland, OR All rights reserved

Review of Activities Manual, Student Edition for Garrison/Jones/Rhodes' Beginning and Intermediate Algebra

Editorial review
Designed as a stand-alone supplement for any beginning or intermediate algebra text, Activities Manual for Beginning and Intermediate Algebra is a collection of activities written to incorporate the recommendations from the NCTM and from AMATYC's Crossroads. Activities can be used during class or in a laboratory setting to introduce, teach, or reinforce a topic. This set of activities facilitates discovery learning, collaborative learning, use of graphing technology, connections with other areas of mathematics and other disciplines, oral and written communication, real data collection, and active learning.

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