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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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