Introductory Modern Algebra: A Historical Approach / Edition 1

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Overview

Presenting a dynamic new historical approach to the study of abstract algebra

Much of modern algebra has its roots in the solvability of equations by radicals. Most introductory modern algebra texts, however, tend to employ an axiomatic strategy, beginning with abstract groups and ending with fields, while ignoring the issue of solvability. This book, by contrast, traces the historical development of modern algebra from the Renaissance solution of the cubic equation to Galois's expositions of his major ideas.

Professor Saul Stahl gives readers a unique opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. By including several pertinent excerpts from the writings of mathematicians whose works kept the movement going, he helps students experience the drama of discovery behind the formulation of pivotal ideas. Students also develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can tell us about multivariate functions and the 15-puzzle. To further this understanding, Dr. Stahl presents abstract groups as unifying principles rather than collections of "interesting" axioms.

This fascinating, highly effective alternative to traditional survey-style expositions sets a new standard for undergraduate mathematics texts and supplies a firm foundation that will continue to support students' understanding of the subject long after the course work is completed.

An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

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Editorial Reviews

Booknews
A textbook for a one-semester introduction for undergraduate mathematics majors and prospective high-school teachers of mathematics. Explains the principles and practices of modern algebra in terms of its historical development from the Renaissance solution to the cubic equation to Galois' exposition of his major ideas. Includes both computer and pencil-and-eraser exercises, the answers to which are in the teacher's manual. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780471162889
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 12/11/1996
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 336
  • Product dimensions: 6.44 (w) x 9.39 (h) x 0.85 (d)

Meet the Author

SAUL STAHL, PhD, is Professor of Mathematics at the University of Kansas and a former systems programmer for IBM. He received his MA from the University of California, Berkeley, and his PhD from Western Michigan University. His main field of expertise is combinatorics. In 1986 he received the Carl A. Allendoerfer Award for excellence in expository writing from the Mathematical Association of America.

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Table of Contents

The Early History.

Complex Numbers.

Solutions of Equations.

Modular Arithmetic.

The Binomial Theorem and Modular Powers.

Polynomials Over a Field.

Galois Fields.

Permutations.

Groups.

Quotient Groups and Their Uses.

Topics in Elementary Group Theory.

Appendices.

Biographies.

Bibliography.

Solutions to Selected Odd Exercises.

Symbols.

Pronounciation Guide.

Index.

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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted August 29, 2000

    An Old-New Approach to Mathematics Teaching

    Some years ago when I took Introductory Algebra at UCLA I discovered Dr Stahl's book, which presents the subject exactly the way it should be; a clear-cut account of the historical development of Algebra, including translations of the original papers (Abel, Galois) which itself makes this book unique. Exercises are numerous and they actually do provide insight into the subject, also a unique feature among today's 'textbooks'. I recommend this book for those who have a genuine interest in the subject, beyond just earning a good grade in the class. I believe that this book put me on the right course in my understanding of what meaningful Mathematics is, a process which culminated in acceptance into a very prestigious graduate programme in Mathematics.

    1 out of 1 people found this review helpful.

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