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Introductory Modern Algebra: A Historical Approach / Edition 1

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Overview

Much of modern algebra has its roots in the solvability of equations by radicals. This look at the history of algebra follows a paper trail from the Renaissance solution of the cubic equation to Galois' description of his ideas. All important concepts are placed in their historical context.
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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.
From the Publisher
“This book is an excellent book for an upper-level, undergraduate, one or two semester course, in modern algebra, for a typical University student population that is not especially strong in proofs.” (MAA Reviews, 13 January 2014)
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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 in the Department of Mathematics at the University of Kansas. In addition to authoring six previous books and more than thirty papers in the field of geometry, Dr. Stahl has twice been the recipient of the Carl B. Allendoerfer Award from the Mathematical Association of America.

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Table of Contents

Preface
1 The Early History 1
2 Complex Numbers 9
3 Solutions of Equations 47
4 Modular Arithmetic 57
5 The Binomial Theorem and Modular Powers 74
6 Polynomials Over a Field 98
7 Galois Fields 129
8 Permutations 152
9 Groups 181
10 Quotient Groups and Their Uses 221
11 Topics in Elementary Group Theory 250
App. A Excerpts from Al-Khwarizmi's Solution of the Quadratic Equation 261
App. B Excerpts from Cardano's Ars Magna 266
App. C Excerpts from A Demonstration of the Impossibility of the Algebraic Resolution of General Equations whose Degree Exceeds Four 271
App. D On the Theory of Numbers 277
App. E The Theory of Groups 285
App. F Mathematical Induction 288
Biographies 297
Bibliography 301
Solutions to Selected Odd Exercises 303
Symbols 315
Pronounciation Guide 317
Index 319
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Customer Reviews

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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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