Introductory Modern Algebra: A Historical Approach [NOOK Book]

Overview

This Second Edition of “one of the best books available to support a one-semester introduction to abstract algebra” (CHOICE) presents pivotal ideas in the evolution of algebra and provides readers with the opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. Including four new appendices and over 1,000 new examples and multi-level exercises, it features new sections covering rings and fields, group homomorphisms, the RSA algorithm, complex ...
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Introductory Modern Algebra: A Historical Approach

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Overview

This Second Edition of “one of the best books available to support a one-semester introduction to abstract algebra” (CHOICE) presents pivotal ideas in the evolution of algebra and provides readers with the opportunity to view the evolution of modern algebra as a consistent movement from concrete problems to abstract principles. Including four new appendices and over 1,000 new examples and multi-level exercises, it features new sections covering rings and fields, group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, the fundamental theorem of algebra, plus more.
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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: 9781118552032
  • Publisher: Wiley
  • Publication date: 9/30/2013
  • Sold by: Barnes & Noble
  • Format: eBook
  • Edition number: 2
  • Pages: 464
  • File size: 8 MB

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

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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