Introductory Modern Algebra: A Historical Approach / Edition 1

Introductory Modern Algebra: A Historical Approach / Edition 1

5.0 3
by Saul Stahl, Stahl
     
 

ISBN-10: 0471162884

ISBN-13: 9780471162889

Pub. Date: 12/11/1996

Publisher: Wiley, John & Sons, Incorporated

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

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.

Product Details

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

Related Subjects

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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Introductory Modern Algebra: A Historical Approach 5 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
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.