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A Concrete Introduction to Higher Algebra

  • Lindsay N. Childs

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Lindsay N. Childs
    Pages 1-7
  3. Lindsay N. Childs
    Pages 8-24
  4. Lindsay N. Childs
    Pages 25-46
  5. Lindsay N. Childs
    Pages 47-62
  6. Lindsay N. Childs
    Pages 63-75
  7. Lindsay N. Childs
    Pages 76-90
  8. Lindsay N. Childs
    Pages 91-117
  9. Lindsay N. Childs
    Pages 118-133
  10. Lindsay N. Childs
    Pages 134-154
  11. Lindsay N. Childs
    Pages 155-179
  12. Lindsay N. Childs
    Pages 180-193
  13. Lindsay N. Childs
    Pages 194-207
  14. Lindsay N. Childs
    Pages 208-230
  15. Lindsay N. Childs
    Pages 231-238
  16. Lindsay N. Childs
    Pages 239-252
  17. Lindsay N. Childs
    Pages 253-276
  18. Lindsay N. Childs
    Pages 277-285
  19. Lindsay N. Childs
    Pages 286-292
  20. Lindsay N. Childs
    Pages 293-301
  21. Lindsay N. Childs
    Pages 302-309
  22. Lindsay N. Childs
    Pages 310-322
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    Pages 323-345
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    Pages 346-352
  25. Lindsay N. Childs
    Pages 353-362
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    Pages 363-377
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    Pages 378-396
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    Pages 397-413
  29. Lindsay N. Childs
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  30. Lindsay N. Childs
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  31. Lindsay N. Childs
    Pages 464-482
  32. Back Matter
    Pages 483-524

About this book

Introduction

This book is written as an introduction to higher algebra for students with a background of a year of calculus. The first edition of this book emerged from a set of notes written in the 1970sfor a sophomore-junior level course at the University at Albany entitled "Classical Algebra." The objective of the course, and the book, is to give students enough experience in the algebraic theory of the integers and polynomials to appre­ ciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes, congruences and congruence classes, Fermat's theorem, the Chinese remainder theorem; and then again for the ring of polynomials. Doing so leads to the study of simple field extensions, and, in particular, to an exposition of finite fields. Elementary properties of rings, fields, groups, and homomorphisms of these objects are introduced and used as needed in the development. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, error-correcting codes, Latin squares, tournaments, techniques of integration, and especially to elemen­ tary and computational number theory. A student who asks, "Why am I learning this?," willfind answers usually within a chapter or two. For a first course in algebra, the book offers a couple of advantages. • By building the algebra out of numbers and polynomials, the book takes maximal advantage of the student's prior experience in algebra and arithmetic. New concepts arise in a familiar context.

Keywords

algebra binomial field finite group homomorphism matrices matrix number theory

Authors and affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8702-0
  • Copyright Information Springer Science+Business Media, Inc. 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98999-0
  • Online ISBN 978-1-4419-8702-0
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site