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A Concrete Introduction to Higher Algebra

  • Textbook
  • © 1979

Overview

Authors:
  1. Lindsay Childs

    1. Department of Mathematics, SUNY at Albany, Albany, USA

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

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Table of contents (49 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Integers

    1. Front Matter

      Pages 1-1
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    2. Numbers

      • Lindsay Childs
      Pages 3-6

    3. Induction; the Binomial Theorem

      • Lindsay Childs
      Pages 7-18

    4. Unique Factorization into Products of Primes

      • Lindsay Childs
      Pages 19-30

    5. Primes

      • Lindsay Childs
      Pages 31-36

    6. Bases

      • Lindsay Childs
      Pages 37-46

    7. Congruences

      • Lindsay Childs
      Pages 47-55

    8. Congruence Classes

      • Lindsay Childs
      Pages 56-61

    9. Rings and Fields

      • Lindsay Childs
      Pages 62-67

    10. Matrices and Vectors

      • Lindsay Childs
      Pages 68-83

    11. Secret Codes, I

      • Lindsay Childs
      Pages 84-89

    12. Fermat’s Theorem, I: Abelian Groups

      • Lindsay Childs
      Pages 90-100

    13. Repeating Decimals, I

      • Lindsay Childs
      Pages 101-104

    14. Error-correcting Codes, I

      • Lindsay Childs
      Pages 105-111

    15. The Chinese Remainder Theorem

      • Lindsay Childs
      Pages 112-117

    16. Secret Codes, II

      • Lindsay Childs
      Pages 118-121

  3. Polynomials

    1. Front Matter

      Pages 123-123
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    2. Polynomials

      • Lindsay Childs
      Pages 125-128

    3. Unique Factorization

      • Lindsay Childs
      Pages 129-135
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Keywords

About this book

This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap­ preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.

Authors and Affiliations

  • Department of Mathematics, SUNY at Albany, Albany, USA

    Lindsay Childs

Bibliographic Information

  • Book Title: A Concrete Introduction to Higher Algebra

  • Authors: Lindsay Childs

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-0065-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1979

  • eBook ISBN: 978-1-4684-0065-6Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIV, 340

  • Topics: Algebra

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