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© 1979

A Concrete Introduction to Higher Algebra

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Integers

    1. Front Matter
      Pages 1-1
    2. Lindsay Childs
      Pages 3-6
    3. Lindsay Childs
      Pages 7-18
    4. Lindsay Childs
      Pages 31-36
    5. Lindsay Childs
      Pages 37-46
    6. Lindsay Childs
      Pages 47-55
    7. Lindsay Childs
      Pages 56-61
    8. Lindsay Childs
      Pages 62-67
    9. Lindsay Childs
      Pages 68-83
    10. Lindsay Childs
      Pages 84-89
    11. Lindsay Childs
      Pages 90-100
    12. Lindsay Childs
      Pages 101-104
    13. Lindsay Childs
      Pages 105-111
    14. Lindsay Childs
      Pages 112-117
    15. Lindsay Childs
      Pages 118-121
  3. Polynomials

    1. Front Matter
      Pages 123-123
    2. Lindsay Childs
      Pages 125-128
    3. Lindsay Childs
      Pages 129-135

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 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.

Keywords

algebra automorphism binomial field matrices matrix polynomial ring

Authors and affiliations

  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90333-0
  • Softcover ISBN 978-1-4684-0067-0
  • eBook ISBN 978-1-4684-0065-6
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XIV, 340
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site