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A Concrete Introduction to Higher Algebra

  • Lindsay Childs

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
    4. Lindsay Childs
      Pages 136-141
    5. Lindsay Childs
      Pages 142-143
    6. Lindsay Childs
      Pages 144-156
    7. Lindsay Childs
      Pages 157-159
    8. Lindsay Childs
      Pages 160-165
    9. Lindsay Childs
      Pages 166-172
    10. Lindsay Childs
      Pages 173-174
    11. Lindsay Childs
      Pages 175-179
    12. Lindsay Childs
      Pages 185-192
    13. Lindsay Childs
      Pages 193-204
  4. Fields

    1. Front Matter
      Pages 205-205
    2. Lindsay Childs
      Pages 207-211
    3. Lindsay Childs
      Pages 212-217
    4. Lindsay Childs
      Pages 218-221
    5. Lindsay Childs
      Pages 222-224
    6. Lindsay Childs
      Pages 225-228
    7. Lindsay Childs
      Pages 229-230
    8. Lindsay Childs
      Pages 237-241
    9. Lindsay Childs
      Pages 242-254
    10. Lindsay Childs
      Pages 255-263
    11. Lindsay Childs
      Pages 264-266
    12. Lindsay Childs
      Pages 267-272
    13. Lindsay Childs
      Pages 273-279
    14. Lindsay Childs
      Pages 280-281
    15. Lindsay Childs
      Pages 282-290
    16. Lindsay Childs
      Pages 291-298
    17. Lindsay Childs
      Pages 299-308
    18. Lindsay Childs
      Pages 309-313

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

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

Bibliographic information

  • 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
  • Print ISBN 978-1-4684-0067-0
  • Online ISBN 978-1-4684-0065-6
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site