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Undergraduate Algebra

  • Textbook
  • © 1987

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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  • The author has also included a chapter on groups of matrices which is unique in a book at this level
  • He also includes Noah Snyder's beautiful proof of the Mason-Stothers polynomial abc theorem

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
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  2. The Integers

    • Serge Lang
    Pages 1-12

  3. Groups

    • Serge Lang
    Pages 13-53

  4. Rings

    • Serge Lang
    Pages 54-71

  5. Polynomials

    • Serge Lang
    Pages 72-111

  6. Vector Spaces and Modules

    • Serge Lang
    Pages 112-143

  7. Some Linear Groups

    • Serge Lang
    Pages 144-157

  8. Field Theory

    • Serge Lang
    Pages 158-183

  9. Finite Fields

    • Serge Lang
    Pages 184-198

  10. The Real and Complex Numbers

    • Serge Lang
    Pages 199-222

  11. Sets

    • Serge Lang
    Pages 223-243

  12. Back Matter

    Pages 245-259
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Keywords

About this book

This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the linear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin­ ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory.

Reviews

From the reviews of the third edition:

"As is very typical for Professor Lang’s self demand and style of publishing, he has tried to both improve and up-date his already well-established text. … Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author’s great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. … The present textbook … will remain one of the great standard introductions to the subject for beginners." (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Undergraduate Algebra

  • Authors: Serge Lang

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9234-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • eBook ISBN: 978-1-4684-9234-7Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: IX, 379

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Algebra

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