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© 2005

Undergraduate Algebra

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-15
  3. Pages 16-82
  4. Pages 83-104
  5. Pages 105-176
  6. Pages 232-257
  7. Pages 258-308
  8. Pages 309-325
  9. Pages 351-371
  10. Back Matter
    Pages 373-389

About this book

Introduction

Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.

For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder’s proof of the Mason-Stothers polynomial abc theorem.

 

About the First Edition:

The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there.

- Hideyuki Matsumura, Zentralblatt

Keywords

Galois theory Vector space algebra field linear algebra matrices

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title Undergraduate Algebra
  • Authors Serge Lang
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/0-387-27475-8
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-22025-3
  • Softcover ISBN 978-1-4419-1959-5
  • eBook ISBN 978-0-387-27475-1
  • Series ISSN 0172-6056
  • Edition Number 3
  • Number of Pages XII, 389
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
    Field Theory and Polynomials
  • Buy this book on publisher's site

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)