Introduction to Abstract Algebra
eBook - ePub

Introduction to Abstract Algebra

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Introduction to Abstract Algebra

About this book

Praise for the Third Edition

". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH

The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.

The Fourth Edition features important concepts as well as specialized topics, including:

  • The treatment of nilpotent groups, including the Frattini and Fitting subgroups

  • Symmetric polynomials

  • The proof of the fundamental theorem of algebra using symmetric polynomials

  • The proof of Wedderburn's theorem on finite division rings

  • The proof of the Wedderburn-Artin theorem

Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.

Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

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Yes, you can access Introduction to Abstract Algebra by W. Keith Nicholson in PDF and/or ePUB format, as well as other popular books in Mathematics & Abstract Algebra. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Wiley
Year
2012
Print ISBN
9781118135358
eBook ISBN
9781118311738
Edition
4
Topic
Mathematics
Subtopic
Abstract Algebra
Index
Mathematics

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Acknowledgments
  6. Notation Used in the Text
  7. A Sketch of the History of Algebra to 1929
  8. Chapter 0: Preliminaries
  9. Chapter 1: Integers and Permutations
  10. Chapter 2: Groups
  11. Chapter 3: Rings
  12. Chapter 4: Polynomials
  13. Chapter 5: Factorization in Integral Domains
  14. Chapter 6: Fields
  15. Chapter 7: Modules over Principal Ideal Domains
  16. Chapter 8: p-Groups and the Sylow Theorems
  17. Chapter 9: Series of Subgroups
  18. Chapter 10: Galois Theory
  19. Chapter 11: Finiteness Conditions for Rings and Modules
  20. Appendices
  21. Bibliography
  22. Selected Answers
  23. Index
  24. End User License Agreement