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Modern Algebra with Applications, 2nd Edition

William J. Gilbert, W. Keith Nicholson

ISBN: 978-0-471-41451-3 November 2003 352 Pages


Praise for the first edition

"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries."

As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing–with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics.

Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject–effectively holding your interest and creating a more seamless method of instruction.

Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text.

Chapter topics include:

  • Boolean Algebras
  • Polynomial and Euclidean Rings
  • Groups
  • Quotient Rings
  • Quotient Groups
  • Field Extensions
  • Symmetry Groups in Three Dimensions
  • Latin Squares
  • Pólya—Burnside Method of Enumeration
  • Geometrical Constructions
  • Monoids and Machines
  • Error-Correcting Codes
  • Rings and Fields

In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes.

Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.

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Preface to the First Edition.

Preface to the Second Edition.

List of Symbols.

1. Introduction.

2. Boolean Algebras.

3. Groups.

4. Quotient Groups.

5. Symmetry Groups in Three Dimensions.

6. Pólya–Burnside Method of Enumeration.

7. Monoids and Machines.

8. Rings and Fields.

9. Polynomial and Euclidean Rings.

10.Quotient Rings.

11. Field Extensions.

12. Latin Squares.

13. Geometrical Constructions.

14. Error-Correcting Codes.

Appendix 1: Proofs.

Appendix 2: Integers.

Bibliography and References.

Answers to the Odd-Numbered Exercises.


“…an ideal starter into algebra for all kinds of students, and a very useful addition to existing textbooks…” (Zentralblatt Math, Vol.1050, 2005)