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Modern Algebra with Applications
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Modern Algebra with Applications

Modern Algebra with Applications

W. Keith Nicholson, William J. Gilbert

334 pages, parution le 03/12/2003 (2eme édition)

Résumé

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.

Contents

  • Preface to the First Edition
  • Preface to the Second Edition
  • List of Symbols
  • Introduction
  • Boolean Algebras
  • Groups
  • Quotient Groups
  • Symmetry Groups in Three Dimensions
  • Pólya–Burnside Method of Enumeration
  • Monoids and Machines
  • Rings and Fields
  • Polynomial and Euclidean Rings
  • Quotient Rings
  • Field Extensions
  • Latin Squares
  • Geometrical Constructions
  • Error-Correcting Codes
  • Appendix 1: Proofs
  • Appendix 2: Integers
  • Bibliography and References
  • Answers to the Odd-Numbered Exercises
  • Index

L'auteur - W. Keith Nicholson

W. KEITH NICHOLSON, PhD, is a Professor in the Department of Mathematics and Statistics at the University of Calgary in Alberta, Canada. Dr. Nicholson has published numerous textbooks and monographs throughout his career. He received his PhD in Pure Mathematics from the University of California at Santa Barbara, and his current research interests include clean rings, morphic rings, and module theory.

L'auteur - William J. Gilbert

DPHil, is a professor in the Department of Pure Mathematics at the University of Waterloo, Ontario, Canada. He received his DPhil in mathematics from Oxford University in 1968.

Caractéristiques techniques

  PAPIER
Éditeur(s) Wiley
Auteur(s) W. Keith Nicholson, William J. Gilbert
Parution 03/12/2003
Édition  2eme édition
Nb. de pages 334
Format 16 x 24
Couverture Relié
Poids 625g
Intérieur Noir et Blanc
EAN13 9780471414513
ISBN13 978-0-471-41451-3

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