Modern Algebra with Applications

W. Keith Nicholson, William J. Gilbert

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

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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.

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	2^eme 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