Synopses & Reviews
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."
CHOICE
As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growingwith 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 subjecteffectively 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
- PólyaBurnside 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.
Review
“…an ideal starter into algebra for all kinds of students, and a very useful addition to existing textbooks…” (Zentralblatt Math, Vol.1050, 2005)
Synopsis
This book blends the theoretical with the practical in the instruction of modern algebra. Modern algebra is usually taught from the point of view of its intrinsic interest, without using applications. Many readers lose interest when they do not see the relevance of the subject and often become skeptical of the explanation that the material will be used later. The author believes by providing interesting and nontrivial applications, the student will better appreciate and understand the subject.
Synopsis
Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of this subject—effectively holding your interest and creating a more seamless method of instruction. Filled with in-depth insights and over six hundred exercises of varying difficulty, this invaluable text can help anyone appreciate and understand this subject.
Synopsis
Blending the theoretical with the practical in the instruction of modern algebra
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 addition to undergraduate mathematics and computer science libraries.
-Choice
Modern algebra guides are often structured from the point of view of the subject's intrinsic interest, offering only vague promises of practical applications in later courses or more sophisticated texts. William Gilbert's classic Modern Algebra with Applications, however, incorporates the applications of modern algebra throughout its authoritative treatment of the subject, not only effectively holding his readers' interest but also creating a more seamless method of instruction.
The 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. Chapter topics include: Boolean Algebras, Groups, Quotient Groups, Symmetry Groups in Three Dimensions, Polya-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.
Modern Algebra with Applications remains an ideal companion to upper undergraduate and graduate level algebra courses.
About the Author
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.
W. KEITH NICHOLSON, PHD, is a professor in the Department of Mathematics and Statistics at the University of Calgary, Alberta, Canada. He received his PhD in pure mathematics from the University of California at Santa Barbara in 1970.
Table of Contents
Introduction.
Boolean Algebras.
Groups.
Quotient Groups.
Symmetry Groups in Three Dimensions.
Polya-Burnside Methods of Enumeration.
Monoids and Machines.
Rings and Fields.
Polynomial and Euclidean Rings.
Quotient Rings.
Field Extensions.
Latin Squares.
Geometrical Constructions.
Error-Correcting Codes.
Bibliography and References.
Answers to Odd-Numbered Exercises.
Glossary of Symbols.
Index.