Modern Algebra with Applications
Wiley Series in Pure and Applied Mathematics
2. Edition November 2003
352 Pages, Hardcover
Wiley & Sons Ltd
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 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 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.
Index.
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.
