Gilbert / Nicholson Modern Algebra with Applications

2. Auflage 2004
ISBN: 978-0-471-46989-6
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 352 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

Praise for the first edition
"This book is clearly written and presents a large number ofexamples illustrating the theory . . . there is no other book ofcomparable content available. Because of its detailed coverage ofapplications generally neglected in the literature, it is adesirable if not essential addition to undergraduate mathematicsand computer science libraries."
-CHOICE
As a cornerstone of mathematical science, the importance ofmodern algebra and discrete structures to many areas of science andtechnology is apparent and growing-with extensive use incomputing science, physics, chemistry, and data communications aswell as in areas of mathematics such as combinatorics.
Blending the theoretical with the practical in the instructionof modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of thissubject-effectively holding your interest and creating a moreseamless method of instruction.
Incorporating the applications of modern algebra throughout itsauthoritative treatment of the subject, this book covers the fullcomplement of group, ring, and field theory typically contained ina standard modern algebra course. Numerous examples are included ineach chapter, and answers to odd-numbered exercises are appended inthe 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 updatedSecond Edition also contains new material on order of an elementand cyclic groups, more details about the lattice of divisors of aninteger, and new historical notes.
Filled with in-depth insights and over 600 exercises of varyingdifficulty, Modern Algebra with Applications, Second Edition canhelp anyone appreciate and understand this subject.

Autoren/Hrsg.

Gilbert, William J.

Nicholson, W. Keith

Inhaltsverzeichnis

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.
Index.

Über Autor(innen)

WILLIAM J. GILBERT, DPHil, is a professor in the Departmentof Pure Mathematics at the University of Waterloo, Ontario, Canada.He received his DPhil in mathematics from Oxford University in1968.
W. KEITH NICHOLSON, PHD, is a professor in the Departmentof Mathematics and Statistics at the University of Calgary,Alberta, Canada. He received his PhD in pure mathematics from theUniversity of California at Santa Barbara in 1970.