Abstract Algebra: An Introduction to Groups, Rings and Fields (Paperback)

Clive Reis

  • 出版商: World Scientific Pub
  • 出版日期: 2011-05-10
  • 售價: $1,200
  • 貴賓價: 9.8$1,176
  • 語言: 英文
  • 頁數: 508
  • 裝訂: Paperback
  • ISBN: 9814340286
  • ISBN-13: 9789814340281

下單後立即進貨 (約5~7天)

買這商品的人也買了...

商品描述

<內容特色>

This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: PolyaBurnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.

Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced via congruence classes to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems.

Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.

<章節目錄>

Logic and Proofs
Set Theory
Cartesian Products, Relations, Maps and Binary Operations
The Integers
Groups
Further Properties of Groups
The Symmetric Groups
Rings, Integral Domains and Fields
Polymial Rings
Field Extensions
Latin Squares and Magic Squares
Group Actions, the Class Equation and the Sylow Theorems
Isometries
PolyaBurnside Enumeration
Group Codes
Polynomial Codes