Abstract Algebra: An Introduction to Groups, Rings and Fields - Couverture rigide

Reis, Clive

 
9789814335645: Abstract Algebra: An Introduction to Groups, Rings and Fields
Couverture rigide
ISBN 10 : 9814335649 ISBN 13 : 9789814335645
Editeur : World Scientific Publishing Co Pte Ltd, 2011

Synopsis

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: Polya-Burnside 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. An entire chapter is devoted to studying the algebraic system of the integers 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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: Polya-Burnside 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. An entire chapter is devoted to studying the algebraic system of the integers 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.

Revue de presse

What makes this book more than just a safe journey from square one to the usual results such as Lagrange's theorem and the Sylow theorems is the discussion of several applications, illustrating both the amazing power of these concepts and the diversity of fields where abstract algebra can prove helpful: Latin squares, Polya-Burnside enumeration and isometries in Euclidean space. --Times Higher Education

These appendices can either be used in the classroom as abbreviated reviews of the material or as a resource for the student to be used as a reference. --Zentralblatt MATH

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2011
Langue
anglais
ISBN 10 
9814335649
ISBN 13 
9789814335645
Reliure
Relié
Nombre de pages
508
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9789814340281: Abstract Algebra: An Introduction To Groups, Rings And Fields

Edition présentée

ISBN 10 :  9814340286 ISBN 13 :  9789814340281
Editeur : Wspc, 2011
Couverture souple