Introduction to Algebra - Couverture souple

Cameron, Peter J.

Couverture souple

ISBN 10 : 0198501943 ISBN 13 : 9780198501947

Editeur : Oxford University Press, 1998

Synopsis

The book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students meet, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, as students gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, an outline of universal algebra, lattices and categories) and to applications such as Galois theory and coding theory. There is also a chapter outlining the construction of the number systems from scratch and proving in three different ways that transcendental numbers exist.

A propos du livre

Présentation de l'éditeur

Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.

Revue de presse

Review from previous edition This clearly written exposition is accompanied by well-chosen exercises. This book should be useful as a textbook for most undergraduates courses on algebra.

This is an extremely engaging introduction to abstract algebra by one of this country's most prolific and creative algebraists. Recognising that although the axiomatic method is unavoidable it is intially uncomfortable for many students, he adopts a relatively informal style which is constantly encouraging without ever lapsing into imprecision. Aided by a relaxed, friendly expository style, his expertise, sureness of touch and contagious enthusiasm for algebra shine through on every page this is a book to study, savour and enjoy

'Altogether this is a concise but solid introduction into algebra and linear algebra' Internationale mathematische Nachrichten

Détails de l'édition

• Éditeur: Oxford University Press
• Date d'édition: 1998
• Langue: anglais
• ISBN 10: 0198501943
• ISBN 13: 9780198501947
• Reliure: Broché
• Nombre de pages: 320
• Coordonnées du fabricant: non disponible