Undergraduate Algebra / Edition 3

by Serge Lang

Overview

This book, together with Linear Algebra, constitutes a curriculum for an algebra program addressed to undergraduates. The separation of the hnear algebra from the other basic algebraic structures fits all existing tendencies affecting undergraduate teaching, and I agree with these tendencies. I have made the present book self contained logically, but it is probably better if students take the linear algebra course before being introduced to the more abstract notions of groups, rings, and fields, and the systematic development of their basic abstract properties. There is of course a little overlap with the book Lin­ ear Algebra, since I wanted to make the present book self contained. I define vector spaces, matrices, and linear maps and prove their basic properties. The present book could be used for a one-term course, or a year's course, possibly combining it with Linear Algebra. I think it is important to do the field theory and the Galois theory, more important, say, than to do much more group theory than we have done here. There is a chapter on finite fields, which exhibit both features from general field theory, and special features due to characteristic p. Such fields have become important in coding theory.

Product Details

ISBN-13:	9780387220253
Publisher:	Springer New York
Publication date:	03/21/2005
Series:	Undergraduate Texts in Mathematics
Edition description:	3rd ed. 2005
Pages:	389
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

The Integers.- Groups.- Rings.- Polynomials.- Vector Spaces and Modules.- Some Linear Groups.- Field Theory.- Finite Fields.- The Real and Complex Numbers.- Sets.

Editorial Reviews

From the reviews of the third edition:

"As is very typical for Professor Lang’s self demand and style of publishing, he has tried to both improve and up-date his already well-established text. … Numerous examples and exercises accompany this now already classic primer of modern algebra, which as usual, reflects the author’s great individuality just as much as his unrivalled didactic mastery and his care for profound mathematical education at any level. … The present textbook … will remain one of the great standard introductions to the subject for beginners." (Werner Kleinert, Zentralblatt MATH, Vol. 1063, 2005)

From the Publisher

Splendid undergraduate text, intended to function as a companion to the distinguished author's Linear algebra and to provide young mathematicians with a secure command of the fundamentals of groups, rings, fields, and related structures. Ten chapters, many excellent problems, written with exemplary clarity and with exceptional sensitivity to what young readers might on first encounter consider to be "scary". Departs from the previous edition (1987) by the inclusion of some new material and exercises. The author has been very well served by the production people at Springer, who have produced a physically beautiful book at a reasonable price. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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