Undergraduate Algebra

ISBN-10: 0387220259
ISBN-13: 9780387220253
Edition: 3rd 2005 (Revised)
Authors: Serge A. Lang
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Description: Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics.  More...

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Book details

List price: $74.95
Edition: 3rd
Copyright year: 2005
Publisher: Springer
Publication date: 3/21/2005
Binding: Hardcover
Pages: 389
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.496
Language: English

Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyders proof of the Mason-Stothers polynomial abc theorem.   About the First Edition: The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt

Lang, Yale University, New Haven, CT.

Foreword
The Integers
Groups
Rings
Polynomials
Vector Spaces and Modules
Some Linear Groups
Field Theory
Finite Fields
The Real and Complex Numbers
Sets
Appendix
Index

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