Algebra

by Saunders Mac Lane, Garrett Birkhoff

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance. This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach--emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s--was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

Genres: Mathematics, Algebra, Textbooks, Reference

626 pages, Hardcover

First published January 1, 1967

Reviews

[Nigel Lim · Rating 5 out of 5]

Well-written and memorably elegant proofs (written by two of the modern pioneers of algebra). Not necessarily easy reading (especially regarding the use of category theory, for one new to it), but develops mathematical maturity and conceptual connections nicely. Covers just about all the algebra a typical undergraduate is likely to cover (likely more, depending on ones emphasis).

[Kumirus · Rating 4 out of 5]

read parts of it, one of the best algebra books i have ever held in my hand

[Samuel Ireson · Rating 5 out of 5]

Belter. Gentle introduction to category theoretic language from the founder of the subject. Would recommend to anyone.