A Survey of Modern Algebra (AKP Classics) (Hardcover)

by Garrett Birkhoff; Saunders MacLane (Author)

Editorial Reviews

Product Description
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.

About the Author
Garrett Birkhoff published more than 200 papers and supervised more than 50 Ph.Ds. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He spent most of his career as a professor of mathematics at Harvard University. During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders MacLane, substantially advanced American teaching and research in abstract algebra. His 1935 paper, On the Structure of Abstract Algebras founded a new branch of mathematics, universal algebra.

Saunders Mac Lane was the author or co-author of more than 100 research papers and six books. Mac Lane was elected to the National Academy of Sciences in 1949. He received the nation s highest award for scientific achievement, the National Medal of Science, in 1989. Mac Lane received two Guggenheim Fellowships and visited Australia as a Fulbright Scholar. Other honors include both the Chauvenet Prize and the Distinguished Service award of the Mathematical Association of America, the Steele Career Prize of the American Mathematical Society, and honorary fellowship in the Royal Society of Edinburgh. --This text refers to the Paperback edition.

Product Details

• Hardcover: 512 pages
• Publisher: AK Peters, Ltd. (January 1997)
• Language: English
• ISBN-10: 1568810687
• ISBN-13: 978-1568810683
• Product Dimensions: 9 x 6.2 x 1.4 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #1,059,088 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

28 of 29 people found the following review helpful:

5.0 out of 5 stars This is how algebra texts ought to be written, April 25, 2002

By A Customer

I have just started reading this book, and already I am
enthralled by the beauty and elegance of the authors'
exposition. Assuming nothing more than an acquaintance with
school algebra and a little geometry, they develop
the basic properties of central algebraic structures, including
rings, groups and fields. These are treated by reference to
familiar examples, such as the ring of integers and the
rational, real and complex fields. Everything that one learned
in school algebra is to be found here, though, as is to be
expected, each topic is treated at a rigorous, mathematically
sophisticated level. In the first two chapters, the properties
of the integers and rational numbers are gradually examined,
ultimately down to the definition of addition and multiplication
on the basis of Peano postulates. The authors then consider
polynomials, the real and complex numbers, vector spaces, linear
algebra and other topics.
The writing style is clear, concise and elegant, with each new
concept being carefully defined as it is introduced. The proofs
achieve a satisfying balance between detail and brevity. Indeed,
reading the proofs and completing the exercises would do much, I
am sure, to enhance a reader's mathematical facility.

If you are interested in acquiring a deeper understanding of
algebra, this book should serve as an excellent introduction.

1 of 6 people found the following review helpful:

3.0 out of 5 stars too concise for its own good, October 16, 2008

By	Furious George (Illinois) - See all my reviews

Any college level math text should have AT LEAST one of the following, but hopefully both:

1) plenty of examples illustrating the use of the taught proofs, theorems, algorithms, procedures, etc.

2) Answers to AT LEAST some of the exercises in the back of the text.

Without one of these, how would you ever know you were grasping the material?

Unfortunately, this book comes up pretty short on #1 and completely empty on #2. there are many sections that are lacking examples, and there are NO solutions to the exercises.

the book reads more like an ordered collection of theorems and corollaries. Not so great if you wanna teach yourself. Probably more ideal for decorating a professor's bookshelf.

4 of 43 people found the following review helpful:

3.0 out of 5 stars A smorgousborg of symmetries of the square, December 12, 2000

By	Andrew Young "ayoung8511" (Manhattan, KS) - See all my reviews

Modern algebra is an extraordinary topic and Birkhoff and MacLane do a superb job of exploring it. However, as is often the case with mathematical texts, the material can be somewhat dry.