A Survey of Modern Algebra (Akp Classics) [Hardcover]

Garrett Birkhoff (Author), Saunders Mac Lane (Author)

Book Description

ISBN-10: 1568810687 | ISBN-13: 978-1568810683 | Publication Date: February 6, 1998

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.

Editorial Reviews

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: A K Peters/CRC Press (February 6, 1998)
• 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: 4.3 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,165,138 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

33 of 35 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

This review is from: A Survey of Modern Algebra (Akp Classics) (Hardcover)

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.

6 of 6 people found the following review helpful:

5.0 out of 5 stars A classic algebra text! Wonderful book..., November 1, 2006

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
(REAL NAME)   

This review is from: A Survey of Modern Algebra (Hardcover)

This is a classic book on Algebra. There is much that I like about it. It is exactly what the name suggests--a survey course. It briefly introduces all sorts of topics, including rings, fields, groups, galois theory, vector spaces, lattices, boolean algebras, and much more. It is written at a fairly elementary level and it generally doesn't go into a great amount of depth in each subject. Interestingly, many (more modern) algebra texts omit a number of rather basic topics in this book. Also, many modern books separate "linear algebra" from "abstract algebra", whereas this book takes a more integrated approach.

I find it exceptionally clear and easy to read. Many of the subjects are made particularly easy; there is a strong concrete flavour to the text. The authors provide good motivation for the material.

I think this book would make excellent reading material for someone who is planning to study algebra. I did not pick it up until early in graduate school, and I wish I had had access to it earlier, when I was first studying ring and field theory. It is a fantastic reference for intermediate students, since it covers just about all the basics of algebra, and does so in a very understandable way. I think this book would make a fine textbook for an undergraduate course as well.

6 of 53 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 (Manhattan, KS) - See all my reviews

This review is from: A Survey of Modern Algebra (Akp Classics) (Hardcover)

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.