Mathematics Form and Function 1986th Edition

by Saunders MacLane (Author)

8 customer reviews

ISBN-13: 978-0387962177

ISBN-10: 0387962174

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Product Details

Hardcover: 476 pages
Publisher: Springer; 1986 edition (December 19, 1985)
Language: English
ISBN-10: 0387962174
ISBN-13: 978-0387962177
Product Dimensions: 1 x 6.5 x 9.8 inches
Shipping Weight: 1.6 pounds
Average Customer Review: 5.0 out of 5 stars See all reviews (8 customer reviews)
Amazon Best Sellers Rank: #1,018,930 in Books (See Top 100 in Books)
- #820 in Books > Science & Math > Mathematics > Mathematical Analysis
- #8668 in Books > Textbooks > Science & Mathematics > Mathematics

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Excellent

ByAmazon Customeron August 8, 2000

Format: Hardcover

This is a survey of the whole of mathematics, at the undergraduate level, which attempts to give the "big picture". If you read and understand it, you will have a better grasp of this big picture than most graduate students. MacLane has written a book which every mathematician (and perhaps philosopher) should read and savour.
There are few technical details in this book. It is not a textbook per se, but a beautiful exposition of mathematics as a whole. It is not for learning any specific topic from; rather it is about appreciating the structure of mathematics as a whole, so that you know how each specific topic stands within that structure.
Indeed, this is an excellent book. Too bad for fashion that it is out-of-print.
N.B. There is a more advanced and technical book by Jean Dieudonne along the same lines. You might want to read it after enjoying your Mac Lane.

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A broad overview, by a 20th century math giant

ByA customeron January 23, 2002

Format: Hardcover

Born 1909, MacLane is one of the great living mathematicians, by virtue of having been the coinventor and chief propagator of category theory. Hence this is an overview of contemporary mathematics, at about the level of a fully competent BA graduate, by someone fully qualified to talk about math. Important points. (1) MacLane is an expert on algebra and gives many examples of the unifying power of abstract algebra. (2) The book includes passages that amount to a gentle introduction to the philosophy of mathematics. MacLane takes exception to what philosophers have written about math, in part because they don't know enough math. (3) This book is also a good introduction to MacLane's radical claim that set theory is an inadequate foundation for math, and that the category theory he coinvented is better for this purpose. (4) Includes many fascinating "road maps" or "flow charts" of the intricate connections among the many branches and topics of mathematics.
Slight disappointment: MacLane does not do justice to the lattice theory his frequent coauthor, Garret Birkhoff, did so much to advance.

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Groundbreaking, Lucid, Timeless and more relevant than ever.

Bymobiusklienon June 20, 2015

Format: Hardcover

Category Theory, which Saunders had a strong hand in inventing has been dragged out of the dustbin of curious arcane thinking and thrust into the light as concepts of functional programming have grabbed IT by storm since 2010. MacLane's book is a very strong overview to the philosophy of mathematics that speaks to the practical applied side. His book is lucid, has pictures of mathematical relationships that resonate today as strongly as they did when this book was published.
The strongest testament to this timeless work is that nearly 40 years AFTER I purchased this and browsed it as a curiosity, I have now put it on my desk as a reference while delving into the construction of rule based systems for infrastructure design.

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Should be in every library

ByDavid A. Johannsenon February 6, 2001

Format: Hardcover

For an elegant overview of much of modern mathematics it can't be beat. How I wish that I had had this book as a first and second year graduate student!

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Best overview of mathematics

ByG Won May 5, 2014

Format: Hardcover

I put this book in the same class of The Princeton Companion to Mathematics, The Road to Reality: A Complete Guide to the Laws of the Universe, and Mathematics: Its Content, Methods and Meaning. This one is the best of four.

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Brilliant and clear description of wide areas of mathematics

ByH. H. L.on April 21, 2016

Format: HardcoverVerified Purchase

Brilliant and clear description of wide areas of mathematics, from the man who saw abstract connections between areas of math thought to be unrelated.

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A tour de force

ByRobert Bechtelon October 29, 2015

Format: HardcoverVerified Purchase

A tour de force by the master.

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Very nice

ByA customeron March 21, 1999

Format: Hardcover

A clear and careful expositio

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