Conceptual Mathematics: A First Introduction to Categories [Paperback]

F. William Lawvere (Author), Stephen Hoel Schanuel (Author)

Book Description

ISBN-10: 0521478170 | ISBN-13: 978-0521478175 | Publication Date: November 28, 1997 | Edition: 1st

The idea of a "category"--a sort of mathematical universe--has brought about a remarkable unification and simplification of mathematics. Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

Editorial Reviews

Review

"Conceptual Mathematics provides an excellent introductory account to categories for those who are starting from scratch. It treats material which will appear simple and familiar to many philosophers, but in an unfamiliar way." Studies in History and Philosophy of Modern Physics

Book Description

The idea of a "category"--a sort of mathematical universe--has brought about a remarkable unification and simplification of mathematics. Written by two of the best known names in categorical logic, this is the first book to apply categories to the most elementary mathematics.

Product Details

• Paperback: 376 pages
• Publisher: Cambridge University Press; 1st edition (November 28, 1997)
• Language: English
• ISBN-10: 0521478170
• ISBN-13: 978-0521478175
• Product Dimensions: 9.5 x 6.7 x 0.9 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (15 customer reviews)
• Amazon Best Sellers Rank: #1,269,276 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

58 of 59 people found the following review helpful:

5.0 out of 5 stars Interesting and Accessible at Many Levels, August 2, 1998

By A Customer

This review is from: Conceptual Mathematics: A First Introduction to Categories (Paperback)

Lawvere and Schanuel have created a book at once accessible and stimulating at a great many levels. It discusses the concepts of Category Theory in a simulated "classroom" setting, addressing common questions of students at crucial points in the book. It also wanders in a care-free manner through an amazing number of topics. The book is interesting to non-mathematicians at a philosophical level, and to (beginning) mathematicians as an introduction to an exciting new area of mathematics. The authors have a great attitude, and offer great starting-points for investigation.

I read it as a first year pure math undergraduate, and though it was at times at too low a level (the 'tests,' for instance, are very easy reviews of basic ideas), it never became boring. For me, it read 'like a novel' (and a page-turner, at that). My only gripe is the lack of an annotated "further reading" section, which would have rounded out the book.

24 of 24 people found the following review helpful:

4.0 out of 5 stars Great book; whether you should read it depends on you, November 30, 2006

By 

Christopher D. Smith (Colorado Springs, CO) - See all my reviews
(REAL NAME)   

This review is from: Conceptual Mathematics: A First Introduction to Categories (Paperback)

Many of the reviews evaluate the book from the perspective of graduate students in mathematics want to learn categories, and it's certainly the wrong choice for that purpose. If you think of this as a serious math textbook, then it fails in that goal: significant proofs are the exception rather than the rule; very few, and trivial, exercises; very lacking in depth.

This is a great book because it provides a motivation for investigating categories. It helped me when I was in the position of hearing from a lot of places that subjects I was interested in often used category theory. I tried to read a few "real" books about category theory, and didn't get very far because they did not make the connections I was looking for. I accumulated three or four such books, all with bookmarks at about page 50 to 75. This book taught me relatively little about the theory of categories or the body of knowledge about them, but it provided a wealth of connections between categories and other topics, which made me better able to finish a couple of the real books and figure out what I needed to know there.

My advice, if you're in anything like that situation, is to read this book. Just don't take it too seriously, and don't try to milk more out of it than is really there. Then go learn more about category theory from elsewhere.

27 of 28 people found the following review helpful:

5.0 out of 5 stars Intuitive Introduction, June 6, 2000

By A Customer

This review is from: Conceptual Mathematics: A First Introduction to Categories (Hardcover)

Highly intuitive introduction to this abstract, but highly practical area of mathematics with one glaring fault. First the good news. I have never seen a more carefully explained introduction into an area of mathematics. Many examples and explanations of the principles behind and applications of concept analysis. However, the glaring fault is organization. Details are given without adequate tie in to how they relate to others. The text bounces from one area to the next so it is easy to lose sight of the whole picture. On balance its strengths far outweigh its weaknesses so I recommend it without reservation.