Subject: categories: Re: [Fwd: du Sautoy]

From: "Marta Bunge" <[email-masked]>
Date: Wed, 19 Apr 2006 07:35:27 -0400

Dear Steve,

>I think this is exactly the key to the success of Mac Lane's book.
>Throughout, he shows how working mathematicians are applying category
>theory already without realizing it. One of the basic expositional
>problems for teaching CT in computer science is that our students do  not
>have the body of mathematical experience that Mac Lane presumed.
>

Of course, by "mathematical experience" one need not assume that it should
be the same for everybody. MacLane was thinking of the pure mathematicians
only, because that was what motivated him all along.

I think that "Conceptual Mathematics" by Lawvere and Schanuel, though
seemingly too elementary, is a great introduction to categorical thinking
that can be widely appreciated, since the examples chosen therein to
illustrate new concepts are simple. I say this in more detail in a review
(in Spanish) that can be found in my home page
(http://www.math.mcgill.ca/bunge/LS.pdf (.ps)). Even so, you must agree that
computer scientists ought to have learnt a certain amount of pure
mathematics, or else how are they going to appreciate the more sophisticated
developments in their field, or even less contribute to it?

I used "Categories and Computer Science" by Bob Walters twice when teaching
"Computability and Linguistics" at McGill. Although I have heard some
negative comments about it (sorry to mention it, Bob), I liked it a lot. The
exercises are often quite demanding, and the exposition clear. I do not know
what you think about it. Of course, with a book like that, as with any
other, it is up to the instructor to use it to his advantage, and to
complement it as needed by the particular audience he has to face.

Nice hearing from you,
Marta