### Teaching category theory to undergraduates

Recently in the Categories mailing list there has been some discussion about whether it is yet time to teach category theory to undergraduates. Some, for example John Baez, expressed the idea that it was still too early - we must wait until there are sufficient teachers who understand category theory etc, etc.

I have been teaching category theory to undergraduates now for twenty years. The first time was in 1989 when I taught a course on categories and computer science to third year undergraduates of mathematics and computer science, a course which lead to my book Categories and Computer Science (Carslaw Publications 1991, Cambridge University Press 1992).

There are many others who have taught category theory at an undergraduate level, some mentioned on the list. One in particular was Gordon Preston who taught a course in Melbourne in the early seventies (reported by Kirill Mackenzie). Another famous course was that taught by Bill Lawvere and Steve Schanuel, which resulted in the book Conceptual Mathematics: A First Introduction to Categories (with Stephen H. Schanuel), Cambridge Uni. Press, 1997 ISBN 0-521-47817-0.

I have been teaching category theory to undergraduates now for twenty years. The first time was in 1989 when I taught a course on categories and computer science to third year undergraduates of mathematics and computer science, a course which lead to my book Categories and Computer Science (Carslaw Publications 1991, Cambridge University Press 1992).

There are many others who have taught category theory at an undergraduate level, some mentioned on the list. One in particular was Gordon Preston who taught a course in Melbourne in the early seventies (reported by Kirill Mackenzie). Another famous course was that taught by Bill Lawvere and Steve Schanuel, which resulted in the book Conceptual Mathematics: A First Introduction to Categories (with Stephen H. Schanuel), Cambridge Uni. Press, 1997 ISBN 0-521-47817-0.

Rather than premature the undergraduate teaching of category theory is overdue.

**Update:** Mike Shulman has written to me saying that perhaps I have misrepresented John Baez. What John Baez wrote was:

*I think it's premature to introduce category theory in the undergrad curriculum. Why? Merely because there aren't enough professors who'd see how to teach the subject at that level.*

I suppose I have always hoped that professors at university level were not so governed by such things as curricula.

Labels: category theory, Optimistic

## 1 Comments:

What John Baez actually said was:

I think it's premature to introduce category theory in the undergrad curriculum. Why? Merely because there aren't enough professors who'd see how to teach the subject at that level.So it sounds to me like you and he are in complete agreement. He wasn't saying that the people who

canteach it shouldn't continue doing so. He didn't say anything passive like "we must wait," rather he said that we can't hope for it to become part of the generalcurriculum(which is distinct from having isolated amazing courses taught here and there) until we lay the groundwork first. In particular, we should focus first on making sure that all graduate students learn it, in order to build up enough professors who'll then be able to teach it to undergraduates.Certainly, it's long past time that all of this

shouldhave happened in an ideal world.## Post a Comment

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