From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3974 Path: news.gmane.org!not-for-mail From: "Micah Blake McCurdy" Newsgroups: gmane.science.mathematics.categories Subject: Talking to Undergraduates about Category Theory Date: Mon, 8 Oct 2007 16:38:24 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019636 11150 80.91.229.2 (29 Apr 2009 15:40:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:40:36 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Oct 8 10:17:50 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 08 Oct 2007 10:17:50 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IesU4-0004Uc-B5 for categories-list@mta.ca; Mon, 08 Oct 2007 10:17:20 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 31 Original-Lines: 53 Xref: news.gmane.org gmane.science.mathematics.categories:3974 Archived-At: Hallo! I have over the last several years repeatedly given to delegates of the Canadian Undergraduate Mathematics Conference a talk about Category Theory, all of which were very well received. I should mention at the outset that I had the (debatable) advantage of _being_ an undergraduate for all three talks. Some elements which went over especially well: 1) Historical considerations, namely, the role of category theory in the development of algebraic topology. The use of category theory as a language for making rigorous certain intuitions, as well as facilitating calculations. This point of view resonates very well with undergraduates, to whom _all_ of mathematics is a more or less hazy mass of intuitions and proofs; who long for clarity and order. 2) Freeing constructions from set by diagrammatic descriptions. For instance, defining the notion of a group object in an arbitrary category C, and then noting that such gadgets are already studied for various C. This appeals for two reasons: it gives an elegant explanation for _why_ similar-seeming things are similar, and, more importantly, it _suggests new questions_, namely, for a new category of study, "what are the internal wombats in this category" for various choices of wombat. Especially for older undergraduates, who are thinking to themselves "Subject X is really very fascinating, but what will I ever do with it?", this is a very appealing notion. 3) Diagrammatic methods in proofs. The device of commuting diagrams to form and illustrate proofs is generally both novel and wonderful to undergraduates. This has many sub-parts, among them: i) One augments a symbolic intuition with a geometric intuition. Thus, proving that a large diagram commutes becomes a sort of tangram puzzle. ii) Proofs become both easier to construct and, more importantly, easier to communicate. This is especially near to the hearts of undergrads who have difficulty constructing proofs, more difficulty understanding the proofs of others, and yet more in having their proofs understood by others. If you were so inclined, you might well introduce string diagrams. The third point, considered strictly, is not really a part of category theory, but I think it is cut from the same cloth. On a perfectly peripheral note, I often place two bottles of (preferably obscure) beer on the desk in front of me before I begin speaking; promising one to the best question after the talk and the other to the best heckling during the talk. I strongly encourage heckling, and I doubt that undergraduates enjoy this any more than other mathematicians. If all goes wrong, you can drink the beer yourself. In any event, good luck. Micah