From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5381 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Thu, 17 Dec 2009 20:09:43 -0800 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1261172833 12308 80.91.229.12 (18 Dec 2009 21:47:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 18 Dec 2009 21:47:13 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Fri Dec 18 22:47:05 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from [138.73.1.1] (helo=mailserv.mta.ca) by lo.gmane.org with esmtp (Exim 4.50) id 1NLkfB-0008EK-85 for gsmc-categories@m.gmane.org; Fri, 18 Dec 2009 22:47:05 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NLkB9-0006v6-B0 for categories-list@mta.ca; Fri, 18 Dec 2009 17:16:03 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5381 Archived-At: Peter Easthope wrote: They won it ... but how prevalent is the > subject in undergraduate programs? Vector > algebra and analysis wasn't taught to engineers > until what, 1900 or later. Now it is ubiquitous. > Interestingly, in the late 1800s there was a period where quaternions were a mandatory examination topic in Dublin - and in some American universities they were the only advanced mathematics taught. Gibbs, who chopped the quaternion into its scalar and vector part and introduced the notation we use today, was the first person to get an engineering PhD in the United States, back in 1863. Absolutely no offense to existing books but what > about an energetic mathematician or two writing > a _Schaum's Outline of Category Theory_? I'd > expect it to sell off the shelves initially. > Great idea! 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. It's bound to happen eventually - but right now we need category theory to become a standard course at the graduate level. Whenever they get a good taste of category theory, math grad students are eager to take a course on it. They think it's exciting, and they see it as a way to learn other subjects more efficiently. But right now it's usually taught as part of algebra, without enough detail, and without enough attention to its applications outside algebra. So, sometimes students start their own seminars on category theory! Once most math grad students take a class on category theory, we'll get professors who can conceive of teaching it at the undergrad level. The only real question is whether our current civilization, based on burning carbon, tearing up forests, and destroying oceans, lasts long enough to see this change. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]