Subject: Re: Four postings From: "David W. Lyons" Date: Wed, 21 Sep 2005 09:29:06 -0400 I have a reply to Brayton Gray's query in today's postings, looking for a topology book that does simplicial homology. A wonderful elementary level book is M.A. Armstrong's "Basic Topology" in Springer's Undergraduate Texts in Mathematics series. He does an elegant, completely elementary presentation of simplicial homology. You'll have to look at it, of course, to see if the topics and level fit what you are looking for. -David Lyons -- David W. Lyons Mathematical Sciences lyons@lvc.edu Lebanon Valley College, 101 N. College Avenue, Annville, PA 17003 717-867-6081 http://mas.lvc.edu/~lyons __________________________________________________________ Subject: re topology courses for undergraduates From: "Ronald Brown" Date: Wed, 21 Sep 2005 16:29:41 +0100 In the 1970s I began to feel my homology course failed the `look, Mummy, what I am doing in my course' test, and switched to knot theory. It also linked with combinatorial group theory courses, and gave lots of nice sums to do; this is even more so today, with knot polynomials, and some good books around. Then I found some of the theory could be realised with tricks which could be demonstrated publicly, and I am still doing this today to children (Wrexham Science Festival: March) and research mathematicians (Louvain-la-Neuve, Hagen: October)! So that switch led by chance followed by chance to all the popmath stuff. In particular, knot theory allows for a nice presentation of the idea of analogy in mathematics (see www.popmath.org.uk, and do a search on `analogy'). Also students could at the end tell others, and interviewing bodies, what the course was about. This was partly because I became clearer what it, and even algebraic topology, was about! or could be about. A problem I had with teaching homology was the gap between the intuition of `gluing bits' and the abelian algebra used to express it, and then the lack (at that level) of startling results which are easily explained. Ronnie Brown www.bangor.ac.uk/r.brown/publar.html ______________________________________________________________________ Subject: Re: Four postings From: Mark Hovey Date: 21 Sep 2005 12:23:06 -0400 In response to Brayton's question, I can quite heartily recommend Allen Hatcher's book "Algebraic topology" which is available for free download from his website and is also quite inexpensive in a paperback version. I like his approach to simplicial homology, which relaxes the annoying simplicial conditions so that a torus can really be built from two triangles. Also, he is leading the way in helping us escape from the publishing nightmare on the book side of things. Mark Hovey __________________________________________________________________ Subject: For Toplist: Homology book From: David Pengelley Date: Wed, 21 Sep 2005 12:05:53 -0600 (MDT) Brayton, Are you aware of the delightful little paperback by Hajime Sato, titled Algebraic Topology: An Intuitive Approach, in AMS Translations of Mathematical Monographs series? I've used it as a supplement. He develops cellular homology. I think lots of people would like this lovely book. Best David