Sunday, January 14, 2007

from Rota's `Indiscrete thoughts' p.48:

``What can you prove with exterior algebra that you cannot prove
without it?" Whenever you hear this question raised about some new
piece of mathematics, be assured that you are likely to be in the
presence of something important. In my time, I have heard it
repeated for random variables, Laurent Schwartz' theory of
distributions, ideles and Grothendieck's schemes, to mention only a
few. A proper retort might be: ``You are right. There is nothing in
yesterday's mathematics that could not also be proved without it.
Exterior algebra is not meant to prove old facts, it is meant to
disclose a new world. Disclosing new worlds is as worthwhile a

Saturday, December 16, 2006

Christopher TownsendI work in locale theory and topos theory. My preoccupation is that the theory of compact Hausdorff spaces and the theory of sets have such a lot in common that they can be expressed as the same theory. Therefore I am developing axioms for a category of spaces in which the theory of compact Hausdorff spaces is dual to the theory of sets (the duality is not standard categorical duality, but is order enriched duality; the category of spaces is order enriched). A further aim is to extend this work to an axiomatization of the category of Grothendieck toposes.

Friday, December 15, 2006

PLT Online Excelente lista de libros online sobre semántica de lenguajes

Sunday, August 27, 2006

The n-Category Café The most interesting thing about this is the usage of MathML. I want to use that in this blog!

Wednesday, May 10, 2006

DBLP: R. Lowen Dubois & Prade dicen que en Lowen 1978 hay un enfoque categorico.
http://mathworld.wolfram.com/FareySequence.html

Farey sequences. Are they related to the sequences obtained from number in base n?

00001111
00110011
01010101in Math world

In wikipedia

Friday, October 28, 2005

Hausdorff distance Hausdorff distance can be defined the same way for closed non-compact subsets of M, but in this case the distance may take infinite value and the topology of F(M) starts to depend on particular metric on M (not only on its topology). The Hausdorff distance between not closed subsets can be defined as the Hausdorff distance between its closures. It gives a pre-metric (or pseudometric) on the set of all subsets of M (Hausdorff distance between any two sets and with the same closures is zero).

Common Errors in College Math page pointed out by Paul Kirk.
Hausdorff metric a good explanation plus applications.

Friday, July 29, 2005

A paper by Goldblatt Seems to be based in the same idea of the paper we did with Larry...

Friday, February 25, 2005

A very good list of electronically available lecture notes on
category theory
, taken from Kurz homepage:


M. Caccamo, J.M.E. Hyland, G. Winskel:
Lecture Notes
in Category Theory.
BRICS Lecture Series, 2001.



M. Fokkinga:

A Gentle Introduction to Category Theory - the calculational
approach.
University of Utrecht, 1992.


Chris Hillman: A
Categorical Primer.
August 2001.


Tom Leinster:

Category Theory.

This page contains an informal
introduction to category theory and, for example, a nice explanation
of the Yoneda Lemma.


Jaap van Oosten:
Basic Category Theory.



D. Turi: Category
Theory Lecture Notes.
LFCS, Univeristy of Edinburgh, 2001.

Indiana University Math departmant: magazine articles

Tuesday, May 25, 2004

ABCNEWS.com : Atiyah, Singer Accept Norway's Abel Prize: "Atiyah, 75, of the University of Edinburgh in Scotland, and Singer, 79, of the Massachusetts Institute of Technology, developed what is now called the Atiyah-Singer theorem about 40 years ago."

Thursday, February 26, 2004