Wednesday, March 07, 2007
Monday, March 05, 2007
Friday, February 16, 2007
Tuesday, February 13, 2007
Thursday, January 18, 2007
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
``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
Monday, January 08, 2007
Tuesday, December 26, 2006
Sunday, December 24, 2006
Monday, December 18, 2006
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
Friday, December 08, 2006
Wednesday, November 22, 2006
Wednesday, November 15, 2006
Tuesday, November 14, 2006
Thursday, November 09, 2006
Tuesday, October 17, 2006
Monday, October 16, 2006
Monday, October 09, 2006
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
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
Farey sequences. Are they related to the sequences obtained from number in base n?
00001111
00110011
01010101in Math world
In wikipedia
Wednesday, May 03, 2006
Saturday, January 28, 2006
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).
Wednesday, October 26, 2005
Sunday, October 23, 2005
Tuesday, September 27, 2005
Monday, September 26, 2005
Saturday, September 24, 2005
Tuesday, September 20, 2005
Wednesday, August 03, 2005
Friday, July 29, 2005
Wednesday, July 20, 2005
Thursday, July 14, 2005
Wednesday, June 22, 2005
Friday, June 03, 2005
Tuesday, March 29, 2005
Friday, March 04, 2005
Friday, February 25, 2005
A very good list of electronically available lecture notes on
category theory, taken from Kurz homepage:
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.
Thursday, February 03, 2005
Kluwer Online Internet Publishing System - Georgian Mathematical Journal: "On Uncountable Unions and Intersections of Measurable Sets"
Monday, January 31, 2005
Friday, January 28, 2005
Wednesday, January 26, 2005
Saturday, January 22, 2005
Thursday, December 02, 2004
Friday, November 26, 2004
Tuesday, November 16, 2004
Friday, November 05, 2004
Friday, October 29, 2004
Tuesday, October 26, 2004
Tuesday, October 12, 2004
Saturday, October 09, 2004
Friday, October 08, 2004
Wednesday, October 06, 2004
Monday, October 04, 2004
Saturday, September 11, 2004
Thursday, September 09, 2004
Thursday, September 02, 2004
Tuesday, August 31, 2004
Friday, August 27, 2004
Saturday, August 07, 2004
Sunday, July 18, 2004
Tuesday, July 13, 2004
Monday, July 12, 2004
Saturday, July 03, 2004
Sunday, June 20, 2004
Tuesday, June 15, 2004
Friday, June 04, 2004
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."
Monday, May 24, 2004
Friday, May 07, 2004
Wednesday, May 05, 2004
Friday, April 30, 2004
Saturday, April 24, 2004
Sunday, April 18, 2004
Tuesday, April 13, 2004
Friday, March 19, 2004
Thursday, March 18, 2004
Wednesday, March 17, 2004
Wednesday, March 10, 2004
Saturday, March 06, 2004
Thursday, February 26, 2004
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