(Warning: I’m trying to talk about things I don’t really understand in this post, so feel free to correct me if you see a statement that’s obviously wrong.) Why are continuous functions the “correct” notion of homomorphism between topological spaces? The “obvious” way to define homomorphisms for a large class of objects involves thinking of [...]
Posts Tagged ‘equivalence relations’
The “correct” definition of a homomorphism
Posted in category theory, order theory, topology, tagged abstract nonsense, contravariant functors, duality, equivalence relations, Hom functors on August 8, 2009 | 15 Comments »
IMO 2009 and proof systems
Posted in abstract algebra, number theory, Putnam / competitions, remarks, tagged Chebyshev polynomials, equivalence relations, Galois theory, Grobner bases, pedagogy, philosophy of mathematics, trigonometry on July 17, 2009 | 3 Comments »
The problems from IMO 2009 are now available. I haven’t had much time to work on them, though. There are two classical geometry problems, which I already know I won’t attempt. While I am well aware that classical geometry often requires a great deal of ingenuity, I am also aware of the existence of the [...]
GILA I: Group actions and equivalence relations
Posted in GILA, group theory, tagged equivalence relations, group actions, Polya theory on June 13, 2009 | 8 Comments »
Sometimes I worry that I should be more consistent or more lenient about the background I expect of my readers. (Readers, I have to admit that I still don’t really know who you are!) Considering how important I think it is that mathematicians value communicating their ideas to non-specialists (what John Armstrong calls the Generally [...]
-
Recent Comments
Qiaochu Yuan on The Yoneda lemma I Qiaochu Yuan on The Jacobson radical Joe Hannon on The Yoneda lemma I Amy Szczepanski on The Jacobson radical Qiaochu Yuan on The Yoneda lemma I -
Recent Posts
Categories
Archives
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- August 2011
- July 2011
- June 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- January 2009
Tag Cloud
