most recent 30 from http://mathoverflow.net 2013-05-21T16:15:43Z http://mathoverflow.net/feeds/user/10316 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/74214/examples-where-its-useful-to-know-that-a-mathematical-object-belongs-to-some-fam/83780#83780 kastberg 2011-12-18T09:08:50Z 2011-12-18T09:08:50Z

<p>One of the proofs of the riemann mapping theorem!</p> <p>The mapping is constructed by considering a family of mappings with a certain property. Then we prove that the maximal member is the mapping we are looking for. It almost feels like cheating.</p> <p>The proof is tedious but certainly accessible to undergraduates.</p>

http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62745#62745 kastberg 2011-04-23T14:34:12Z 2011-04-23T14:34:12Z

<p>In Swedish, a field is called a 'kropp', a body. This of course from the German word Körper.</p>

http://mathoverflow.net/questions/60981/are-problems-in-complexity-theory-dependent-on-set-theory kastberg 2011-04-07T18:39:21Z 2011-04-07T18:43:34Z

<p>I was pondering the fact that maybe the classical hard complexity-theoretic questions are undecidable, not because they are so themselves, but because some set-theoretic foundations makes the complexity-theoretic foundations shaky.</p> <p>My thoughts was that perhaps something like the Continuum hypothesis makes P vs NP undecidable. So my question is, is there a "finitary" or otherwise obviously sane environment for complexity theory that would discount this theory immediately? I'm aware of simpler structures where P vs NP has been decided, but I don't know how that would fit in.</p> <p>I apologize in advance if this doesn't make sense.</p>

http://mathoverflow.net/questions/59450/boundaries-of-the-eigenvalues-of-a-symmetric-matrix-or-of-its-lapacian/59474#59474 kastberg 2011-03-24T20:45:28Z 2011-03-24T22:36:21Z

<p>There's a whole area of algebraic graph theory, but without any information on a the graph, I can't remember anything graph specific right now</p> <p>What is relevant is <a href="http://en.wikipedia.org/wiki/Gershgorin_circle_theorem" rel="nofollow">Gershgorin circle theorem</a></p> <p>Which for example would mean that a undirected graph without loops, the adjacency matrix would have eigenvalues smaller than the maximum degree of a vertex, that is |M-1|. And for the Laplacian we should get something like 2|M|.</p>

http://mathoverflow.net/questions/52107/the-concept-conjugate-class-in-monoids/57522#57522 kastberg 2011-03-06T01:29:09Z 2011-03-06T01:29:09Z

<p>This seems to be a relevant paper:</p> <p><a href="http://www2.math.uu.se/research/pub/Mazorchuk46.pdf" rel="nofollow">On three approaches to conjugacy in semigroups</a></p>

http://mathoverflow.net/questions/102845/spaces-with-a-specified-fundamental-group kastberg 2012-08-02T08:43:08Z 2012-08-02T08:43:08Z

Sorry, what is Z-hat?

http://mathoverflow.net/questions/7584/what-are-the-most-misleading-alternate-definitions-in-taught-mathematics/61299#61299 kastberg 2011-04-11T17:22:01Z 2011-04-11T17:22:01Z

This. I'm working on semigroup representations and been having problems getting a clear mental image about induced representations. I've been looking at the group-oriented literature but am wary of getting my intuition wrong for semigroups.

http://mathoverflow.net/questions/60981/are-problems-in-complexity-theory-dependent-on-set-theory kastberg 2011-04-07T19:31:20Z 2011-04-07T19:31:20Z

Nice catch, also the paper linked to there, <a href="http://www.scottaaronson.com/papers/pnp.pdf" rel="nofollow">scottaaronson.com/papers/pnp.pdf</a> seems very useful.