Recent content by dvs

turbo-1, that's a 'g' in Lebesgue, not a 'q'! -- I've always wondered about the pronunciation of Urysohn. My Ukranian friend pronounces it "Uri-shown", whereas just about everyone else pronounces it "Uri-son". Any ruskis around to comment?

A famous application of rep theory to group theory is the proof of Burnside's pq theorem, see: http://en.wikipedia.org/wiki/Burnside_theorem. And as matt mentioned, another famous example is the classification of finite simple groups, which wouldn't have been completed without the use of rep...

I don't think Amazon has anything to do with this. It's probably the publisher's fault. In fact, it's very likely that Amazon doesn't even have the softcover edition.

Yup: "isomorphic" vs "equal to" is the problem. What wiki has is definitely true, as can be seen just by comparing dimensions. The direct sum in this case is the "exterior" direct sum of vector spaces, not the "interior" direct sum of subspaces. Your prof's counterexample shows that V is, in...

Don't math majors and psych majors take different calculus classes anyway?

quasar987: It's sometimes helpful to think about tensoring as a "change of base" type operation, and this is one of these times. For more info, see the section of Dummit & Foote on tensor products of modules. This type of thinking will also be helpful, e.g., when you try to construct homology...

Well, I was curious and I had some time to kill, so I decided to look at where non-emeriti regular faculty got their PhDs. The count: Toronto: Harvard 4 MIT 0 Princeton 8 Berkeley 5 Waterloo: Harvard 3 MIT 3 Princeton 2 Berkeley 6 (and this is excluding the mathematically inclined...

Use the characteristic function of a set that's Lebesgue but not Borel.

Zorn it!

EbolaPox- Here are a few more good functional analysis and operator theory groups that haven't been mentioned yet: Vanderbilt http://www.math.vanderbilt.edu/~ncgoa/people.html Texas A&M http://www.math.tamu.edu/~kdykema/LAN/lanpeople.html Waterloo (Canada)...

A function f:R->C can be decomposed into its real and imaginary parts, say f=u+iv, where u=Re(f) and v=Im(f). The definition of the Riemann/Lebesgue integral of such a function is \int f = \int u + i \int v. The integrals \int u and \int v are just the usual real integrals. Does this clear...

sin(n)^n doesn't converge to 0. Hint!

http://www.gethappy.com/watchmore.html

But how would you know, khemix? Very recently you have started a thread that clearly demonstrates your lack of experience in math, yet here you are dishing out advice about graduate schools? For what it's worth, Waterloo has an extremely strong combinatorics group and very strong analysis...

I believe that the conclusion in #3 is indeed correct, and follows from the fact that operators on finite dimensional complex spaces have eigenvectors (hence 1-dimensional invariant subspaces).