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seen Oct 24 '13 at 6:40

Sep
22
awarded  Nice Answer
Aug
21
awarded  Revival
May
30
awarded  Yearling
Jul
4
comment Evaluating definite integrals
There are certainly real integrals which are much more easily computed with contour integration in the complex plane (for example, $\int_{-\infty}^\infty \frac{1}{1+x^n}$) but as the other comments suggest, I'm not sure that this methodology precludes being a technique of "real analysis."
Jul
4
awarded  Critic
Jun
23
comment Is there any direct application of Gödel's Theorems outside of logic?
Philosophers have certainly tried to use it.
Jun
23
comment Studying quantum mechanics without physics background
You should probably feel comfortable with basic material before proceeding to Quantum Mechanics at the graduate level. Math in QM includes a lot of linear algebra, as well as some more advanced material, like the representation theory of Lie Groups. Even if you have a handle on the math, physics isn't always formal, and you will certainly need to have a well-tuned intuition. It sounds like you mostly have the background, just brush up on the basics.
Jun
19
comment Funny identities
Sophomore's Dream?
Jun
18
answered What is a good book to study linear algebra?
Jun
11
comment Set {1,1} = Set {1}, origin of this convention
Computer scientists tend to think of sets this way.
Jun
11
comment Question about flat modules and exact sequences
I agree with Serkan's answer, but it's worth noting that in your example, $\mbox{Ker}(f) = 0$ and $\mbox{Im}(g) = C,$ just by exactness. So the equivalence you desired actually holds.
Jun
7
awarded  Commentator
Jun
7
comment Conjugacy classes and irreducible representations of GL_2(q)
A good reference for this is Fulton and Harris. They have a very complete analysis of the irreps of $GL_2(\mathbb{F}_q).$
Jun
7
comment Is there really no way to integrate $e^{-x^2}$?
Sure, just use polar coordinates. That's what Gauss did.
Jun
6
comment Winding number on a simply connected region
A simply connected open set is, by definition, is a set in which every closed chain is homologous to a point. I.e., an open set in which, by definition, every closed chain has winding number 0. There's not necessarily an intuitive reason, but the motivation for the definition is that these are exactly the open sets in which you can define the logarithm.
Jun
6
answered Application residue theorem for improper integrals
Jun
3
comment Order of Essential Singularity
No. The term order only applies to removable singularities. Your functions both have "infinite order" poles; $e^{1/z^3}$ certainly does not have a singularity of order 3 at 0.
Jun
3
awarded  Supporter
Jun
3
comment Applications of monads in general topology?
As Sl2 said, adjoint pairs give rise to monads (and conversely, every monad gives rise to an adjoint pair of functors). These objects are ubiquitous in topology. The modern approach to homotopy theory relies on a categorical framework, and many theorems are framed in this language.
Jun
3
comment How to prove there are an infinite number of squarefree numbers of the form $2^p-1$?
Well, if you believe that there are infinitely many Mersenne primes, you automatically believe this fact. My guess would be that this is a hard fact.