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2d
revised Spivak Calculus on Manifolds, Theorem 5-2
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2d
comment Spivak Calculus on Manifolds, Theorem 5-2
@RRTT: Thank you for catching that; you're absolutely right. Looking back on this, there are several things I don't quite like about what I have here. Hm...
Jul
27
comment Contractible spaces has trivial fundamental group.
Zach L: I'd be interested in hearing what your "clever transformation" $I^2 \to I^2$ is.
Jul
27
awarded  Popular Question
Jul
13
awarded  Nice Question
Jul
11
revised Which Fourier series are “legal”?
rolled back to a previous revision
Jul
7
awarded  Popular Question
Jul
1
answered How “far” a differential form is from an exterior product
Jun
30
awarded  Good Question
Jun
24
comment Integral becomes improper after a substitution
@AdamHughes: I'm sorry, but I don't quite see how this answers the question. What specifically is wrong with $\int_{\pi/4}^{\pi/2}\frac{1}{\sin(x)}\,dx = \int_{1/\sqrt{2}}^1 \frac{1}{z\sqrt{1-z^2}}\,dz$? (Do you agree that these two integrals are equal?) The question is: why should the substitution $z = \sin(x)$, where $x \in (\pi/4, \pi/2)$ return an improper integral?
Jun
21
comment Is $(-\infty, \infty)$ an interval?
@BenjaminRoycraft: "If a function is continuous on a closed interval, then it's bounded." That statement assumes that your definition of "interval" is "bounded interval." Because if you consider the closed interval $[0, \infty)$, say, then that statement is false.
Jun
15
awarded  Nice Answer
Jun
3
comment How to study math to really understand it and have a healthy lifestyle with free time?
I may be misreading this post, but there seems to be a suggestion that it isn't worth pursuing an academic career in pure mathematics if one is mediocre or second-rate. I'm not sure how I feel about that suggestion. There's also no mention of that other part of being a professor, namely teaching. That omission makes me uneasy: there are reasons other than research to consider academia.
May
30
comment Non Existence of a proper holomorphic map from the punctured unit disc to an Annulus
Not every continuous map is proper.
May
26
revised gauge-theory wiki description
added 318 characters in body
May
26
revised gauge-theory wiki excerpt
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May
26
wiki created gauge-theory description
May
26
wiki created gauge-theory excerpt
May
26
suggested approved edit on gauge-theory tag wiki
May
26
suggested approved edit on gauge-theory tag wiki excerpt