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Aug
28
comment Importance of Exercises in Mathematics for Self-Studying
"reading the prose of a text is a time sink and not that useful." Not that useful for what? What end do you have in mind?
Aug
19
answered The Riemann Sphere Interpretation
Aug
16
awarded  Notable Question
Aug
13
awarded  Nice Question
Aug
4
awarded  Yearling
Aug
2
comment Does $\displaystyle\sum^{\infty}_{n=1}\left(\frac{n!}{n^n}\right)$ converge or diverge?
I'm not sure I agree with your last two lines.
Jul
28
revised Spivak Calculus on Manifolds, Theorem 5-2
added 100 characters in body
Jul
28
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.