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Jul
5
accepted Characterization of the space of integrable functions stable under multiplication
Jul
5
asked Characterization of the space of integrable functions stable under multiplication
Jun
29
comment A good book on humankind’s understanding of primes?
Thank you for your recommendation. The book seems to be on freshman level, though, and only covers the Riemann hypothesis as you already stated. Anyway, thanks for bringing it up!
Jun
23
revised A good book on humankind’s understanding of primes?
deleted 1 character in body; edited title
Jun
21
asked A good book on humankind’s understanding of primes?
Jun
19
revised How to interpret material conditional and explain it to freshmen?
reworded the build-up to the questions
Jun
14
accepted Justifying the integral identity “$\int \mathrm{e}^{cx} \sin bx\, \mathrm{d}x = \frac{\mathrm{e}^{cx}}{b^2 + c^2}(c \sin bx - b \cos bx)$”
Jun
14
asked Justifying the integral identity “$\int \mathrm{e}^{cx} \sin bx\, \mathrm{d}x = \frac{\mathrm{e}^{cx}}{b^2 + c^2}(c \sin bx - b \cos bx)$”
Jun
7
revised Remember the implicit function theorem
edited body
Jun
2
awarded  Notable Question
May
31
comment Show that a map $f:X\to Y$ is onto iff $f(f^{-1}(C))=C$ for all subsets $C\subseteq Y$.
@Andrew You mean “$f(x) ∈ C$”. Other than that, the preimage of $C$ under $f$ is defined as $f^{-1}(C) = \{x ∈ X;~f(x) ∈ C\}$ and can be defined for any map $f$ – it doesn’t need to be surjective. (Maybe you thought of $f^{-1}(C)$ as the image of an inverse $f^{-1}$ of $f$ which would only exist if $f$ was already bijective. But that’s not how the symbol “$f^{-1}$” is used in this case.)
May
29
comment Why is the cartesian product so categorically robust?
I don’t know all of these categories, but – at least as far as I know – for most of them the corresponding forgetful functor has a left adjoint, thus is continuous. Morally speaking, I’d guess that so many of these forgetful functors have left adjoints because mathematicians (for historic reasons alone) tend to build stuff from sets and that already suggests a forgetful functor as well as an left adjoint for it.
May
28
comment How to not feel bad for doing math?
@AsafKaragila Why not? It’s a real concern to some and I guess it can be a real mood killer if you’re considering spending 3–5 years working hard on one particular problem/question. Even though I don’t pursue a career as a mathematician, I can relate to this concern. Why not take it seriously?
May
28
comment How to not feel bad for doing math?
@Did I added a comma and read the sentence as “It’s the only job I can think of, which doesn’t contribute to bettering the world somehow.”.
May
23
comment How to insert Gothic letters in Word?
That’s not a math question, though.
May
23
accepted Are binomial series multiplicative in their bases?
May
23
asked Are binomial series multiplicative in their bases?
May
21
answered Proving that the ball is converx
May
21
comment Proving that the ball is converx
Invoke the definition of convexity and the triangle inequality.
May
15
comment If a field extension contains a cyclotomic extension is it solvable?
Recall that a solvable group requires a subnormal series in which all factors are abelian. What can you really say about $\mathrm{Gal}(L/M)$? As an extreme case, take any non-solvable extension $L/K$ and choose $M = K$, which trivially is a cyclotomic extension.