All Questions
3,560 questions
74
votes
15
answers
18k
views
$f(f(x))=\exp(x)-1$ and other functions "just in the middle" between linear and exponential
The question is about the function $f(x)$ so that $f(f(x))=\exp (x)-1$.
The question is open ended and it was discussed quite recently in the comment thread in Aaronson's blog here http://...
- 24.7k
2
votes
0
answers
526
views
How much of math could be taught without using mathematical notation? [closed]
Given that mathematics is not about number, and that it is not even about the cryptic notation used to describe mathematical problems, how much of mathematics could be taught without reference to ...
13
votes
2
answers
863
views
Motivation for BMO
At the moment, I don't have access to the early 1960's paper of John and Nirenberg that (from what I understand) introduced the space BMO (bounded mean oscillation). Why were John and Nirenberg ...
- 261
72
votes
9
answers
16k
views
Why do functions in complex analysis behave so well? (as opposed to functions in real analysis)
Complex analytic functions show rigid behavior while real-valued smooth functions are flexible. Why is this the case?
- 1,093
18
votes
3
answers
1k
views
Uniformization theorem in higher dimensions
Let $M$ be a 4-manifold with a complex structure.
Does there exist a finite list of simply connected complex 4-manifolds $M_1, ... , M_n$ such that M is the quotient of some $M_i$ by the action of a ...
- 7,062
12
votes
2
answers
3k
views
What are conditions on real coefficients for zeros of a polynomial to be on the unit circle?
My complex analysis is decades in the rear view mirror. Perhaps someone here can help. I am looking for necessary and sufficient conditions on the coefficients of of a real polynomial of one complex ...
- 299
12
votes
4
answers
3k
views
Elliptic Curves, Lattices, Lie Algebras
I've recently started to look at elliptic curves and have three basic questions:
Is it correct to say that elliptic curves $E$ in the projective plane are in bijective correspondence with lattices $...
- 1,462
6
votes
4
answers
2k
views
Space of $(1,0)$-holomorphic forms on a Riemann surface
In a complex analysis course I have been given the following definition:
Let $X$ be a Riemann surface, denote by $H(1,0)$ the space of all $(1,0)$-holomorphic forms on $X$ and consider the quotient ...
- 143
22
votes
13
answers
8k
views
Category theory sans (much) motivation?
So I have a friend (no, really) who's taking algebra and is struggling to gain intuition for it. My story is as follows: I used to hate abstract algebra, with pretty much a burning passion, until I ...
80
votes
7
answers
20k
views
Teaching statements for math jobs?
What is the purpose of the "teaching statement" or "statement of teaching philosophy" when applying for jobs, specifically math postdocs? I am applying for jobs, and I need to write one of these ...