3
votes
3answers
305 views

Embedding Theorem for topological spaces, and in general

There are many examples throughout mathematics of abstracting the formal properties of a "familiar" structure, but then having a theorem stating that all models of the abstract axioms embed into one ...
14
votes
2answers
2k views

The non-traveling mathematician problem

This is a career question. I have just begun a research postdoc position in Southern California. It has been hard, but I've enjoyed teaching my first graduate courses and working on research and ...
11
votes
4answers
821 views

Applications of full integral weight modular forms in elementary number theory

Except for Eisenstein series having the divisor functions as their Fourier coefficients, is there any other full integral weight modular form (of some level, preferably full) having arithmetic ...
3
votes
0answers
1k views

What would an ideal mathematical note-taking/organizer/PIM software look like?

I'm struggling with this problem for a long time, and I'm sure a lot of you out there are having similar problems too: when studying from a e-textbook I read and annotate in one app and make ...
14
votes
5answers
2k views

Where to publish a paper on the Mafia game?

I wrote a research paper "A mathematical model of the Mafia game" (arXiv:1009.1031 [math.PR]). However, I do not know where to publish it. As an undergraduate studying majorly physics, I have little ...
36
votes
6answers
10k views

Best tablet computer for mathematics [closed]

I'm not sure if this is completely appropriate, but I thought I'd ask here. I'm in the market for a tablet computer. Unfortunately, my (mathematical) needs are very different from the needs of the ...
7
votes
4answers
1k views

Infinite games: are they well defined?

It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am ...
6
votes
7answers
1k views

What subfields of mathematics better lend themselves to visualization?

In some of my classes (e.g. graph theory, mechanics), the professors encourage the students to visualize solutions to problems; I do well in these classes. In other classes (e.g. linear algebra), we ...
14
votes
6answers
4k views

What's the notation for a function restricted to a subset of the codomain?

Suppose I have a function f : A → B between two sets A and B. (The same question applies to group homomorphisms, continuous maps between topological spaces, etc. But for simpicity let's restrict ...
11
votes
1answer
720 views

What is happening to Martin Gardner's files?

Martin Gardner kept voluminous correspondence with amateur and professional mathematicians worldwide throughout his career. His files are a treasure trove of information about all areas of ...
23
votes
14answers
3k views

Making sure that you have comprehended a concept

Hi, I have a question that I've been thinking about for a long time. How can you assure yourself that you've fully comprehended a concept or the true meaning of a theorem in mathematics? I mean how ...
12
votes
1answer
2k views

Anything going on for a mathematician stuck at New York?

First of all, apologies for the really non-standard question/announcement. I know this is not what MO was intended for, but in this situation it is the easiest way to reach (perhaps) the right person. ...
4
votes
2answers
1k views

Why are the Dynkin diagrams E6, E7 and E8 always drawn the way they are drawn?

The Dynkin diagrams of type ADE are ubiquitous in mathematics as solutions of various classification problems. The diagram E6 is usually drawn by five dots in a row with a sixth dot above the third, ...
19
votes
6answers
2k views

Generalizations of “standard” calculus

We have the usual analogy between infinitesimal calculus (integrals and derivatives) and finite calculus (sums and forward differences), and also the generalization of infinitesimal calculus to ...
5
votes
5answers
708 views

Visual representation of mathematical research interrelationships

I remember seeing a visualization in the form of a 2d (nodal) graph of all areas of academia, with math, physics and engineering over in one section, connecting in an arc to the central area of ...