# Tagged Questions

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

88 views

### Is a pure mathematics degree worth it from a financial standpoint? [closed]

I know this isn't a math question but this has been on my mind for quite some time. I am a second year university student who is planning on getting a degree in pure mathematics. I really enjoy the ...
141 views

### Lonely theorems [on hold]

What are some instances of theorems which are especially unique in mathematics, i.e. for which there are not many other theorems of a similar character? An example I have in mind is Pick's theorem, ...
20 views

### Maximum data storage in a paper sheet? which theory should I look for?

I'd love to study a problem: How much information can be stored in a blank paper sheet. with those considerations: "store in a sheet" means writte letters or numbers or equations, with a pen and a ...
832 views

### How do I tell if I am able to go to graduate school in math? [closed]

This is my first question on this site, and this question may sound disturbing. My apologies, but I truly need some advice on this. I am a sophomore math major at a fairly good math department (top ...
77 views

### Can Local Martingales be characterized only using their FV process and BM?

See Theorem 1 here. Theorem 1 Any continuous local martingale $X$ with $X_0 = 0$ is a continuous time-change of standard Brownian motion (possibly under enlargement of the probability space). ...
31 views

### How can I remember whether finite or countable cartesian product of countable set is countable

I always forget this result Is cartesian product of countable set countable under finite or countable cartesian products? Is there a good way to remember this? Like a proof sketch where the ...
39 views

### How can I study probability?

I want to have a deep understanding of probability. I've tried William Feller's first book on Probability, and E.T Jaynes' Probability theory - the logic of science (which is very different from most ...
56 views

### Are there any “default” properties which hold for almost all topological spaces in analysis?

What is the simplest/most general commonly used (type of) topological space in analysis? For instance, every example I can think of in analysis is first-countable. I don't think it can be metric ...
115 views

### Should a high schooler be concerned with the abstraction of mathematics? [closed]

I'm currently studying precalculus in high school and have no hands-on experience with advanced mathematics (calculus and beyond). Every time I learn something new, I feel the need to connect it with ...
68 views

### Topology on $\mathcal{C}(X,Y)$ to work with homotopy.

We know that the compact open topology on $\mathcal{C}(X,Y)$ is a good choice for topology on the set of continuous maps, but this seems really efficient, both naively and with respect to existence of ...
22 views

### Is the infinitesimal generator for Lie groups the same as the infinitesimal generator of a Markov semigroup?

Is the infinitesimal generator for Lie groups related to the infinitesimal generator of a Markov semigroup? Or are they totally different concepts? https://en.wikipedia.org/wiki/Lie_group#...
135 views
+50

### Can we characterize all infinite Euclidean-domains having exactly one invertible element?

$\mathbb Z_2$ and $\mathbb Z_2[x]$ are two euclidean-domains having exactly one invertible element ; my question is ; Can we characterize all euclidean domains $D$ having exactly one invertible ...