# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

2answers
176 views

### Are there powerful ways to use the topological definition of continuity in real analysis?

In the lectures for introductory real analysis, my professor repeatedly told the class that the topological definition of continuity (preimage of open is open) is the most powerful version of ...
0answers
28 views

### Understanding foundational terms: notions, objects and meta-objects

I am trying to take my problem solving skill to next level. It looks like It takes a lot of mathematical discipline. Here, This post buys me to get better at proof writing. So, I think is useful to ...
0answers
72 views

### Self Learning — Number Theory

I was wondering if there were any good online courses/lecture videos (preferably courses/videos but books would work too) for self learning algebraic number theory. I have seen sites like MIT ...
0answers
23 views

### Good introductory book on mathematical morphology

What is a good introductory book on mathematical morphology? It should outline the basic theory and a focus on applications would be nice. If possible, it should be approachable for a determined ...
1answer
24 views

### Marginilizing in multivariate Statistical Distributions

Suppose we draw $X = [x_1,...,x_i,...x_r,...,x_t...,x_j,...x_N]$ from $N(0,\Sigma)$. is there any way to compute $E[x_ix_j]$ and how about $E[x_ix_jx_rx_t]$ ? How can I compute the marginal ...
3answers
216 views

### Self study plan [closed]

I don't want to go to college and I came up with plan in the following order: ...
4answers
175 views

### What's the best way for an engineer to learn “real” math?

I'm an electrical/computer engineering student and have taken fair number of engineering math courses. In addition to Calc 1/2/3 (differential, integral and multivariable respectfully), I've also ...
9answers
9k views

### What's the point in being a “skeptical” learner [closed]

I have a big problem: When I read any mathematical text I'm very skeptical. I feel the need to check every detail of proofs and I ask myself very dumb questions like the following: "is the map well ...
1answer
49 views

### Why is the map $f(x)=e^{i2\pi x}$ from $[0, 1)$ to the unit circle continuous?

This seems to be a really silly question, I just couldn't think it straight. The definition of a continuous map: $f: X \to Y$ is continuous if for any open set $U$ in $Y$ , $f^{-1}(U)$ is open in $X$...
0answers
54 views

### How do I memorize mathematical proofs?

I first started wanting to know about the derivation of theorems because certain ones help you memorize the theorems better. But as I take harder math classes, it turns out better for me to use ...
3answers
146 views

### Learning mathematics for physicists from scratch

i am a freshman physics student and naturally my curriculum includes math-classes. The thing is, that -at least for the time being- teachers cover only the surface of topics so as to have only a ...
3answers
276 views

0answers
20 views

### Checking if estimators are sufficient

For an i.i.d. sample of random variables Xi distributed according to a normal distribution, known variance. I found a sufficient statisticâ€”the sample mean. How do I check if other statistic like (...
1answer
91 views

### Important topics to know in Algebra [closed]

I'm trying to prepare for graduate algebra but after looking at Dummit and Foote I realized that there's a lot of material (1000 pages). Which topics do you think a student should study in D&F to ...
1answer
78 views

### self-teach: In what order should I structure my studies?

I'm a 19 year old, who will be 20 in may. I didn't go to the greatest high school, and I didn't get the proper education to prepare me for college. I need to make a study plan for myself to truly ...