# Questions tagged [learning-roadmap]

The learning-roadmap tag has no usage guidance.

The learning-roadmap tag has no usage guidance.

21
questions

16
votes

8
answers

3k
views

I am a Masters student of math interested in physics. When I was an undergraduate, I took the introductory course of physics, but it is just slightly harder than high school physics course. To be ...

9
votes

1
answer

866
views

I would like to know which books I should read to understand the paper "The local Langlands correspondence for $\mathrm{GL}_n$ over $p$-adic fields" written by Peter Scholze.
I only know ...

6
votes

0
answers

438
views

I'd like to be able to start studying p-adic Hodge theory and hope that by posing this question, I can be better prepared to work towards it. I ask for a roadmap because I understand that I have a lot ...

0
votes

2
answers

2k
views

I immediately apologize for my English, Google translator is my assistant. I couldn't find the information in my own language.
My question is addressed to people who understand mathematics. I hope for ...

4
votes

0
answers

324
views

There are some MO posts about the uses of topological modular forms:
Why should I care about topological modular forms?
What can topological modular forms do for number theory?
I am interested in ...

2
votes

1
answer

130
views

I was wondering if anybody has a suggested self-study path to understand the mathematical aspects on Hamiltonian Monte Carlo.
In this paper The geometric foundations of Hamiltonian Monte Carlo
it is ...

19
votes

8
answers

5k
views

I am a 17 years old student and I am really interested in category theory due to its abstraction and beauty. I wanted to know if you'd have any advices to approach this theory and if you have papers ...

14
votes

2
answers

832
views

I am a PhD student in algebraic topology, and I would like to learn something about group cohomology.
The final goal would be to present one or two seminars on this topic, in order to give my mates a ...

7
votes

2
answers

975
views

Generative Adversarial Networks were introduced in http://papers.nips.cc/paper/5423-generative-adversarial-nets and has more than 20000 citations.
The paper introduced key paradigm changes which ...

18
votes

2
answers

2k
views

I want to learn the classification of finite simple groups. But it is often commented that it is a theorem spanning tens of thousands of pages of research papers. So it is quite intimidating to an ...

8
votes

1
answer

726
views

Question
Suppose you grasped and enjoyed reading Quillen's "Higher Algebraic K-theory I". Now, if you could go back in time to when you started studying algebraic topology and create a reading list / ...

11
votes

0
answers

337
views

I have been lurking here for a long time just enjoying the scenery from my beginner's viewpoint. I have a math.SE account but I think this question is appropriate here based on the nature of the ...

39
votes

8
answers

4k
views

(At the risk of being vapulated and downvoted, I'll ask this here.)
Suppose you work in a field that has nothing to do with the foundations of mathematics, but thanks to MO, you are becoming more and ...

5
votes

2
answers

871
views

I am a student of mathematics, and have some background in
Algebraic Topology (Hatcher, Bott-Tu, Milnor-Stasheff),
Differential Geometry (Lee, Kobayashi-Nomizu),
Riemannian Geometry (Do Carmo),
...

26
votes

3
answers

2k
views

There are lots of introductions to number theory out there, but typically they are streamlined to assume as little prerequisite knowledge as possible. I'm looking for a text which does the opposite -- ...

4
votes

0
answers

162
views

I want to know a "knowledge road" to holomorphic foliations. I assume that differential geometry and complex analysis is needed, but, what else? For example, I want to be able to read Lins Neto's book ...

6
votes

0
answers

1k
views

I am a senior Mathematics Major, and I am interesting in learning about Modular Forms. I have a layman's general sense of what they are but I was wondering if there is a lecture(I am willing to pay) ...

13
votes

1
answer

2k
views

I'm very keen to deepen my understanding of arithmetic and diophantine problems. In the past I studied some algebraic, analytic and sieve based number theory. Recently I've been reading Weil - Basic ...

7
votes

0
answers

265
views

I've always been secretly fascinated with the rich structure and applications of finite-dimensional associative unital algebras over complete fields. In particular, I am very much interested in the ...

12
votes

5
answers

2k
views

There is a wikipedia article. There is a paper by Elisha Peterson. I tried reading these but they don't seem to click for me.
Are there books or other resources for learning how to do linear algebra ...

19
votes

9
answers

5k
views

What are resources on invariant theory? Basically I've run into a need to teach myself some of the basics of invariant theory and was looking for a good place to start. I'd prefer online / freeish ...