Questions tagged [learning-roadmap]

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Good references to understand sub-Riemannian geometry and Heisenberg groups

I'm looking for books and articles to understand a little about the Heisenberg group and sub-Riemannian geometry, specifically why the Heisenberg group is an example of a sub-Riemannian manifold, and ...
Ilovemath's user avatar
  • 575
21 votes
1 answer
886 views

Roadmap to Ergodic Theory

I have recently been interested in going deeper into ergodic theory, beyond an introductory level of knowledge. Background wise, my training has mostly been in stochastic analysis, and I have a ...
Nate River's user avatar
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11 votes
0 answers
1k views

Roadmap to geometric Langlands for a mathematical physics student

I am a student of both mathematics and physics, who has recently been studying string theory. My mathematics background is mostly differential geometry (principal bundles, Lie groups, etc.), although ...
Daniel Waters's user avatar
18 votes
9 answers
5k views

How does a Masters student of math learn physics by self?

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 ...
LZB's user avatar
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10 votes
1 answer
2k views

Roadmap to understand the Scholze's proof of the local Langlands correspondence for $\text{GL}_n$ over $p$-adic fields

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 ...
user860322's user avatar
10 votes
0 answers
1k views

Roadmap for p-adic Hodge theory

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 ...
Thigh High Crocs's user avatar
0 votes
2 answers
8k views

Mathematics Roadmap [closed]

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 ...
Student's user avatar
  • 25
4 votes
0 answers
492 views

A learning roadmap for topological modular forms

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 ...
Descartes Before the Horse's user avatar
2 votes
1 answer
193 views

Self study guide to Hamiltonian Monte Carlo

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 ...
22 votes
8 answers
7k views

Mindset to understand category theory

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 ...
15 votes
2 answers
1k views

A road map through group cohomology

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
1k views

Mathematics of GANs (generative adversarial networks)

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 ...
Turbo's user avatar
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20 votes
2 answers
2k views

Roadmap to learning the classification of finite simple groups

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 ...
ArB's user avatar
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8 votes
1 answer
855 views

Roadmap for Quillen 1

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 / ...
Quetzalcoatl's user avatar
11 votes
0 answers
418 views

Roadmap to homotopical group theory

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 ...
Alex Petzke's user avatar
38 votes
8 answers
5k views

Learning roadmap for Foundations of Mathematics (for the working mathematician)

(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 ...
efs's user avatar
  • 3,089
5 votes
2 answers
1k views

Background needed to understand modern research on knot homology theories

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), ...
user142103's user avatar
27 votes
3 answers
2k views

Where's the best place for an algebraic geometer to learn some algebraic number theory?

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 -- ...
Tim Campion's user avatar
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4 votes
0 answers
171 views

Road to holomorphic foliations?

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 ...
HeMan's user avatar
  • 319
6 votes
0 answers
1k views

What is the best way to learn about Modular Forms?

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

Arithmetical results to help study arithmetic geometry?

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 ...
Brennan.Tobias's user avatar
7 votes
0 answers
279 views

A roadmap to learn about finite-dimensional commutative associative real or complex unital algebras

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
3k views

How can I learn about doing linear algebra with trace diagrams?

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 ...
Kim Greene's user avatar
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47 votes
7 answers
14k views

Classification of (compact) Lie groups

I would like to study/understand the (complete) classification of compact lie groups. I know there are a lot of books on this subject, but I'd like to hear what's the best route I can follow (in your ...
20 votes
10 answers
6k views

Resources on invariant theory

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 ...
streklin's user avatar
  • 690