Questions tagged [learning-roadmap]

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4
votes
0answers
215 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 ...
2
votes
1answer
108 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 ...
17
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8answers
4k 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 ...
12
votes
2answers
648 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
2answers
716 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 ...
16
votes
2answers
1k 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 ...
8
votes
1answer
605 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 / ...
11
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0answers
288 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 ...
31
votes
6answers
4k 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 ...
5
votes
2answers
703 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), ...
26
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3answers
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 -- ...
4
votes
0answers
150 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 ...
5
votes
0answers
961 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
1answer
1k 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 ...
7
votes
0answers
260 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 ...
10
votes
5answers
2k 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 ...
18
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9answers
5k 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 ...