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cg30e | 1 year ago | on: Reinforcement Learning: An Introduction (2018)

"Grokking Deep Reinforcement Learning" by Miguel Morales and "Deep Reinforcement Learning in Action" by Alexander Zai and Brandon Brown both look promising, though the code might be outdated. Looks like they use the OpenAI Gym environment, which has since been forked and maintained as Gymnasium.

cg30e | 4 years ago | on: Physics Student Earns PhD at Age 89

For sure. I'll list some books for introduction to proofs, abstract algebra, real analysis, topology and category theory. These are not comprehensive, just listing books off the top of my head. I'll definitely be leaving off personal favorites other people have. You'll like some better than others. Some of these are beginner books and some are more advanced. A good tutor can help you get through the more advanced books. I tried to list the most beginner friendly book first in the list under each subject. Then the more advanced books later in the list.

Introduction to Proofs:

Just pick one of these that speaks to you the most. All three are good.

Discrete Mathematics with Applications - Epp

Discrete Mathematics and Its Applications - Rosen

Mathematical Proofs: A Transition to Advanced Mathematics - Chartrand, et al.

Abstract Algebra:

How to Think about Abstract Algebra - Alcock

Abstract Algebra - Pinter

Abstract Algebra: A First Course - Saracino

Algebra - Artin

Abstract Algebra - Herstein

Abstract Algebra - Dummit & Foote

Linear Algebra:

Maybe an engineering based book first if you haven't seen linear algebra in a while (e.g. Strang or Linear Algebra: Step by Step by Singh).

Then:

Linear Algebra - Friedberg, et al

Linear Algebra Done Right - Axler

Linear Algebra - Hoffman & Kunze

Real Analysis:

How to Think About Analysis - Alcock

Understanding Analysis - Abbott

Tao's Analysis text

Principles of Mathematical Analysis - Rudin

Topology:

Topology - Munkres

Topology A Categorical Approach - Tai-Danae Bradley, Tyler Bryson, and John Terilla

Check out this list:

http://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf for others.

Category theory:

Categories and Toposes: Visualized and Explained - Southwell

Conceptual Mathematics: A First Introduction to Categories - Lawvere

Category Theory for Programmers - Milewski (if you like functional programming)

Programming with Categories - Fong, Milewski, Spivak (if you like functional programming)

Category Theory in Context - Riehl

There are a few others by Spivak which you may like.

If you don't know category theory whatsoever then I like Southwell the best (pair them up with his youtube videos). Eugenia Cheng also has a nice set of lecture videos.

If you already know math pretty well, then Riehl is a favorite.

Hope that helps!

cg30e | 4 years ago | on: Physics Student Earns PhD at Age 89

This is very inspiring. I too am young and been in the work force for several years, but unlike the other comments in this thread I am not settled down as an older student returning to school.

I am willing to give up a high paying salary to return back to school as a PhD student and I am not tied down with a mortgage or anything else.

I find mathematics simply too interesting to not learn at the highest level. Working in industry will simply not teach me the material I want to learn. I’m considering going back for either a PhD in Math or a math heavy PhD in CS. I read math textbooks for fun and worked with tutors to ensure my proofs are done correctly. I can do this for hours on end without external motivation. I taught myself a lot of math and can see myself doing this as a career. I want to do research.

Most people my age say the same things in the comment sections in this thread (tied down to a mortgage, make too much money to return). I’m glad generalizations like these don’t apply to me and can’t wait to get back to school

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