I'm studying very basic Lie group theory by working through John Stillwell's Naive Lie Theory. The end-goal in this direction is to acquire the basics of modern differential geometry. If I make it to the end of this book, I've got Janich's Vector Analysis (differential manifolds, differential forms, Stokes' theorem in the modern setting, de Rham cohomology) and Loomis & Sternberg Advanced Calculus (all this and more, starting from basic linear algebra and multivariable calculus in a principed way). Not decided yet which of them I'll try to work through or both.
Independently of this, I would like to refresh probability and acquire statistics in a mathematically rigorous way. I tried Wasserman's All of Statistics that is sometimes recommended, but it's too dry and unmotivating for me. I like the look of David Williams's Weighing the Odds, which seems to be both suitably rigorous and full of illuminating explanations, but I haven't really tried reading it yet.
I'm with you on the probability & statistics. I think we might diverge in the end game for that particular result, but that's a long way from here.
So you've done analysis or not(?). I'm with you if you haven't.
This is a thread to connect rationalists who are learning the same thing, so they can cooperate.
The "learning" doesn't necessarily mean "I am reading a textbook / learning an online course right now". It can be something you are interested in long-term, and still want to learn more.
Rules:
Top-level comments contain only the topic to learn. (Plus one comment for "meta" debate.) Only one topic per comment, for easier search. Try to find a reasonable level of specificity: too narrow topic means less people; too wide topic means more people who actually are interested in something different than you are.
Use the second-level comments if you are learning that topic. (Or if you are going to learn it now, not merely in the far future.) Technically, "me too" is okay in this thread, but providing more info is probably more useful. For example: What are you focusing on? What learning materials you use? What is your goal?
Third- and deeper-level comments, that's debate as usual.