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Anatoly_Vorobey comments on What are you learning? - Less Wrong
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Math
I'm working through a group theory / analysis syllabus to remedy my gormlessness with proofs. If anyone else is gormless with proofs, we could form a Remedial Proofs Club, where we all fruitlessly push variables round a page for three quarters of an hour before giving up. It'd be like a secret handshake.
I've also been sitting on the Daniel Solow and Polya books with minimal motivation to work through them. Remedial Proofs Book Club, maybe?
I was about to begin trying to work through Elias Zakon's Basic Concepts of Mathematics, available free online at here. My motivations are similar to yours, and the idea of a Remedial Proofs Book Club is attractive to me. I chose this particular text only because it was free online and seemed to be written specifically for people at my level (got a 5 on the Calculus AB AP exam after high school, thought I was hot shit, took a rigorous Calculus course my first of year of college, couldn't do a single problem, cried real tears, traumatized). If you had a strong preference for different source material, I would switch to it if we could work through it together.
I want a deep understanding of elliptic curve cryptography. This led me to study algebraic geometry, which led me to study category theory. I think I'm ready to go back to algebraic geometry now.
I am not sure how comfortable you are with mathematics (and algebra in particular), but my courses in algebraic geometry were among the hardest I have taken so far (and the study of elliptic curves is a specialisation of the study of algebraic geometry). After studying algebra for 4 years I can now finally understand most of the introductory chapter of my book on elliptic curves, though not all of it. Since you want to learn about a specific algorithm rather than all of elliptic curves I think it shouldn't take you the 4/5 years that it is taking me, but be warned that acquiring a deep understanding might prove to be very hard.
This sounds like an interesting project. I've studied quite some category theory myself, though mostly from the "oh pretty!" point of view, and dipped my feet into algebraic geometry because it sounded cool. I think that reading algebraic geometry with the sight set on cryptography would be more giving than the general swimming around in its sea that I've done before. So if you want a reading buddy, do tell. A fair warning though: I'm quite time limited these coming months, so will not be able to keep a particularly rapid pace.
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 haven't read Weighing the Odds, but for what (very little) it's worth I attended one course lectured by Williams years ago and I thought he was an outstandingly clear lecturer.
I'm trying to learn Linear Algebra and some automata/computability stuff for courses, and I have basic set theory and logic on the backburner.
What's going on with your linear algebra. What text's are you looking at right now? I am interested in computability, and am working through some set theory right now.
Not sure this counts as a math problem, but I've been inconsistently playing go for about four years, and my current rank is 13 kyu. In the KGS server I'm username Waleran.
I haven't been playing on KGS recently, but if you're interested in a teaching game send me a PM and we can schedule something. I'm around 4k.
I've been working on relearning calculus, after noticing that I had forgotten most of what I learned in high school. I'm doing this with a text-book someone send me a pdf of (in a bunch of other books for learning about AI). The theory is going pretty well, but I find that I have some trouble actually getting the problems solved. I've been told this would get better with practice.
My impression is that the conceptual parts of calculus are valuable, but the "here is how to integrate by hand" parts are useless.
I just recently started to learn basic multivariable calculus (using this book + Khan academy etc.) to make progress on my economics self-study (using this magnificent book). This turned out to involve some of relearning of single-variable also, because much of what I learned in college and high school didn't quite stick. What's the book you're using? Are you aware of the best textbooks thread? Why do you want to study calculus?
Some statistics, especially confidence interval calculation for hypergeometric and binomial distributions. While not really necessary, adding proper confidence intervals to graphs of population samples of certain natural language phenomena makes the graphs look more professional (and fitting more rigorous).
Learning as in "want to understand what's going on and which equation to use", not as in "being able to derive the equations with paper and pencil without external help".