Compilation of helpful books, links, resources, etc.

Feel free to comment on anything (even vaguely) related below; that’s one of the biggest advantages of having these lists on a blog page.

All of my personal share-able things are on Dropbox here. (If the link is broken, try my MIT webpage, which I’m least likely to forget to update in such an event.) The main issue is organization: if I have time I might organize my AoPS posts, a lot of my ramblings, etc. into more usable forms. Currently the most helpful file in the Dropbox folder is in the “MOP 2014 handouts” folder, which is really just a organized repository for anything I find cool (especially those that don’t get enough treatment or clarification most of the time), or want to explore but need the pressure of teaching to actually do (a to-do list of sorts).

I’ll probably maintain a list of links and blogs in the standard WordPress format (always at the bottom of the page), but as above it would be nice to organize them somehow, since sometimes the truly great resources hide themselves very well: to give a recent example, I hadn’t realized the awesomeness of the (education), (big-list), (soft-question), etc. tags on MathOverflow, Math StackExchange, and Mathematics Educators StackExchange. Or the pseudonymous HroK blog (or a similar project, Radically Elementary Mathematics).

More generally, this seems like a good place to include small bits of advice; once there’s enough, perhaps almost anyone can find useful ideas. For example, in Olympiads people tend to start emphasizing a “mostly-just-do-problems” approach after some point (past books like AoPS, Engel PSS, Zeitz ACoPS), which leaves out a lot of the beautiful and inspiring story/theory/context/background of the problems. It is true that the exact resources don’t “matter” in some sense, but more guidance (even if students only internalize their favorite bits and pieces) and collective discussion (on these largely missing aspects) could only help (perhaps bridge the gap between Olympiads and higher math, among other things).

AoPS Olympiad Articles forum. Everyone seems to be dropping things here, and this could be a good place to crowd-source ideas and such. (One thing I did in my MOP 2014 handout was to link to discussion forums whenever possible, which I think makes the handout less “isolated” than it would be otherwise. But there’s still so much more room for exploration in this direction. For instance, Yufei Zhao and Holden Lee have great handouts and such, but everyone could gain so much more if these resources were somehow centralized, and constantly up for easy editing, active discussion, etc. See also Evan Chen’s website and recommendations.)

This also seems like (and this in fact inspired this page) a good place to compile off-the-beaten-path book recommendations. For example, Victor V. Prasolov’s Polynomials is quite interesting, and I’ll add more when I have time.