November 2014 Monthly Bragging Thread

elharo

Your job, should you choose to accept it, is to comment on this thread explaining the most awesome thing you've done this month. You may be as blatantly proud of yourself as you feel. You may unabashedly consider yourself the coolest freaking person ever because of that awesome thing you're dying to tell everyone about. This is the place to do just that.

Remember, however, that this isn't any kind of progress thread. Nor is it any kind of proposal thread. This thread is solely for people to talk about the awesome things they have done. Not "will do". Not "are working on". Have already done. This is to cultivate an environment of object level productivity rather than meta-productivity methods.

So, what's the coolest thing you've done this month?

I agree that not learning calculus is absolutely crippling. If the OP has not yet learned calculus, then I would say learning calculus should take precedence. On the other hand, if the OP has already learned calculus, then depending on the circumstances, studying an AoPS algebra book might not be a bad use of his/her time. (Or really just any AoPS book, really; from my experience with AoPS, they tend to write very good math books--or at least very good practice problems.)

Unfortunately, I have very little to say on the topic of increasing fluid intelligence. Outside of some basic introductory texts, my experience in the fields of cognitive science is close to nil, so anything I say about this can and probably should be taken with a generous helping of salt. I will point out that in my experience, getting better at math seems to have helped my general reasoning skills in ways largely unrelated to math; however, seeing as I would strongly like this to be true, it's possible that I am allowing myself to notice a trend where there is none. Additionally, it seems plausible to me that learning new math might not help intelligence due to domain-specificity, but that using already-learned math in extremely difficult situations might make a difference because in the latter case, the actual skill domain itself is less important than the mental gymnastics--and the increased ability to do those gymnastics might be transferable. Going through every theorem in the book and proving it, then, would probably fall into the latter category rather than the former.

So with all of that said, the question is: when you say you "[study] math intensely", do you mean covering new material, or doing inventive things with old material?

Going through every theorem in the book and proving it

This is how I study math. A result I've come across a few times is that trying a problem before learning how to do it, even if you fail, will result in you learning how to solve the problem better (this study (pdf), for instance). AoPS pedagogy reflects this; they encourage the reader to try each problem before reading how to solve it, even if they don't succeed. (I've been doing this long enough that I forget that this is a minority approach rather than common sense. Reminds my of this paper. tl;dr,... (read more)