I had a student at MOP ask me something equivalent to “how should I study while at MOP?”1 For those of you that don’t know, MOP is the three-week summer camp for the USA’s team to the IMO. At first I was going to just link my FAQ. But then I thought about it a… Continue reading How to make the most out of MOP
Category: Learning Meta
Thoughts on teaching multivariable calculus
In my last semester of MIT I led a recitation (i.e. twice-a-week review) session1 for multivariable calculus (18.02) at MIT (although the first few weeks are all linear algebra). It’s different from many contexts I’ve taught in before; the emphasis of the class is on doing standard procedures, but the challenge is that there is… Continue reading Thoughts on teaching multivariable calculus
2011 N1 = 2024 A2
I am always harping on my students to write solutions well rather than aiming for just mathematically correct, and now I have a pair of problems to illustrate why. Shortlist 2011 N1 Here is Shortlist 2011 N1, proposed by Suhaimi Ramly: For any integer $latex {d > 0}&fg=000000$, let $latex {f(d)}&fg=000000$ be the smallest positive… Continue reading 2011 N1 = 2024 A2
MOHS was a mistake
I remember reading a Paul Graham essay about how people can’t think clearly about parts of their identity. In my students, I have never seen this more clearly than when people argue about the difficulty of problems. Some years ago I published a chart of my ratings of problem difficulty, using a scale called MOHS.… Continue reading MOHS was a mistake
A story of a town
This was originally a diary entry, but I showed it to some students who told me I should put it in my blog instead. Imagine you’ve moved to a new town, and want to explore the local offerings, because there’s a lot to do and see, and you’re expecting to live here a while. The… Continue reading A story of a town
Yet another reason I don’t give much generic advice
So I have an FAQ now for contest-studying advice, but there’s a “frequently used answer” that I want to document now that doesn’t fit in the FAQ format because the question looks different to everyone that asks it. The questions generally have the same shape: “would it be better to do X or Y when… Continue reading Yet another reason I don’t give much generic advice
Everything I need is on the ground
For me the biggest difference between undergraduate math and PhD life has been something I've never seen anyone else talk about: it's the feeling like I could no longer see the ground. To explain what this means, imagine that mathematics is this wide tower, where you start with certain axioms as a foundation, and then… Continue reading Everything I need is on the ground
Sometimes the best advice is no advice
信言不美，美言不信。 I get a lot of questions that are so general that there is no useful answer I can give, e.g., "how do I get better at geometry?". What do you want from me? Go do more problems, sheesh. These days, in my instructions for contacting me, I tell people to be as specific as… Continue reading Sometimes the best advice is no advice
On choosing exercises
Finally, if you attempt to read this without working through a significant number of exercises (see §0.0.1), I will come to your house and pummel you with [Gr-EGA] until you beg for mercy. It is important to not just have a vague sense of what is true, but to be able to actually get your… Continue reading On choosing exercises
Understanding with System 1
Math must be presented for System 1 to absorb and only incidentally for System 2 to verify. I finally have a sort-of formalizable guideline for teaching and writing math, and what it means to "understand" math. I've been unconsciously following this for years and only now managed to write down explicitly what it is that… Continue reading Understanding with System 1
Power Overwhelming 