The whole problem was that I was taught to study math one page at a time, one sentence at a time, and never move on to the next thing until you understood the current thing. That's definitely not how I read a math text, anyway! I start by identifying what the main theorem is, and reading whatever definitions and preliminaries I need in order to understand the theorem, and also the bits about why the theorem is important. Then I identify what theorems/lemmas are needed to prove the main theorem, often by drawing a diagram showing how the different theorems/lemmas hang together and lead to each other. And then after that I dive into the proofs (if I actually need to--sometimes you just need to use the theorem).
I don't know that I necessarily needed to have harder problems in high school, or early in my university education. It might have been good, but actually I think we got a fairly okay progression. The master thesis was a sort of mini-graduate project, after all, and before that was various smaller projects. I think I just hit...well, it was partly about my abilities (I don't think I have it in me to be a brilliant mathematician), but also about my interests. I'm often serially geeky, and I had moved on to other geeky interests.
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Re: Grad school
Date: 2023-01-10 09:10 pm (UTC)That's definitely not how I read a math text, anyway! I start by identifying what the main theorem is, and reading whatever definitions and preliminaries I need in order to understand the theorem, and also the bits about why the theorem is important. Then I identify what theorems/lemmas are needed to prove the main theorem, often by drawing a diagram showing how the different theorems/lemmas hang together and lead to each other. And then after that I dive into the proofs (if I actually need to--sometimes you just need to use the theorem).
I don't know that I necessarily needed to have harder problems in high school, or early in my university education. It might have been good, but actually I think we got a fairly okay progression. The master thesis was a sort of mini-graduate project, after all, and before that was various smaller projects. I think I just hit...well, it was partly about my abilities (I don't think I have it in me to be a brilliant mathematician), but also about my interests. I'm often serially geeky, and I had moved on to other geeky interests.