Studying Math

I’ve finished year one (of two) of a Master’s in Mathematics

For years, I had tried to learn higher math on my own. It’s tough going when one works in a challenging industry and moves quite a bit, but beyond that, there were some issues with my approach.

Hurrying

When I was in my early twenties, I hoped I could give myself the equivalent of a full math education. There were so many subjects that interested me. So much to learn. I bought many books. Then in my thirties, after failing in my twenties, I wanted to cram yet more into yet less time. The clock was ticking.

I’d start a book. I’d make progress. I could understand the concepts and the proofs. I’d press on. But this is a siren song with math books. Math books are dense. You need to do exercises, you need to go back and re-read, you need to mull over things. A quick read won’t do.

So, inevitably, an intense period at work would come, or a trip, or some other situation. I’d neglect my reading for a few weeks, and on coming back to study, I’d find myself out of pace, but also, in unfamiliar territory. I had not absorbed what I had read previously. I’d be crestfallen.

With classes, I got pacing. Some weeks I’d find the going easy, some would be a challenge. I’d go back over concepts again and again on exercises, then on exams. Just hearing the professor mention something as “well known” would show me that I needed to review some concept.

Insecurity

I wanted to know everything. All topics, all books.

This year, the prequel for the master’s degree, I’ve studied six subjects. And those are a lot. I’m happy with the amount I’ve learned.

Wanting to know it all, right away, is the same thing as wanting to read all the classics, or to know all the music. It is not an interesting goal.
Rather, it’s better to enjoy some music, some books, absorb them, and then go out for more if and when you feel like it.

It is reassuring to know that a committee of professors decided that these six classes would be adequate gap filling for someone coming from engineering.

This summer I plan to read three math books. Short ones, on topics I know something of already. Just want to prepare a bit for next year. A humbler goal than I used to have, and I think, an achievable one.

I am looking forward to the 2020 / 2021 session, with six new subjects I’m excited to learn.

Isolation

Having classmates and a professor, you’re in a rich environment of people who care about the subject you’re studying, whether geometry or algebra or set theory. Or greek poetry or biology.

A famous computer scientist who studied children said that if you want to learn French, you should be in an environment where French is spoken, and so it was for math. This particular professor, Seymour Papert, had studied with Jean Piaget, and thought computers had the potential to provide children with a math-land.

Papert’s work is very interesting, and his book, Mindstorms, is great.
In my case, though, the environment I was missing was more of the social kind.

You could practice basketball on your own for years, and be totally unprepared for a game.