I don't know if any of you might have any ideas or input, but I want to eventually study mathematics at the university. I'm currently at Precalculus and elementary Trig towards a Calc I/II/III sequence. I'm sure to have questions on these subjects. I guess I'm hoping to stack a curriculum on-top of this until I reach the university. Number theory and discrete mathematics definitely look interesting to me.
that sounds like a lot of fun. lots of directions to go in discrete math. i am happy to entertain any questions. my memory is broken but i do remember a trick or two from time to time.
a word of warning, and maybe others will disagree: in my view, discrete math is phenomenally harder than non-discrete math. it's like another dimension of difficulty. but it is also very accessible without refined tools.
if you have any interest in computer programming, it can be a useful assist in discrete math. a lot of the simpler propositions in discrete math are testable via small amounts of computer programming.
Nothing is going to turn you into Qiaochu. Although he never finished his degree, he knows and has a deep understanding of many, many fields of mathematics. Memorization of definitions is important.
In general, working lots of exercises and exploring examples and counterexamples is a good way to develop. Of course, that assumes you have some way if knowing if you've give correct proofs/solutions.
a class taught out of his algebra book was the best algebra class i ever took. but the instructor filled in a lot of gaps. the book itself was too intelligent.
i still have those notes. i should promote them from 'in storage above the garage' to 'in my office bookcase.' not a lot of things get taken there but they are good notes.
i cat-sat for one of his friends and he'd leave weird stream of consciousness messages on his answering machine. things to catch up on later. his mind was very, very fast.
not weird, i guess. just, most of us think at the speed that we talk and he was clearly at like 10x that and trying to get as much as he could down. it must have been frustrating for him to deal with normal people
i was on a call yesterday where i gave a very lawyerly answer to something. opposing counsel was trying to get me to shed light on something i had no real understanding of. i said, as if it were an answer, "i don't have an answer to that question." because i said it like it solved something, that was the end of it.
tone can do so much. substance, less so.
another person from our side was taking notes of the call, she wrote it down verbatim. she said it was lucky she was on mute because she couldn't stop laughing. it just shut the conversation down.
that's my answer, if you're in doubt. just say "i don't have an answer to that question."
leslie, you should have tried my technique. Chern and Satake were the examiners at my 1-hr oral on algebra . We were early, so I asked them a question I was stuck on. After 5 minutes, they had no idea and said we'd better get started. I aced the exam.
i had algebraic topology, of all things, as my minor topic. i was doing computations in the cohomology ring of something or other at one point. acting like i knew what i was talking about.
@leslietownes what's great about Algebraic Topology? I know it once was the main motivator of Hom. Algebra, which is now at the end of all areas of math
it's very common in the biological sciences. i advised someone on venture capital a while ago, i said, this startup looks like a jobs program for people who graduated from prof. X's lab. do not invest. i was right.
but sometimes i'm wrong and people make a billion dollars.
biology and chemical engineering are a classic place for people to set up startups that just limp along for about a decade, burn through all the money, and go nowhere.
most startups fail, and dramatically. in "STEM" it is often people just wanting to give jobs to people they know. the first thing a successful startup does is usually to throw the founders out.
i'll cut you a deal. $1200 for an hour of my time.
i do wonder how much of simons's thing was cleverness vs. market position. i don't think half of the people they hire are a quarter as clever as jim simons.
i can't count the number of times i've sent something as i go to bed and then in the morning my first email is absolutely everything i need from the vendor.
