Self studying the MIT applied math curriculum (2019)

I would love to self study with more vigor. I studied Mechanical engineering, but I find Math to be so beautiful. I think I chose the right education for the work I find meaningful in the world, but I wish I had more time to learn math that isn't directly relevant to what I am doing.

I'll certainly check out your site and save it for when the world is more peaceful.

Wow that's what I was gonna write. I did engineering too, and all of the topics listed in the course. But something about doing it to apply to other things is wrong, hard to say what. I remember in high school being quite fascinated by certain beautiful things in maths, and the applied stuff just isn't the same. I guess it just seems like tools. All the theorems are just kinda unsurprising, as far as I recall. Things like Stokes Theorem are kinda foreshadowed as you're doing your reading. Or various statements of continuity (DivGradCurl).

Luckily he left a link for the pure maths course.

I self study machine learning here https://learnaifromscratch.github.io/ai.html it's an early and shitty draft and proof of concept that you can do self-directed learning for these topics while looking up the background you need to know, which for me is much more interesting than taking a generalized math curriculum of absolutely everything. The courses so far we haven't escaped the content of Wasserman's 'All of Statistics' book yet on classification or probabilistic graphs, so you could if you wanted watch the lectures and only do Wasserman's book.

If you want to try the OCW linear route of taking everything for whatever reasons, you will have to get up to MIT student levels trying to unravel the algebra done in the early calculus courses and later where they just assume you possess this background. One way to do that is those problem solving books like this one which 'bridges the gap between highschool math and university' https://bookstore.ams.org/mcl-25 at least you then get worked out solutions. Another way is Poh-Shen Loh's Discrete Math course he opened up on YouTube which is done the same way he holds the CMU Putnam seminar, working through a bunch of combinatorics and algebra will more than prepare you to understand those continuous math OCW courses https://youtu.be/0K540qqyJJU

Like everybody else there is of course the issue of: who is going to check my work. For me I went with the time tested tradition of hiring a tutor, a local grad student and paid them once a week to go on chat/zoom or meet at a coffee shop before the pandemic and spend a few minutes going over everything I'm doing wrong. In the early days however I used constructive logic ie: 'proof theory', to audit my own work: https://symbolaris.com/course/constlog-schedule.html and read a huge amount of Per-Martin Lof papers on the justifications of logical operators like implies, disjunction, conjunction, etc. Of all the math I've ever taken I would say that proof theory was the most useful for somebody by themselves who isn't sure of what they are doing (I'm still not 100% sure.. hence why I hire people now).

If you want a great Calculus text that explains those nasty looking Euler's e nested statistics distributions try Mathematical Modeling and Applied Calculus by Joel Kilty everything from partial derivatives, gradients, x^n, e^x, trig, integrals, limits is explained in terms of parameters to modeling functions, if you write software it will be easy to understand. I haven't posted it yet but I tried going through Allan Gut's probability book using only that math modeling calc text and have not run into anything applied, as in concepts about limits or integrals, that wasn't already covered. Of course the concepts are much more abstract measuring a bunch of intervals and a different method of integration and I don't pretend I'll be making any advances in this area beyond applied usage but it can be done, jump in and pick up the background as you go as opposed to doing all the background at once, losing interest and giving up.