Learning higher-mathematics on your own [closed]

manpreet Best Answer 2 years ago

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting.

I graduated with an M.S. in Computer science about a decade ago, standard curriculum that I believe is still somewhat taught (Calc, Multivariate Calc, Dif Eq, Linear Algebra, Discrete Math, etc.). I work as a software engineer (they give us a title of Computer Scientist for some reason) for an Contract R&D (gov stuff).

I have found my math skills withering over the years, probably for lack of use of particular fields. For the past couple of years, I am constantly reading research papers (computer science related) for background when developing a new algorithm. What I notice is that I will often get stuck on some mathematical notation or methodology that I am unfamiliar with, when trying to understand the paper. I have been attributing this to my withering math skills, and having to do with fields I never studied in school (or deeply enough).

I try to go back and review what I need to understand the paper, but this leads to a seeming unending link of I need to know this before I can understand that, etc.. With sometimes unsatisfying results.

I was wondering what people have experienced as the best way to learn higher math (advanced calculus, advanced prob and stats, tensor calculus, advanced linear algebra, etc.) as well as refreshing what they were taught in school MANY years ago.

I have tried looking course work on MITs website, to see what graduate math students are being taught. I procure those books and notes, and try to go through the class syllabus myself. But I guess its the lack of rigor, that is failing me the most (school imposed a strict rigor), so I end up just glossing over things when I should be trying to deeply understand thee material (trying to get at the meat of what I am trying to understand, for the task at hand). But over-all this seems ultimately flawed and I only come out with partial understanding.

I want to try to follow a method that would eventually get my math skills on par with a computer science PhD graduate level of understanding of the involved math (say with a focus on computer vision, AI, ML, and computer graphics). What I have been doing over the years is not working for me.

Any suggestions?