Comment by nathan_douglas a day ago
I third MathAcademy. I graduated high school >25 years ago with almost no math skills and had a major struggle with the math prerequisites for my CS degree ~15 years ago. I've been wanting to get into higher math recently, so a few months back I started hitting MathAcademy heavily. Its structure and modularity is exactly what I needed.
(I'm actually set to complete Mathematical Foundations II next week, after completing Mathematical Foundations I recently.)
Thank you for your comment. I had a very nontraditional path to engineering, even in an era of self-taught programmers, and I feel a lot of pain and despair and bitterness and, uh, a vicarious feeling of disappointment, I guess... so discussing this sort of journey does me some good.
> I feel like I learned "Discrete Math", but in the sense that all the lessons were discrete and I couldn't draw connections between them.
Very reasonable takes. I think you're spot on. I do have a lot of trouble with the abstractness and disjointedness of it. I'm hoping that repetition will improve it. So far I'm still struggling with the same things I struggled with in college - combinatorics, for whatever reason, just seems to slide right out of my brain.
By "modularity" I meant that I could squeeze in 10-15 minutes here or there without having to commit multiple hours to a single concept, and that I could take a day off without destroying anything, but that's probably connected to the "discreteness" you mention, without a holistic, oceanic kind of cohesion or connectedness.
I'm actually working on a project now, an educational site that's kind of along these lines but focused on areas of CS I've always struggled with - Lambda Calculus, Type Theory, Lisp, that sort of thing. I think I have some good ideas. I hope I come up with more, because I definitely want to build a rich mesh of knowledge rather than a catalog of disconnected facts and tools without any underlying meaning.
> Its structure and modularity is exactly what I needed.
Through great effort, I completed Mathematical Foundations I & II. I talked about it a bit here [1][2]. If you read through MathAcademy's methodology and reasoning, it's incredibly strong [3], but in practice I never felt confident in my understanding or execution, everything felt quite discrete and I didn't understand the relationships or purposes of what I was doing. I kept going because I was getting better, and because people online who were quite good at math said not to try too hard to understand things fully at first, since the abstraction level of math is so high.
The weeks before finishing MFII, my motivation was higher than ever. The day I finished, I felt nothing, and in the following weeks I decided that it was time to let it go for now.
I think MA is good. I've never done so many exercises in my life, and although I wasn't super confident, I was far better at math than I'd ever been. But I think MA probably needs a lot more multi-part exercises so you understand what you're doing and where to use things. I feel like I learned "Discrete Math", but in the sense that all the lessons were discrete and I couldn't draw connections between them.
https://news.ycombinator.com/item?id=42519882
https://news.ycombinator.com/item?id=43275665
https://www.justinmath.com/files/the-math-academy-way.pdf