3 ms·

I share a similar experience. I have a course on Numerical Optimization, and I feel that I have learned more linear algebra, and matrix calculus in 2 weeks than

I share a similar experience. I have a course on Numerical Optimization, and I feel that I have learned more linear algebra, and matrix calculus in 2 weeks than I did my whole undergraduate course. I also delved a bit into differential geometry to argue the correctness of the implementation of my gradient functions using the finite difference method. Honestly, this has been the most fun I have had in a course in a long time. It's difficult at times, and there are many things one needs to learn, but this is how learning should be done imho.

samhw 5y ago
That's really cool. If you have any pointers to any resources along those lines, I'd be really interested. And I absolutely agree. It's a tragedy that maths is taught in such a dry, unengaging way. I think far more people would enjoy it and excel at it if only it were taught in a way that motivated them. Your experience is one of a million demonstrations of that. For what it's worth, there are a couple of Wikipedia pages which I found to be great jumping-off points - effectively 'sitemaps of mathematics' - to explore mathematics and what parts you may not know yet: https://en.wikipedia.org/wiki/Mathematical_structure https://en.wikipedia.org/wiki/Mathematical_structure https://en.wikipedia.org/wiki/Outline_of_mathematics https://en.wikipedia.org/wiki/Outline_of_mathematics They also present 'ways of looking' at mathematics which I find can be eye-opening with any subject. I don't know if you're a lumper or a splitter (https://en.wikipedia.org/wiki/Lumpers_and_splitters https://en.wikipedia.org/wiki/Lumpers_and_splitters), but I'm a lumper, so it helps to see connections and unities between things deep down. (Anyone who's ever read the annoyingly separate study areas of automata vs state machines, and the replicated abstractions and principles – despite them being literally the fucking same thing – will probably see what I mean.)

samhw 5y ago

That's really cool. If you have any pointers to any resources along those lines, I'd be really interested. And I absolutely agree. It's a tragedy that maths is taught in such a dry, unengaging way. I think far more people would enjoy it and excel at it if only it were taught in a way that motivated them. Your experience is one of a million demonstrations of that. For what it's worth, there are a couple of Wikipedia pages which I found to be great jumping-off points - effectively 'sitemaps of mathematics' - to explore mathematics and what parts you may not know yet: https://en.wikipedia.org/wiki/Mathematical_structure https://en.wikipedia.org/wiki/Mathematical_structure https://en.wikipedia.org/wiki/Outline_of_mathematics https://en.wikipedia.org/wiki/Outline_of_mathematics They also present 'ways of looking' at mathematics which I find can be eye-opening with any subject. I don't know if you're a lumper or a splitter (https://en.wikipedia.org/wiki/Lumpers_and_splitters https://en.wikipedia.org/wiki/Lumpers_and_splitters), but I'm a lumper, so it helps to see connections and unities between things deep down. (Anyone who's ever read the annoyingly separate study areas of automata vs state machines, and the replicated abstractions and principles – despite them being literally the fucking same thing – will probably see what I mean.)