I finished my math education some 15 years ago, around calculus 1 / linear algebra 1. I'd like to brush it up and learn more advanced concepts, just for pleasure. Ideally something practical, progressing towards mathematical understanding of modern physics (I know it's a long road, hence "progressing"). Tensor algebra/calculus seem like a fun and approachable goal to reach.
Now of course there are tons of great books and video lectures, but they all seem to lack practical exercises. At best they contain a few creative problems/puzzles for every chapter. I think it's because it's easier & more fun for the authors to explain things than come up with mundane practice sessions, kind of like writing application code is more fun than writing unit tests for it.
Meanwhile I really needs equations to solve, and lots of them, I never learned anything merely by reading about it. The ideal approach would be something like: here's an algorithm to multiply two numbers, now solve these 100 examples of AxB=?, here are some rules to derive a derivative, use it on those 100 examples of f'(x)=?. It's fine if part of the algorithm involves for example writing a python program to compute things numerically, as long as there is a clear set of inputs and outputs that you can test it on.
Any hints for finding such resources?
Now of course there are tons of great books and video lectures, but they all seem to lack practical exercises. At best they contain a few creative problems/puzzles for every chapter. I think it's because it's easier & more fun for the authors to explain things than come up with mundane practice sessions, kind of like writing application code is more fun than writing unit tests for it.
Meanwhile I really needs equations to solve, and lots of them, I never learned anything merely by reading about it. The ideal approach would be something like: here's an algorithm to multiply two numbers, now solve these 100 examples of AxB=?, here are some rules to derive a derivative, use it on those 100 examples of f'(x)=?. It's fine if part of the algorithm involves for example writing a python program to compute things numerically, as long as there is a clear set of inputs and outputs that you can test it on.
Any hints for finding such resources?