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Feedback. You can try to do math on your own, but you'll have a high chance of failing. You need to get feedback. Just like you can't learn a foreign language
by credit_guy 7y ago
Feedback.
You can try to do math on your own, but you'll have a high chance of failing. You need to get feedback.
Just like you can't learn a foreign language without interacting with the speakers of that language, it's very hard to learn math without speaking with people who know math.
So, by all means, find good books, good youtube videos (you can't go wrong with 3blue1brown), Khan academy, all those will help. But if you don't get feedback from people, it's easy to think you make solid progress when you actually don't. It's easy to not know what direction to pursue among hundreds of options.
How do you get feedback? If you can afford it, just pay for it. Nowadays there should be various online services that offer math tutoring. Get in touch with them, and tell them you'd like to go through Calculus 1, or Ordinary Differential Equations, for example. With a competent tutor, you can learn calculus in, let's say, 3 weeks, on your own, you could spend 3 months and still have serious gaps.
Edit: Because of feedback, it's actually easier to get good at programming than at math. In programming, you write programs, if they run and product the result you expect, that's great, if they don't, you realize right away you made a mistake.
So, if you can find a little coding project that forces you to learn math, you can get valuable math feedback by seeing that the program runs as expected. Ray tracing comes to mind. Maybe building an n-body simulator could be a fun exercise too. The phenomenal book "Turtle Geometry" teaches you math in this way, it asks you to write and run (and play with) various programs to produce quite some pretty pictures. You could go through it, and write all those programs in Python rather than Logo (Python has a turtle package embedded). With that book you can really learn a ton of math, including some Riemannian geometry.