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by asdflkj
6705 days ago
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Start with mathematical logic, set theory, abstract algebra and number theory, in that order. Do not follow the usual course of calculus, differential equations, linear algebra and so on. That is, do learn those things, but later on. The problem with math education is that "the basics" (things that I recommend you start with) are neither easy to understand nor obviously useful in "the real world". Or at least the latter was true before computer science came along. But most educational programs were established before CS, so basic math is regarded as something you don't really need to know. But you do, if your goal is to understand math, and not to be able to design bridges as soon as possible. Now universities are gradually fixing the situation. They still start you off with calculus and such, but before you go on to more rigorous classes like Analysis or abstact algebra, they give you a "transition course", which is essentially a survey of the basics. |
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When I first started learning set theory, I wondered why this wasn't taught first since it was so fundamental. It took me a while to realise that I wouldn't have understood any of it, because you need some measure of number sense and a moderately well-formed abstract reasoning to appreciate this stuff.
Throughout my experiences in learning, I've always found that it is a zig-zag path - learning the superficial or applications, before drilling down to the fundamentals, and then going back to applications with a new sense of appreciation and so on. Going from the bottom up sounds to me like a recipe for losing interest in the subject very quickly.