For programmers wishing to learn to do applied math: I'm very sorry to tell you, the solution is obvious and you've thought of it already: hard graft. Pick a

For programmers wishing to learn to do applied math: I'm very sorry to tell you, the solution is obvious and you've thought of it already: hard graft. Pick a project, work at it, read text books and watch video lectures as you come across unfamiliar territory. Solve lots of problems. Rinse, lather repeat. (Yes, I've been through that journey, and I can slowly see myself coming out the other side. Took me about 2 years so far, it's still the beginning but it's not scary anymore.) Tips: - You ARE smart enough. It's this hard for almost everybody else, too. Our brains were designed to gather fruit. - Find other people to physically sit and work through problems with. (This is really where college shines). - Read some meta-math books. Like How to Prove It and How to Solve It. - Use Gershenfeld's "The Nature of Mathematical Modelling" as a guide. Do all problems. Find other sources on each topic, use those to help you. - Get on MIT OCW and do 18.085 and 18.086. Do all the problems. If you haven't had linear algebra, calculus, or diff EQs, do those courses too (this will take a while if you have to do all of it from scratch). - If you want to use (rather than invent) basic stats/ML, all you need is probability, simple linear algebra, simple calculus, and convex optimization (free book from Boyd). For many applications, you need substantially less. - Spend time in a technical library. Just browse. Find a book that's interesting and in which the first two chapters seem comprehensible (though probably not obvious). Take it home and do all problems. - Read Peter Szekeres "Modern Mathematical Physics". This book more than any other made me realize math is fascinating rather than scary. - It sounds stupid, but I learn better (and enjoy it more) when I let myself get genuinely excited about the material. Even the Intermediate Value Theorem is seriously cool when you really think about it. Remember: there's a lot to learn. You're trying to teach yourself what people spend years paying $50k/year to (barely) learn from lifelong teachers. It's always hard. But it can also be fun, once you're not totally lost.