![]() If your concerns are more broad - something along the lines of "what topics should I study if I want to give myself the rough equivalent of an undergrad degree in mathematics" - then your best bet is to pick out a few course catalogs from some top programs and systematically study each subject in whatever way works best for you. This coursework is often missing when using online material, hence my reasons for guiding my studies with textbooks. However, reading the definition and the proof and understanding both is much different than sitting down and working my way through a dozen delta-epsilon proofs. ![]() For example, I can absolutely understand the definition of continuity offered in analysis. Perhaps that is just me? I think having lots of exercises really helps reinforce my understanding of ideas. If nothing else, those structured courses are likely to more thoroughly cover each subject, which helps you avoid holes in your understanding of each subject.Īs I have begun to teach myself advanced topics in my spare time, I've found that working my way through books while supplementing with online materials works best. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. I think subscribing to a structured course, such as those offered through MIT's open courseware program, might be a better idea. ![]() However, Khan Academy is better used, in my opinion, as an ancillary resource. ![]() I enjoy it because I can focus specifically on those topics that I want to focus on. I've used Khan Academy here and there while earning my degree in mathematics to reinforce my understanding of topics that were covered hastily during lecture etc.
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