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I'm mostly self-taught and while I know (and use) many advanced mathematical topics, I often enough find holes in my understanding of lower level math. Is there an exam (or series of exams) I could self administer to evaluate where I need to focus to improve my understanding?

The scope of such testing should run from elementary algebra and geometry through advanced linear algebra and partial differential equations. It isn't that I need to study the entire topics, just I think I've skipped or forgotten small concepts here and there.

Shaun
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ConfusedStack
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  • Khan Academy has some kind of self-test that might be useful. It obviously wouldn't cover though Linear Algebra and PDEs, though. – apnorton Jan 29 '14 at 17:14
  • One place to look for more advanced material is graduate school entrance/qualifying exams. Many schools post their old exams - just search for "graduate math qualifying exams" or something. (For instance, I know UNC posts theirs). Also, GRE study books (general and subject) should help. – icurays1 Jan 29 '14 at 17:24
  • One way to approach this is to get a book on the topic you are interested in and then see whether you know what each chapter is about and understand its contents. On the other hand, what is in the books, what is in the tests, what is useful in applications/research are all different things. – dtldarek Jan 29 '14 at 17:34
  • Does this answer your question? Learning mathematics as if an absolute beginner? – user1147844 Oct 07 '23 at 09:24

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I think what you are doing right now is fine. If you need something, read up on the matter. In my experience, when trying to learn "preemptively," it will often happen that when you need something you'll have forgotten (or perhaps there is now a better way, or new textbooks/lecture notes have shown up).

On the other hand, if there are areas that you repeatedly find have holes, get serious on studying them. The lecture notes by William Chen cover much of the undergraduate curriculum in clear, approachable style. I'm sure you'll find other suggestions digging here.

vonbrand
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