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Gerhard Paseman
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Ask lots of other what they are interested in and why, so that you can acquire a high level view of subjects quickly, even if you don't understand it.

My undergraduate education was spotty, and not well structured. I managed to graduate after taking classes in complex analysis, real analysis, measure theory, point set topology, algebraic topology, partial differential equations, differential geometry, undergraduate abstract algebra, martingales, mathematical physics, and a smattering of other topics, many of which I did not master. (There were also service courses and engineering courses, from which I deviated in my second year.) When I went to graduate school, I felt minimally prepared to study other subjects, namely recursion theory, algebraic number theory, and beginning model theory among others.

Looking back on it, I find it was more of an adventure that could have ended poorly if I hadn't found a supportive advisor and a subject I really enjoyed (universal algebra). Also, many of the other subjects I have forgotten as I never practiced them after first exposure. Now though, I feel I could enter those classes again and master the material because of my practice of learning. Instead, I have recently branched into subjects outside mathematics, and am finding myself using my abilities and training to prioritize learning parts of these other subjects.

Keep searching to find what you love to learn. For the stuff you don't love, leave it in some place where you can pick it up again when you change your mind about it later. Also, keep trying different techniques on areas you feel you need to master.

Gerhard "For The Love Of Questions" Paseman, 2020.03.09.

Gerhard Paseman
  • 13k
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  • 63