How to Study Mathematics (2017)

Something I would add : Find out where the mathematics you're learning comes from : who first developed it? what problems where they trying to solve? why were they trying to solve those problems? what problems does it solve for us today? In my mathematical education I noticed that I had a more pleasant time and felt more motivated to learn the material when the teacher gave us this kind of background story. Since most teachers don't do so today…

PhD in math here with several published papers. And my recommendation is a metaprinciple: enjoy mathematics. Benjamin Finegold said similarly that the secret to chess is to enjoy every move. Personally, I had no trouble in mathematics, ever. And I think the reason for that is that I really enjoy just doing it, writing symbols down, learning about new theories, and even inventing my own. Not everyone will enjoy mathematics at first sight. But I think at least 50% of…

Also, use computers! I use SAGE extensively to get a feeling for lots of mathematical objects! 1. Grobner bases: http://bollu.github.io/computing-equivalent-gate-sets-using-... 2. Localization: https://github.com/bollu/bollu.github.io/blob/8cd335687ff3ef... 3. More broadly, an answer on math.stackexchange on how to debug math: https://math.stackexchange.com/questions/1769475/how-to-debu... 4. (WIP) continued fractions to compute pi: https://bollu.github.io/fractions/index.html And so forth. I find the…

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