Unsurprisingly(?) often, Cartesian products and general exhaustive combinatorial enumeration is pretty greathttps://twitter.com/krzhang/status/1268986931079024645 …
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Yeah I think combinatorics would be particularly fun for you at the amateur level because of how much you can do with just a couple of books. It’s one field where people had a lot of success getting minorities (whatever metric) involved since the show-of-value is very fast
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I wouldn’t do partitions at that time tbh. Lots of more rewarding subfields / books! (Generating functions, transfer matrix method, Catalan numbers, beautiful statistical mechanics models, designs...)
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