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Meet Bob. He's in his late twenties, and has not done any math since high school, where he was a B- student in STEM-related subjects and moderately disliked most of them. Bob is of above average intelligence, but not exceptionally bright (think +1 SD, midwit extraordinaire territory). One day Bob decides to renounce his wordcel ways and try to learn enough math in his spare time to leave his fake e-mail job and join a rigorous quantitative PoliSci program.
How many hours of intensive study do you estimate it would take Bob to get to the level of mathematical prowess of an average incoming first-year grad student in such a program?
Claude seems to ballpark that number at 600-800 hours (200-300 to relearn math up to Calculus, and 400-500 hours for undergrad math). To me this feels like a real lowball (there are like half a dozen videogames where I have twice as many hours, surely learning an extremely valuable skill must take a lot more time and effort – otherwise everyone would do it, right?), but maybe math is that easy, and Bob, like many people, just never really tried.
I find your estimate fair, if you take into account that Bob is not at the level of a skilled mathematician or programmer, for whom advanced math is bread and butter. A STEM graduate working in the profession can spend about 3-6 hours a day on math before getting tired, but for Bob two hours a day would probably be his limit. Time estimate is not as important as ability to use this time efficiently and meaningfully.
About 95% of programmers never use math beyond basic arithmetics. Exception is when you have to deal with physics and such (games, simulations, etc.) and crypto (but regular programmer would never ever roll their own crypto, they'd use a pre-made library), or maybe financial calculations. Of course, if you consider algorithms, computation theory and things like graph theory "advanced math", it's different but it's not the same kind of math as calculus or linear algebra are, I think.
Yes, graph theory is math, or at least the math department that gave me a doctorate for a dissertation in graph theory seems to think so :)
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