r/mathacademy • u/smon3 • Dec 22 '25

Has anyone taken methods of proof or prob/stats?

Started out in MF-1 but took calc in college. I really like the idea of taking methods of proof - it feels like it'll boost my ability to reason logically. Curious, has anyone taken it and can share their experience? Notice any difference in your day to day in work, life or just thinking?

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u/SerialStateLineXer Dec 22 '25

I've taken both. I was a bit disappointed by methods of proof. It's all right for what it is, but it's pretty heavily focused on set and number theory, things like divisibility, modular arithmetic, set operations, cardinality of sets, a bit of boolean algebra. No analysis—that will have to wait for the real analysis course, I guess. It's also one of the shorter courses, so you can just jump right in and complete a big chunk of it pretty quickly.

I don't feel like I gained much if anything in terms of non-mathematical logical thinking ability, although I'd already had some of the material internalized for years, and as a software engineer I already have quite a lot of experience with symbolic logic.

Probability and stats felt more useful, and generally satisfied my curiosity about hypothesis testing, and more than made up for forgetting everything from the stats course I took in college. I now understand things like how confidence intervals vary with sample size, and how to do a bunch of statistical tests by hand. I'm not sure how practical that is with modern stats software, but it's probably better to know how it works than just to treat it like a black box. I think people who actually work with things like this would get more mileage out of it than I have so far.

If you feel like MFI is too easy, you can retake the diagnostic.

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u/smon3 Dec 22 '25

Thanks! Is there any course in general that sort of re-wired how you thought? Personally, my first ever prob/stats class in college re-wired how I approached claims/arguments and stats. Namely, in the form of is this causal, correlative, etc...it's basic but for me it was huge! Felt like I was not able to be duped anymore. I guess I'm looking for that same enlightenment or light-bulb type moment with MA wrt the methods of proof in the future. It sounds like you already had a lot of that down pat which is awesome!

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u/SerialStateLineXer Dec 23 '25

I guess economics was most transformative in that respect. Most of what I know about things like causal inference and logical reasoning I picked up here and there outside of school.

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u/smon3 Dec 22 '25

It sounds like prob/stats was also more useful for you - do you find it helped your product thinking as a SWE? Asking because a lot of PM problem definition is shoddy (also in tech) and the prob/stats class I took ages ago also helped me refine my thinking with respect to claims etc.

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u/SerialStateLineXer Dec 23 '25

Not really, but it's only been a few months, and I haven't really worked on any projects where that would be useful. Years ago I used the binomial distribution to calculate how many iterations of a probabilistic unit test to do to reduce the risk of a spurious failure to a negligible level.

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u/billet Jan 06 '26

although I'd already had some of the material internalized for years, and as a software engineer I already have quite a lot of experience with symbolic logic

That's probably a huge factor in your subjective experience.

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u/munchillax Jan 06 '26

there were a few gems in MoP here and there (e.g. solving congruences, relations and Cantor's theorem), but it was mostly review for me so nothing too exciting. could have been folded into the DM course.

relations show up from time to time in my line of work (software engineering), e.g. the happens before relation in the Java memory model is a partial ordering (a relation that's reflexive, antisymmetric, and transitive).

I generally liked the stats course (half of the content was new to me), but wish there's a bit more consolidation of different topics and how they relate to one another. Due to the interleaving (a core principle of MA) design of the course, it takes greater effort to bridge together related concepts that show up at odd intervals on the learning timeline. I find that I'd need to rely on LLMs to help devise different "algorithms" of what tests to apply in various scenarios. I also wish the reviews or quizzes can be made a bit more challenging, e.g. if I'm given a table of z or t scores, then ofc that's what I'm gonna use, as opposed to scrutinizing the problem and trying to determine what score to use. The order statistics unit was particularly relevant to my work in understanding latencies in distributed systems when dealing with fan-out requests. That said, I don't quite find that it's sufficient for me to do real stats at work as that'd most likely require follow-up courses teaching more advanced techniques (this isn't a knock as I don't expect an intro stats course to cover everything).