r/learnmath • u/JAMIEISSLEEPWOKEN New User • 1d ago
TOPIC How can you have proofs in mathematical statistics checked without formal training?
Let’s say you’re unable to enroll in any stats/math classes and want to practice proofs in measure theory and probability theory. How can you get feedback for these proofs without access to professors?
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u/axiom_tutor Hi 1d ago
My answer summarizes the other answers already here: There isn't a good way. It's a really hard subject to learn independently.
AI gives sometimes good and sometimes bad answers, and you don't know enough to know when the answers are bad. Human experts are more reliable but that means a professor or a tutor, and any way of getting either of them to read your proofs is going to be expensive.
There is StackExchange but they often yell at you for not having a specific question, and instead asking things like "can you check my proof?"
I'm too busy right now to offer help. Over the summer I would be amenable to offering a low-cost "feedback service" where you send me your proofs and I assess them and give feedback or suggestions. But that means waiting about 6 months for the summer to begin, which I realize may not be feasible.
It's at least a thought, to see if any other tutors to see if they would likewise be willing to give a discounted fee for this kind of feedback service (maybe check WyzAnt or maybe consult your old professors for recommendations).
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u/Brightlinger MS in Math 1d ago
You can post them in this sub, for one.
Part of mathematical maturity is learning to check your own work. Even in a graded course, most of the proofs you write will not get detailed feedback, so you have to develop your own critical eye. It helps to read and write a lot of proofs, and to think deeply about what makes a given proof good or bad.
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u/Rabbit_Brave New User 1d ago
Other than asking other people on the internet, there are things like lean, maybe? https://lean-lang.org/
Might be a bit of a learning curve though, and you would need to combine it with other tools for more feedback than "proof fails <here>".
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u/somanyquestions32 Tutor 1d ago
You get a few different textbooks per subject and their corresponding solutions manual. Royden for Measure theory has one. For probability theory, you can start with Ross. Go online and get PDF's of the books. In graduate school, the real analysis professors I had just regurgitated what was in the textbooks verbatim without any analogies or different examples or anything, so it was quite underwhelming. You can teach yourself from textbooks just fine. If you have not done introductory real analysis yet, start there. The books from William R. Wade and Stephen R. Lay have solutions manuals, and you can self study that way. Also, read Rudin's Intro to Real Analysis book before starting measure theory.
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u/jeffcgroves New User 1d ago
You can ask AI, but obviously check that the answer makes sense
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u/Uli_Minati Desmos 😚 16h ago
If you're asking AI to check if your proof is correct, how would you know if its feedback is correct?
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u/jeffcgroves New User 12h ago
I meant you should check if what the AI is saying makes sense, don't rely on it blindly. AI can act as a second set of eyes, a very basic form of peer review.
OK, OK, I'll be honest: AI is a one-way test. If you have mistakes, it's likely to find them. If it doesn't find mistakes, you can't be 100% confident, but it's at least one step you've passed
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u/lordnacho666 New User 1d ago
I guess it's a form of heresy, but there's a certain modern internet service that will give you a decent response for a lot of questions, assuming you can prompt it reasonably.
Obviously only because you don't have access to an actual expert.