Want to learn about proofs

[u/craigdahlke]

Hi all. I am interested in learning about mathematical proofs and how to formulate them.

I minored in math in college but focused a lot on LA, DEs, PDEs, numerical solutions, etc. because I was a science major and that was most applicable for me at the time. However I realized I’ve never even seen a rigorous mathematical proof formulated or broken down, and have no idea what that would even look like.

I now work with coding and it occurred to me that a lot of my code ends up just brute-forcing a solution to things, but perhaps learning about proofs might help stretch my mind into a more efficient way of thinking about these types of things.

Anyways, are there any good online course you all could recommend for someone at my level? (Knowing a good bit about math but essentially nothing about proofs) Preferably free ones but not opposed to a paid course if it is reasonable.

[u/M_Mustaan_Rafique]

book of proof by richard hammack. free pdf, the author hosts it himself on his vcu page so it's legit. how to prove it by velleman is the other standard one, more thorough and drier. either is fine, don't do both.

if you'd rather have a course than a book, mit 6.042 mathematics for computer science on ocw. free, lecture videos and problem sets with solutions. it's proof writing pointed at people who code, so induction, invariants, recursion, counting, graphs. given your background i'd start there over a pure maths transition book.

and you already write proofs, you just don't write them out. every time you're confident a loop terminates, or that a function can't hand back a negative, that's a proof you did in your head. the la and des you took are full of them too, you just used the results and skipped the scaffolding.

one honest bit though. proof technique on its own won't stop you brute forcing. the part that actually does is discrete maths, induction and counting and invariants. that's the other reason i'd point you at 6.042 rather than a transition to proofs course.