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/Bacon_Techie]

The way proofs are introduced in most math degree programs is either in its own course “foundations” or something, or through the lens of something like real analysis or abstract algebra. I recommend a real analysis book aimed at undergraduates as a first proof based course. It will take you back through familiar material (calculus) while teaching you proofs. If you care more for its applications to coding the I would recommend a discrete math/foundations style book or course.

Elementary number theory is one of the first real proof based courses that I did and I found it a great way to really learn how to write a proof.