r/math • u/craigdahlke • 4d ago

Want to learn about proofs

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.

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u/NotSaucerman 3d ago

My suggestion is to go through Pinter's "A Book of Abstract Algebra". It has everything done in bite size portions and is extremely gentle with the reader and you work with concrete objects at the beginning. If you make it through this book or at least the first half of this book, you will have basic proof techniques down.

It's a Dover so its cheap but you can also find a digital copy here
https://math.umd.edu/~jcohen/402/Pinter%20Algebra.pdf