[Fr0styMatt88]

For proofs, could you recommend any good resources for a beginner? Is there a 'beginner proof' that's great to start with?

I figured out I actually like maths waaaay after I'd left uni. From that time at uni I have a vague memory of proofs being something like a whiteboard full of equations that I got lost somewhere in.

I have a vague feeling that what I'm thinking of is 'formal proofs', but I'm not sure.

[gumby]

Euclid. He tried to prove theorems of basic plane geometry (hence "euclidean geometry). Since we all have an intuitive understanding of (at least the basics of) plane geometry you can look at the work and not have to also learn the domain.

People recommending the classics can come off as pretentious so I will add that I am serious: a modern book of Euclid's methods should be quite accessible.

As a followon bonus: Minsky's and Papert's 1967 book "Perceptrons" (the one that said you can't do XOR with a single-layer network, though you can with a multilayer one) that lead to 25 years of lack of interest in neural networks is entirely about using neural networks on Euclid. So you can go from one to the other!

[aschismatic]

The first upper-division course I took in college concerned itself solely with learning the art of mathematical proofs. I had an excellent professor, so I can't really say how much this book helps with the learning process when used by itself, but we were assigned An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, by Peter J. Eccles. Might be a good place to start!

[ghufran_syed]

I really like "Mathematical proofs - A transition to advanced mathematics" by Polimeni, Chartrand and Zhang If you're looking for a free option, "Book of proof" by Hammack also looks good, but I have less experience with it ( https://www.people.vcu.edu/~rhammack/BookOfProof/ )