I am taking a seven week proof based course this summer called into to abstract mathematics (bridges the gap between calculus and proofs) and am using this book: Reading, Writing, and Proving: A Closer Look at Mathematics by Ulrich Daepp edition #2. I have never taken a proof based course, but will appreciate some tips on how to go about learning how to do proofs.
Topics we will cover: problem solving, logic, sets, relations, functions, modular arithmetic, induction and pigeonhole principle, sequences, and cardinality.