Ages
16+
"Proofs: A Long-Form Mathematics Textbook" is a book about proof that focuses on commentary, motivation and explanation rather than dry proofs and examples. The book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. It also contains appendices on proof methods, especially beautiful proofs and writing advice. The proofs are accessible and in many cases the draft or "behind the scenes" work within the proof is included before the proof, so that students can see how they might begin constructing similar proofs.