Proofs and discrete maths

Topics, in order

1. Logic and quantifiers
2. Direct proof, contrapositive, and contradiction
3. Induction
4. Sets, functions, and relations
5. Cardinality and countability
6. Counting and combinatorics
7. Divisibility and modular arithmetic
8. Graphs

Final exam

A few questions from every topic, to check you are ready to move on.

Learn from

• Hammack, Book of Proof (free online)
• Velleman, How to Prove It
• MIT OpenCourseWare 6.042J

Move on when

You can write a clean induction proof and a proof by contradiction.