Basic Methods: We define composition of mappings and draw parallels to multiplication of real numbers. Items include associativity, identity, and commutativity. Consideration of multiplicative inverses leads to the definition of an inverse mapping, and we give conditions for its existence.

1. Propositional Logic
2. Logical Equivalence
3. Formal Proofs
4. Methods of Proof
5. Example of Complete/Strong Induction
6. Example of Induction (Advanced): Balanced Strings
7. Naive Set Theory
8. Set Operations
9. Two Tough Set Equalities
10. Binary Relations
11. Mappings 1: Examples
12. Mappings 2: Basic Properties
13. Mappings 3: Composition and Inverse Mappings
14. Cardinality 1: Finite Sets
15. Cardinality 2: Infinite Sets
16. Divisibility Properties of the Integers
17. The Euclidean Algorithm for the Integers

Math Doctor Bob provides a brief course on logic, proofs, sets, and the integers. Intended as a prerequisite playlist for Abstract Algebra and Real Analysis courses.