Basic Methods: We define cardinality as an equivalence relation on sets using one-one correspondences. In this talk, we consider finite sets and counting rules.

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.