
Lecture Description
Basic Methods: We introduce basic notions from naive set theory, including sets, elements, and subsets. We give examples of showing two sets are equal by mutual inclusion. Then we define the power set and note Russell's paradox.
Course Index
- Propositional Logic
- Logical Equivalence
- Formal Proofs
- Methods of Proof
- Example of Complete/Strong Induction
- Example of Induction (Advanced): Balanced Strings
- Naive Set Theory
- Set Operations
- Two Tough Set Equalities
- Binary Relations
- Mappings 1: Examples
- Mappings 2: Basic Properties
- Mappings 3: Composition and Inverse Mappings
- Cardinality 1: Finite Sets
- Cardinality 2: Infinite Sets
- Divisibility Properties of the Integers
- The Euclidean Algorithm for the Integers
Course Description
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.
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