Experience the thrilling pursuit of a mathematical proof in this course suitable for everyone from high school students to math lovers.
Overview
Syllabus
- By This Professor
- 01: What Are Proofs, and How Do I Do Them?
- 02: The Root of Proof-A Brief Look at Geometry
- 03: The Building Blocks-Introduction to Logic
- 04: More Blocks-Negations and Implications
- 05: Existence and Uniqueness-Quantifiers
- 06: The Simplest Road-Direct Proofs
- 07: Let's Go Backward-Proofs by Contradiction
- 08: Let's Go Both Ways-If-and-Only-If Proofs
- 09: The Language of Mathematics-Set Theory
- 10: Bigger and Bigger Sets-Infinite Sets
- 11: Mathematical Induction
- 12: Deeper and Deeper-More Induction
- 13: Strong Induction and the Fibonacci Numbers
- 14: I Exist Therefore I Am-Existence Proofs
- 15: I Am One of a Kind-Uniqueness Proofs
- 16: Let Me Count the Ways-Enumeration Proofs
- 17: Not True! Counterexamples and Paradoxes
- 18: When 1 = 2-False Proofs
- 19: A Picture Says It All-Visual Proofs
- 20: The Queen of Mathematics-Number Theory
- 21: Primal Studies-More Number Theory
- 22: Fun with Triangular and Square Numbers
- 23: Perfect Numbers and Mersenne Primes
- 24: Let's Wrap It Up-The Number e
Taught by
Bruce H. Edwards
