Prove It: The Art of Mathematical Argument

Experience the thrilling pursuit of a mathematical proof in this course suitable for everyone from high school students to math lovers.

• 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