Prove It: The Art of Mathematical Argument

[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