TTC – Bruce H. Edwards – Prove It – The Art of Mathematical Argument

TTC – Bruce H. Edwards – Prove It – The Art of Mathematical Argument
English | Size: 4.69 GB
Category: Tutorial

Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. The experience is the closest you can get to glimpsing the abstract order behind all things.


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

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