Prove It: The Art of Mathematical Argument

Offered By: The Great Courses Plus

Tags

Mathematical Induction Courses Number Theory Courses Logic Courses Set Theory Courses

Course Description

Overview

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

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

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