The Art and Craft of Mathematical Problem Solving (2 Book Set The Great Courses)

The Art and Craft of Mathematical Problem Solving by Professor Paul Zeitz (2 Book Set) The Great Courses

Part 1

Lecture 1: Problems versus Exercises

Lecture 2: Strategies and Tactics

Lecture 3: The Problem Solver's Mind-Set

Lecture 4: Searching for Patterns

Lecture 5: Closing the Deal-Proofs and Tools

Lecture 6: Pictures, Recasting, and Points of View

Lecture 7: The Great Simplifier-Parity

Lecture 8: The Great Unifier-Symmetry

Lecture 9: Symmetry Wins Games!

Lecture 10: Contemplate Extreme Values

Lecture 11: The Culture of Problem Solving

Lecture 12: Recasting Integers Geometrically

Part 2

Lecture 13: Recasting Integers with Counting and Series

Lecture 14: Things in Categories--The Pigeonhole Tactic

Lecture 15: The Greatest Unifier of All-Invariants

Lecture 16: Squarer Is Better-Optimizing 3s and 2s

Lecture 17: Using Physical Intuition and Imagination

Lecture 18: Geometry and the Transformation Tactic

Lecture 19: Building from Simple to Complex with Induction

Lecture 20: Induction on a Grand Scale

Lecture 21: Recasting Numbers as Polynomials-Weird Dice

Lecture 22: A Relentless Tactic Solves a Very Hard Problem

Lecture 23: Genius and Conway's Infinite Checkers Problem

Lecture 24: How versus Why-The Final Frontier