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

The Art and Craft of Mathematical Problem Solving (DVD & GUIDEBOOK)

Professor Paul Zeitz is a specialist in mathematical problem solving. A Professor of Mathematics at the University of San Francisco, he won the USA Mathematical Olympiad and was a member of the first American team to participate in the International Mathematical Olympiad. Since then, he has helped train several American International Mathematical Olympiad teams, most notably the 1994 team-the first to achieve a perfect score.

24 lectures/30 minutes per lecture

DISC 1

1 Problems versus Exercises

2 Strategies and Tactics

3 The Problem Solver's Mind-Set

4 Searching for Patterns

5 Closing the Deal-Proofs and Tools

6 Pictures, Recasting, and Points of View

DISC 3

DISC 2

7 The Great Simplifier-Parity

8 The Great Unifier-Symmetry

9 Symmetry Wins Games!

10 Contemplate Extreme Values

11 The Culture of Problem Solving

12 Recasting Integers Geometrically

13 Recasting Integers with Counting and Series

14 Things in Categories-The Pigeonhole Tactic

15 The Greatest Unifier of All-Invariants

16 Squarer Is Better-Optimizing 3s and 2s

17 Using Physical Intuition-and Imagination

18 Geometry and the Transformation Tactic

DISC 4

19 Building from Simple to Complex with Induction

20 Induction on a Grand Scale

21 Recasting Numbers as Polynomials-Weird Dice

22 A Relentless Tactic Solves a Very Hard Problem

23 Genius and Conway's Infinite Checkers Problem

24 How versus Why-The Final Frontier