The Art and Craft of Mathematical Problem Solving
In 24 mind-enriching lectures, The Art and Craft of Mathematical Problem Solving conducts you through scores of problems—at all levels of difficulty—under the inspiring guidance of award-winning Professor Paul Zeitz of the University of San Francisco, a former champion "mathlete" in national and international math competitions and a firm believer that mathematical problem solving is an important skill that can be nurtured in practically everyone.
These are not mathematical exercises, which Professor Zeitz defines as questions that you know how to answer by applying a specific procedure. Instead, problems are questions that you initially have no idea how to answer. A problem by its very nature requires exploration, resourcefulness, and adventure—and a rigorous proof is less important than no-holds-barred investigation.
Think More Lucidly, Logically, Creatively
Not only is solving such problems fun, but the techniques you learn come in handy whenever you are presented with an unfamiliar problem in mathematics, giving you the confidence to try different approaches until you make a breakthrough. Also, by learning a range of different problem-solving approaches in algebra, geometry, combinatorics, number theory, and other fields, you see how all of mathematics is tied together, and how techniques in one area can be used to solve problems in another.
Furthermore, entertaining math problems sharpen the mind, stimulating you to think more lucidly, logically, and creatively and allowing you to tackle intellectual challenges you might never have imagined.
And for those in high school or college, this course serves as an enriching mathematical experience, equal to anything available in the top schools. Professor Zeitz is a masterful coach of math teams at every level of competition, from beginners through international champions, and he knows how to inspire, encourage, and instruct.
01. Problems versus Exercises
02. Strategies and Tactics
03. The Problem Solver’s Mind-Set
04. Searching for Patterns
05. Closing the Deal—Proofs and Tools
06. Pictures, Recasting, and Points of View
07. The Great Simplifier—Parity
08. The Great Unifier—Symmetry
09. 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
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
02. Strategies and Tactics
03. The Problem Solver’s Mind-Set
04. Searching for Patterns
05. Closing the Deal—Proofs and Tools
06. Pictures, Recasting, and Points of View
07. The Great Simplifier—Parity
08. The Great Unifier—Symmetry
09. 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
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
