TTC Video - The Art and Craft of Mathematical Problem Solving With Paul Zeitz

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TTC Video - The Art and Craft of Mathematical Problem Solving With Paul Zeitz

Course No. 1483 | .AVI, XviD, 640x480 | English, MP3@96 kbps, 2 Ch | 24x30 mins | + PDF Guidebook | 4.47 GB

Instrucctor: Professor Paul Zeitz Ph.D. | Genre: eLearning, Mathematics

 

One of life's most exhilarating experiences is the "aha!" moment that comes from pondering a mathematical problem and then seeing the way to an elegant solution. And many problems can be solved relatively quickly with the right strategy. For example, how fast can you find the sum of the numbers 1 + 2 + 3 up to 100? This was famously answered in the late 1700s by the 10-year-old Carl Friedrich Gauss, later to become one of history's greatest mathematicians. Young Gauss noticed that by starting at opposite ends of the string of numbers from 1 to 100, each successive pair adds up to 101:

 

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

 

and so on through the 50th pair,

 

50 + 51 = 101

 

Gauss was already thinking like a good problem solver: The sum of the numbers from 1 to 100 is 50 x 101, or 5,050-obtained in seconds and without a calculator!

 

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.

 

Course Lecture Titles:

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

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

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

 

 

 

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