seminar ppt.ppt
- 2. Introduction • Solving a problem is not unlike climbing a mountain. • A good math problem, one that is interesting and worth solving, will not solve itself. • For beginners especially, strategy is very important. • Begin with psychological strategies that apply to almost all problems. • The solution to every problem involves two parts: the investigation and argument.
- 4. • The moral of the story, is that good problem solver doesn't give up. • Most beginners give up to soon, because they lack the mental toughness attributes of confidence and concentration. • Math problems are easier to deal with. • Start with easy problems, to warm up, but then work on harder and harder
- 5. Example
- 6. Solution
- 9. B. Creativity • Most mathematicians are "Platonist" • The good problem solver, then, is highly open and receptive to ideas. • The elusive receptiveness to new ideas is what we call creativity.
- 10. Example 1
- 11. Solution
- 12. • Learn to shamelessly appropriate new ideas and make them your own. • One way to heighten your receptiveness to new ideas is to stay "loose", to cultivate a sort of mental peripheral vision. • You need to relax your vision and get ideas from the periphery.
- 13. Example
- 14. Solution
- 15. Theme • Dont let self-imposed, unecessary restrictions limit your thinking. • Break or at least bend a few rules. • Toughen up, loosen up, and
- 16. Strategies for Getting Started
- 20. Example
- 24. Methods of Arguments • Arguments should be rigorous and clear • The more complicated the argument the harder it is to decide if it is logically correct. • Three distinct styles of argument: straightforward deduction, argument by contradiction, and mathematical induction.
- 35. Example
- 43. Strategies for Investigating Problems 1. Psychological Strategies A. Mental Toughness B. Creativity 2. Strategies for Getting Started A. The first step: Orientation B. I'm oriented. Now what?
- 44. 3. Methods of Arguments A. Common Abbreviations and Stylic Conventions. B. Deduction and Symbolic Logic C. Argumented by Contradiction D. Mathematical Induction 4. Other Importatant Strategies A. Draw a Picture! B. Pictures dont help? Recast the problem in other ways! C. Change your point of view.