Day 02: Heart of Mathematics

Last Time

Next Time

Announcements:
- There should be a copy of the text on reserve at Steely Library, if you don't have a copy yet.
- Hand in your agreements
- Assignment (for next time):
  1. Finish understanding the stories (you may now peek at section 1.3, if you must!).
  2. Read Section 1.4, and have a look at problems #2, 5, 8, 9, 14 for discussion. Part of this assignment will be handed in:
    Pick two of those problems to write up and hand in. Your solutions should be typed up -- you can use this template (you can draw any diagrams by hand, but text should be typed). By the way: your work will be graded for presentation (including spelling, grammar, etc.), as well as for mathematical content.
    I suggest that you describe one problem that you managed to solve, as well as one that you couldn't. For the one you solved, show me how; for the one you couldn't solve, what did you learn? What is it that stops you from solving it?
    Due: Friday, 9/5/2008
    We'll discuss these next week.
- Have you taken the attitude survey about mathematics? You do this on blackboard. Take the survey by Sunday night (it's under assignments).
What do you think of the book? (First Impressions)
We will start by talking about the process of approaching solutions, rather than about the "solutions" themselves:
- I asked you to look at five problems:
  - Meanie Genie
  - Fountain
  - Dodge Ball
  - Let's Make a Deal!
  - Dot of Fortune
- Without giving away solutions, what made these puzzles hard? easy? fun?
- Without giving away solutions, what strategies did you employ to attempt to solve them?
- Did you follow the rules, and were they helpful:
  1. Make an earnest attempt to solve each puzzle.
  2. Be creative.
  3. Don't give up: If you get stuck, look at the story in a different way.
  4. If you become frustrated, stop working, move on, and then return to the story later.
  5. Share these stories with your family and friends.
  6. HAVE FUN!
- Did you find the hints helpful (Section 1.2, if you used any)? If so, which ones?
- Were any of the "lessons for life" helpful?:
  1. Just do it.
  2. Make mistakes and fail, but never give up.
  3. Keep an open mind.
  4. Explore the consequences of new ideas.
  5. Seek the essential.
  6. Understand the issue.
  7. Understand simple things deeply.
  8. Break a difficult problem into easier ones.
  9. Examine issues from several points of view.
  10. Look for patterns and similarities.
Now we'll take a look at a few of the games...
- Let's start with Story #7: Let's Make a Deal!
  - How's the game played?
  - Let's play it a bit: with a partner play the game 10 times, and decide between yourselves if either sticking or switching is a better strategy.
  - Is one strategy better? If so, how much better?
  - Can you justify your answer?
  - Does it help to "playing it fast?"
  - Does it help to "playing it bigger?"
  - Can we apply it to "life"? Can we become more effective thinkers?
- Now let's divide up for a look at the remainders:
  - Meanie Genie
    - Don't be a turkey!
  - Fountain
    - Just do it!
    - What other quantities can we make work? What won't?
  - Dodge Ball
    - Can you always win?
  - Dot of Fortune
    - What part do your opponents play in your play?

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