Day 03: Heart of Mathematics

Last Time

Next Time

Announcements:
- Reminder: no class Monday
- Assignment (for next time, Wednesday, 1/20):
  1. We'll be starting a unit on estimation. Read section 2.1, and try to decide if you have more hairs than Ed Burger or not.
  2. Finish your first submitted homework problems (due Wednesday, 1/20).
- Have you taken the attitude survey yet? You do this on blackboard. Take the survey by Tuesday night, 1/19 (it's under assignments).
Last time, in discussing the book, we made some important observations, such as that
1. The authors are trying to keep it entertaining.
2. You may need to read passages more than once.
3. While the stories are probably not meant to be deceptive, you may need to work a little harder to interpret them correctly.
4. The mathematics you're encountering may be unfamiliar, making it seem confusing.
Remember: Just do it! Give it the old college try....
We were taking a look at Story #7: Let's Make a Deal!
- Data:
  
  Strategy Initial Guess (# students
  who think this strategy
  is better) Guess after simulation
  
  Stick 17 2
  
  Switch 12 21
  
  Equal 8 7
  
  After simulation, you (collectively) decided to "switch to switching": let's see what the data looked like: for example, Nick and Andy played 10 games, and switching won 7 and lost 3 (which means that sticking would have lost 7 and won 3! -- that's an example of using symmetry in a problem).
  What did others discover? Let's look at the data....
- Now: can anyone explain why switching is, in fact, better?
  One way to convince yourself that switching is better is by planning a "bigger" game: what if there were one million doors, and you chose one -- then Monty Hall opened all but one of the doors to show mules.
  Would you switch, or stick with your initial guess?
Now let's look at any of the remaining problems that you'd like to ask about (having perhaps seen the solutions, and perhaps not!):
- 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?
  - The reason I find this one hard is because it involves psychology -- and making assumptions about other players.
New today: Let's take a look at the cannibal and missionary problem, #8 from section 1.4.
- Finding a solution is important
- Finding the most elegant solution is also important (in this case, the fewest steps).
- What about symmetry? Can we find a solution which is "symmetric" in some sense?

Website maintained by Andy Long. Comments appreciated.

Strategy	Initial Guess (# students who think this strategy is better)	Guess after simulation
Stick	17	2
Switch	12	21
Equal	8	7