Class will be organized around discussions of material, and
activities. You must be prepared to contribute! My role will be
to present and clarify, but mostly to moderate the
discussions, and be a resource.
What's this project all about? Something you love, I
hope! You might discover mathematics in a game that you enjoy,
something you've noticed in a garden or at the zoo?
Here are some guidelines.
Hopefully you'll be working with a partner.
Our goal is more than just mathematics -- there are "Lessons for life"
that we should focus on:
Just do it.
Make mistakes and fail, but never give up.
Keep an open mind.
Explore the consequences of new ideas.
Seek the essential.
Understand the issue.
Understand simple things deeply.
Break a difficult problem into easier ones.
Examine issues from several points of view.
Look for patterns and similarities.
Don't be a turkey -- be a dog! (this one may require a little
explanation....)
I want you to think about finding mathematics in your everyday life. For
example, one of my favorite poets, Robert Graves, provides us with an
introduction to two ideas that we will study in his poem Warning to Children:
Do you have any stories about math from your youth?
Now, let the fun and games continue!
We'll begin with a famous mathematical example called "Let's make a deal!"
There are three doors, behind which are two donkeys and a car.
You choose one: Monty Hall then shows you a door behind which
appears a donkey, then offers you the chance to either
"stick" with the door you chose at first, or "switch"
for the third door.
Do you stick or switch? How can we decide?
It turns out that there is an "optimal strategy". Your
mission: determine what strategy is best.
Is it possible that by restricting the game, or by extending the
game, we might learn more?
Maybe we can simulate the game....
Let's break into groups to play:
Three cards represent the three doors; choose one card to be the "car", and the other two to be the donkeys.
Try 10 (or more) plays using the sticking strategy
Tally up the successes of each strategy (realizing that if
sticking wins, switching would have lost, and vice versa).
Is one strategy better? If so, by how much? "What are the odds?"
Then we'll combine the class's data, to "see what the data
says".
Now: Can you justify/explain your answer?
To give you more confidence in the answer (and perhaps to
learn more!), we may consider extending the game: what if we
have ten doors?
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