Day 01, MAT115

• For you to be successful, your attitude is as important as your ability.
• What you do shows what you are.

1. Name
2. Year (Freshman, etc.)
3. Major
4. Hometown
5. Something special about yourself.

• Class will be organized around discussions of material, and activities. You must be prepared to contribute! My role will be to present and help clarify, but preferably to moderate discussions, and be a resource.
• I find that students are best at explaining ideas to other students. So what I shoot for is some students to get the idea in class, and then to "infect" the rest of the students.
• If you're expecting this to be a "practical math" course, you will be disappointed. This is a course incorporating material for a broad range of liberal arts disciplines. Some of them will be interesting to you, some of them may not. But this is not another algebra course. You may never have seen any mathematics quite like the things that we're going to study in this course!

1. Keep an open mind.
2. Just do it. Jump in. Make mistakes and fail, but never give up.
3. Often when we've done it once, we do it again. Follow up one good deed with another!
4. Understand simple things deeply.
5. Break a difficult problem into easier ones.
6. Look for patterns and similarities.
7. Explore the consequences of new ideas. Generalize.
8. Examine issues from several points of view.
   Don't be a turkey -- be a dog! (this one may require a little explanation....)

Now add your birthday (just month and day) to your card. We're about to find out!

Perhaps you have some other questions, which I hope that you'll take a moment to think about:

1. What is probability? What's the probability that a die comes up 5? 6? 5 or 6? (This is the focus of your first reading.)

2. What values do probabilities take?

3. Is there such a thing as "being due"? If my probability of making a freethrow in basketball is 1/2, and I miss this shot, will I (of necessity) make the next? If I miss three in a row, am I due?

4. Betting (and odds) is an equivalent way of thinking about this: how much would you bet against my bet of $20 that there will be two people in this room with the same birthday?

   Even money? If so, then you would be saying that the probability of there being two people with the same birthday is 1/2.

   You should only bet even money if the odds are in your favor...

• It's a famous problem, because it was popularized in a Parade Magazine column by Marilyn vos Savant. Here's how the problem arose, according to the Let's Make a Deal website: The controversial "problem" began when Marilyn vos Savant published a puzzle in her Parade Magazine column. One of her readers posed the following question:

  "Suppose you're on a game show, and you're given a choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number. 3, which has a goat. He says to you, `Do you want to pick door number 2?' Is it to your advantage to switch your choice of doors?"

  Ms. Savant, who's listed in the Guinness Book of World Records Hall of Fame for "Highest IQ" (228), answered "Yes." She received an estimated 10,000 letters in response, many arguing that she was wrong.... Was she?

• Another "Let's Make a Deal" applet (that keeps track of historical trends)