Day 01, MAT115

Next Time

Welcome!
Some thoughts for the day, and for the course:
- For you to be successful, your attitude is as important as your ability
- What you do shows what you are.
- Wherever you are, be all there. Jim Elliot
Most days there will be a "Question of the day": today's is

What's the probability that two people in this room have the same birthday?
I'm guessing that many of you like to gamble. I should definitely say that I don't encourage it!:) If you do end up gambling, I'd like you to gamble intelligently. Only gamble if you have inside information -- and that's often provided by mathematics.
3x5 cards: Please fill out the card, indicating
1. Name
2. Hometown
3. What is your calling? ("a calling has to do with one's larger purpose, personhood, deepest values, and the gift one wishes to give the world.... A calling is about the use one makes of a career." David Orr, Earth in Mind)
4. What is your dream job?
5. What is something special about you?
Introductions
The syllabus.
- 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.
  But I will have to lecture some....
- 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 with the idea.
- This to not going to be a "practical math" course: you will not learn how to balance a checkbook.
  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!
I will be using on-line materials as a text. (It's cheap!)
Because of scenes like this:

and this:

I have instituted the "Class Agreement".
Your first assignment is on-line: there is a reading (short, on-line) and an optional (extra credit) assignment, of explaining how a card trick works that I'll show you today.
In a sense this assignment is optional, but it might be good to give this first one a go. If you successfully solve the trick, you will receive one "GOHF" ("Get Out of Homework Free") card.
A GOHF card offers you a replacement for a missing assignment, or for an assignment that didn't go well. I drop those. This is automatic -- you don't need to do anything. At the end of the semester, I simply rank your assignments, and then drop as many of the lowest ones as you have GOHF cards. Then I compute your average.
What is this "Logo"? Here are a few examples that former students have done:
Our goal is more than just mathematics -- there are "Lessons for life" that we should focus on:
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 need to decide how much to bet that two people in this room have the same birthday.... And there's no sense betting if you can't win!
In math, you also don't bet if the odds of coming out ahead are against you. Which is why you shouldn't play the lottery. But I want you to see that math can be profitable....
Against my better judgement, I'll bet $20 against a student's $1 that there are two people in here with the same birthday. Anyone want to take that bet? [Hint: your expected payoff, dollar for dollar, is bigger than that of the Power Ball with a payout of a billion dollars!]
Now, once we get that out of the way, we should think about
1. how many should be in the room before you'd make an even money bet (my $1 against your $1) that there is a shared birthday;
2. and we might think about how to generalize this to other bets you could make!
Now, while you're thinking about those questions, let's get to that card trick that I mentioned awhile ago. It's all about your favorite kind of ice cream. I'll need a volunteer (or two)....
Your assignment, should you choose to accept it:
- How does the trick work?
- Does it always work (for all flavors of ice cream)?
- What is the secret to success?

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