Day 02, MAT115, Spring 2009

Introduction to Mathematics for Liberal Arts

Last Time

Next Time

Announcements:
- If you weren't here last time, please fill out a 3x5 card with the following information:
  1. Name
  2. Year (Freshman, etc.)
  3. Major
  4. Where you're from
  5. Something special about yourself.
- Please hand in your class agreement.
- We also need you to take an attitude survey about mathematics. You do this on blackboard. Visit our blackboard site, and take the survey by Sunday (under assignments). We won't use Blackboard much, but you're free to use it as you wish.
  You'll repeat this survey at the end of the course, to see if anything changes in your responses. If you complete both ends of this survey, you'll receive a 100% score on a homework.
- You have a Chapter 1 homework assignment for Monday, 1/26. See your assignment page.
- Please read Section 2.1 for next time: Counting
You should have read the chapter "Welcome" (pages xi-xiv) and Section 1.1;
Attempted stories #1, 3, 5, 6, 9 from Section 1.1.
You may have read Section 1.2 (hints), but did not proceed to read 1.3 (solutions).
The authors claim that our goal is more than just mathematics -- there are "Lessons for life (from our textbook, page 28)" that we should focus on:
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.
The course begins with some games. Last time we looked at one of the "fun and games" in chapter 1: "Let's Make a Deal!".
- And we even reached a few conclusions, after playing a few rounds:
  
  Strategy Votes
  
  Stick beats Switch 5
  
  Stick ties Switch 19
  
  Stick beaten by Switch 5
- Is one strategy better? If so, by how much?
- Can you justify your answer?
- Does it help to "play it bigger?"
- Your text may have come with a CD, loaded with some resources (like a version of this game) to help you with the material.
- Let's play it a bit using the CD version.
- How does generalizing the game help us see which strategy was more effective?
- Can we apply it to "life"? Can we become more effective thinkers?
Here's one you didn't see in Chapter 1: Let's try a little gambling game... about birthdays.
- We're going to go around and check birthdays (just month and day, not year!)
- A wager...
- Let's start with the months, and then we'll just check all those with the same months.
- What's the chance that two student in this room have the same birthday (month, day)?
- What are the odds? (What are "odds"?!)
Now: which of the games that you played in Chapter 1 would you like to investigate? I'll give you all first choice, before I choose.... Here are the games:
- Meanie Genie:
  - What other numbers of stones could we weigh and still solve the mystery, subject to these conditions?
- Fountain:
  - What other quantities of liquid can we dispense with these cups? Are there quantities that we can't dispense, subject to these same conditions?
- Tight Weave:
  - Suppose it takes an amount of Gold G to cover the rug.
  - If each of the eight smaller purple squares becomes a perfect replica of the original rug, then each of the smaller squares will have exactly G/9 of the gold in them.
  - The center square is entirely gold, of course.
- Dodge Ball:
  - Can you always win?
- Dot of Fortune:
  - What part do your opponents play in your play?
One question you may have is this: what will exam questions look like? On an exam, you may see a problem like one of these. Ideally, you might solve it; on the other hand, if you can't, if you can propose and justify some of the strategies that our authors suggest, or some that we've discussed in class, that will get you some credit even if you don't arrive at the right answer. So pay careful attention to the strategies for solving problems!
Number one of course is "Just do it!": if you merely write "I have no idea how to approach this," imagine how many points you'll get....

Website maintained by Andy Long. Comments appreciated.

Strategy	Votes
Stick beats Switch	5
Stick ties Switch	19
Stick beaten by Switch	5