Math Perspectives Final Project and Homework

All work in this assignment should be neatly typed. (Mathematical formulas which are hard to type may be neatly inserted.) Any references used should be cited. All calculations should be shown and explained.

Please turn in the following statement with your work:

I have worked independently on this assignment. All of this is my own work.

Signed:__________________________________________________

1. Take a Golden Rectangle and attach a square to the longer side. Is the new rectangle a Golden Rectangle? Suppose you repeat the same operation with the new larger rectangle?

2. In Lavery Library near the Reference desk is a globe where you can answer the following question. Fill in this table. Write a paragraph which describes your methodology and contains any measurements you made.

Two cities	Latitude distance	Great Circle Distance
Beijing, China Chicago, Illinois
Mexico City, Mexico Bombay, India
Sydney, Australia Santiago, Chile

3. Pick an area with a lot of famous people such as baseball, acting, writing, politics, etc. Look up the birthdays of 40 baseball players or actors or writers or politicians or whatever. (Hand in your list.) How many had the same birthday (month and day, not year)? Write a paragraph or two explaining why or why not your result was surprising.

4. Suppose you manage a company with one major rival. For example you have a film rental store and there is one other in your town. On any given week, you have two strategies – high cost advertising and low cost advertising. Your rival has the same options. This table gives the payoffs in terms of additional profits. (Plus is good for you.)

	High cost ads	Low cost ads
High cost ads	-3	+1
Low cost ads	+7	-4

Assume the same issue arises each week. What strategy should you adopt if you think your rival understands game theory as well as you do? Show how you can increase profits if your rival doesn’t follow a game theory strategy.

5. If you throw a die seven times, what is the probability that exactly two times a 1 or 6 come up? I.e. What is the probability that you see a total of two 1’s or 6’s E.g. 561442 or 133645 or 562364

6. Write a 1-2 page essay explaining some use of statistics. This paper should reflect an imaginary scenario in which you think you could someday be involved. For example you may someday be a coach, store manager, researcher, politician, etc. Be imaginative but use the statistical concepts covered in class.

7. Write a 1-2 page essay explaining how Mathematical thinking differs from other areas. You can choose any topic covered in our text whether we covered it or not. Or you can choose to be more general.