B:  Find an example of a physical or simulation model used in everyday life (at least for someone – so models specific to professions are allowed).  Give a brief description of the model, what makes it a model, and what assumptions are being made in the model.

Note:  Your answer is clearly going to be in English, so I expect you to use appropriate grammar and spelling, and for your answer to be legible (in other words, if your writing is atrocious, type it).  I expect each to be about one or two paragraphs.  I would be surprised if either was more than a page.

a)  Give two fundamentally different goals for creating the groups.  (What does the camp counselor want to accomplish with the groups?)

b)  Choose one of your goals and create the groups based on that goal. 

c)  Write a paragraph or two to justify your group formations as if you were discussing their formation to the parents of the children.

A:  For the setting of Ex. 1.1, prove that if there are n players then you can not have a team with exactly n-1 players on it.

The proposal should be typed.  It should include a brief summary of your idea and a brief explanation of the level of mathematics or calculation required.  It should only be two to three paragraphs.

A:  Find the group preference ranking using the method of pairwise comparison with simple majority rule and the data on which electives you would most like to take.

B:  Find the most preferred alternative using sequential voting for the data on which electives you would most like to take.  Use at least three different sequences of comparing the electives.  Note that the same elective wins every time.  Explain why that will happen in this case.

C:  Find the group preference ranking using the Borda Count method on the data on which electives you would most like to take.

A:  Find the most preferred elective from the class survey using the Plurality-with-Elimination method.

A:  Use a Monte Carlo simulation to approximate the integral of exp(-x²) from -10 to 10.  Use a fairly large N.

B:  a)  Use a Monte Carlo simulation to approximate the integral of sin(x⁵)tan(5x²sqrt(x))/(1+e^xcos(e^sqrt(x)+2)) from 0 to 1.5.  Use N=1000 and run the simulation 10 times (record the answer for each).

     b)  Graph the integrand and speculate on what is wrong.