Mathematical Contest in Modeling

Jim Morrow

The mathematical contest in modeling will be held on February 3-7, 2005. Teams consist of three undergraduate students. Each university can sponsor at most four teams and each department (and advisor) at most two teams. The Math Department will sponsor two teams. And we will probably get Amath to sponsor the others. I will be willing to serve as informal advisor to all teams, but we will need to get an additional faculty advisor (Rekha Thomas?) for the other two teams. We don’t need to make any of these decisions now. The Math Department will pay the registration fees for the math teams.

   My website, http://www.math.washington.edu/~morrow/mcm/mcm.html, has a lot of local informa-
tion. The MCM website is http://www.comap.com/undergraduate/contests/mcm/. You can find past

problems on this site. In addition there are two journals, The UMAP Journal and the journal Interfaces, which you can access from University computers and read on-line. You’ll need to get the password from the math librarian for the UMAP journal. You should spend some time reading the UMAP Journal as it has

winning papers plus a lot more. The MCM Prep website is http://www.math.washington.edu/~morrow/mcm/mcmprep.html.

As you can see, a winning paper has several characteristics.

• It has a precise statement of a mathematical problem that rephrases, at least partially, a vaguely stated question.

Then it has a solution of the problem. Solutions often involve combinatorics, graph theory, discrete mathematics, probability, differential equations, linear algebra, and calculus of one and several variables – mostly second and third year mathematics; and often they involve first or second year physics. It helps to be a double major as you get a good feel for the uses of mathematics and how to deal with uncertainty.

Then there is the exposition of the solution.

• You will need to learn L^{A}TEX.

   An introduction can be found in http://www.ams.org/tex/short-math-guide.html or also
http://www.math.washington.edu/Computing/Tex/. You will get computer accounts at MSCC which

give you access to the L^{A}TEXsoftware.

• It is important that the salient items be highlighted (as with this bullet).

Don’t bury important items inside lengthy paragraphs. Use graphics and tables to illustrate your points. That means you need to be prepared with L^{A}TEXtemplates in which to include the text and figures. The UMAP journal includes many comments and recommendations by judges. In particular they point out that there are few judges and hundreds of papers. There is a triage system. Each paper is given an quick (5-15) minute reading. You must make the first cut. Then a more careful reading is made. To make the “finals” your paper must be very good. The judges recommend that you not spend precious space deriving a known mathematical or physical result. Give a reference and procede. Don’t include computer code; at most include simple pseudo-code. Explain your methods in direct simple terms.

• Be ready to write programs in Matlab. Think of Matlab as a calculator where the data type is a matrix. Lots of documentation is available on-line.

• Use the Internet. You will have to find data and such search engines as Google are very useful.

We will arrange for you to have access to the MSCC computer lab in off-hours. This may be a problem if we have four teams, since we need to make sure there is a “firewall” between teams (no communication). If any of you can get access to rooms and computers other than MSCC that will help.

Let’s meet again next Friday at 4:30 and go over any suggestions and questions. Also think about how the teams should be formed. Each team should have someone skilled in L^{A}TEX, at least one with programming skills, all should be able to write well, and there should be a broad base of knowledge. During the contest you will want to divide up duties: one person writing, another computing or working on models, another searching the Internet, etc.

• Next meeting: Friday, October 15, 4:30 in Padelford, C401.