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The Mathematical Contest in Modeling (MCM) is coming up in a couple of weeks. With the idea that the competition is ultimately about teaching students to become better at mathematical modeling, I was wondering if anyone else on the site who has participated in the MCM or who coaches would be willing to share strategies they have for preparing for the competition. Since I'm bringing up the question, I'll start.

For those who aren't familiar with the MCM, the Wikipedia page also gives a brief overview.

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I've requested that this question be made community wiki. –  Mike Spivey Jan 31 '11 at 4:15
    
I am glad this question has been asked, but it might be too unfocused? When responding I wasn't sure what exactly to address. I felt like my answer would do better as a blog post or short essay. But since this is CW, it is probably ok. +1 –  BBischof Jan 31 '11 at 15:48
    
Congratulations on your team's outstanding result last year, Mike. –  whuber Feb 1 '11 at 22:02
    
@whuber: Thanks! :) –  Mike Spivey Feb 1 '11 at 22:56

4 Answers 4

In my personal experience(Meritorious both years I participated), one of the more obvious but important aspects is overlooked by many teams:

Delegate.

Our team began both competitions by selecting a "Coder, Writer, and Researcher". This should play off your strengths, but essentially, the code was substantial enough that our coder did only that. The Researcher spent the first half of the competition finding out what had been done and communicating with the Writer about the introduction and direction of the report. The writer spent the first half of the competition helping write the algorithm with the Coder, and working out the mathematical models to be used. Also the Writer attempted to synthesize the work of the Researcher into the start of the report. The second half of the project was a bit more hectic, the researcher obtained as much information as possible that might be available and useful. This was particularly important for important real world data into our models. The writer spend the second half... writing. Literally just writing non-stop.

This worked fairly well for us. I also recommend spending the first 1-3 hours letting the members think individually about the problem, then spending about 30-60 minutes explaining to one another their attack. Sometimes people aren't forthcoming with really great ideas.

Another recommendation is SLEEP! The first year we hardly slept at all for the entire competition. We drank insane amounts of caffeine and worked through the weekend. The second competition, we slept about 6 hours each night. We got the same ranking both times, but we did better the second year. Looking back, the quality of the writing was better. The code had less bugs, and we managed to produce more mathematics. Don't underestimate the power of getting a good nights rest.

Another general reference is consider a spherical cow which is a fairly standard reference. It is fun to read, and somewhat enlightening.

Perhaps I will think of more later, but for now this is all.

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Some of these are covered in the article from Mike's post. –  BBischof Jan 31 '11 at 20:22

The core of the preparation at my university (where I have coached the MCM teams the past few years) is a zero-credit, pass-fail, weekly seminar each fall semester. Students spend about three weeks each on three or four old MCM problems, and then we look at an outstanding solution and possibly the judges' commentary on each problem. (These are published in one of the UMAP Journal issues from that year.) We also spend a little time on software that may be useful during the competition, such as LaTeX and Mathematica.

I also go through this paper, Quest for the MCM, written by three students from the University of Colorado who received the top designation in the competition three years in a row. It's got a lot of good advice.

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I have participated once and I think the single most useful skill is for at least one member of the team to be fluent in some powerful programming language, like C++. We used it for numerical simulations, for drawing pretty pictures, for testing hypotheses and assumptions and so on. If somebody on the team can code almost any modelling situations very quickly, that makes the competition much easier and also much more fun, since it is then easier to concentrate on the mathematical aspects.

Of course, LaTeX is a must and is also worth practising, since many undergraduates will spend inordinate amounts of time writing up their submission.

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I agree with you about the utility of programming skills. Every team but one we've had the last few years that has done well in the competition has had a significant programming component to their solution. –  Mike Spivey Jan 31 '11 at 7:20

COMAP (Consortium for Mathematics and Its Applications: http://www.comap.com/) which runs MCM has lots of materials dealing with the mathematical tools that often are of use in modeling problems. It also has a collection of modeling problems available at:

http://www.mathmodels.org/

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