MCM student competitionMCM, the Mathematical Contest in Modelling, challenges teams of undergraduate students to clarify, analyse, and propose solutions to open-ended problems. The contest attracts diverse students and faculty advisors from roughly 1000 institutions around the world. Features of the contest include:
- The selection and adjudication of realistic problems chosen with the advice of experts in industry and government.
- A weekend for teams to prepare solution papers within a clearly defined format.
- The ability of participants to draw on outside resources including computers and texts.
- An emphasis on clarity of exposition in judging, with the best papers published in professional journals.
Major funding for MCM is provided by the National Security Agency. Additional support is provided by the Institute for Operations Research and the Management Sciences (INFORMS), the Society for Industrial and Applied Mathematics (SIAM), and the Mathematical Association of America (MAA).
The Division of Applied Mathematics at Stellenbosch University has taken part in this competition for many years by enlisting one or two teams of three third year students every year. Prof. Jan van Vuuren has acted as advisor for the department's teams from 1997 to 2007. Prof. André Weideman was advisor from 2008 to 2010 and was succeeded by Dr Willie Brink in 2011. The participating teams and the competition problems tackled by these teams during the period 1999-2012 are outlined below.
MCM student competition: 2017
After a haiatus of a few years, two teams from Stellenbosch were entered into the Mathematical Contest in Modelling in 2017 - one consisting of Renè Spoerer and Jeandrè Boshoff, and the other of Sarah Selkirk, Anthonie de Beer, and Esmari Marè.
Team 1: Jeandrè Boshoff and Renè Spoerer. Team 2: Anthonie de Beer, Sarah Selkirk, and Esmari Marè.
Team advisor: Dr Nick Hale
There were three questions to choose from and both teams chose the problem involving toll plazas. In short, there are always more tollbooths than there are lanes in the road. Thus drivers need to merge lanes in the area following the tollbooths, and this can cause traffic delays. Our task was to model traffic flow and to determine how toll plazas should be designed to optimise merging behaviour.
Much of our time was spent writing computer code, creating graphs, and debating over the best phrasing of our findings; often late into the night. However, over the course of the four days, we also had much fun and had an unforgettable experience. We are still awaiting the results of the competition.
MCM student competition: 2012Our division entered two teams for this contest, which took place in February 2012. The complete problem statements and results can be viewed at the MCM website.
"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. PROBLEM B: Camping along the Big Long River Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar-powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River's rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time.
- MCM student competition: 2011 (the problems of the 2011 contest can be found here)
- MCM student competition: 2010 (the problems of the 2010 contest can be found here)
- MCM student competition: 2009 (the problems of the 2009 contest can be found here)
- MCM student competition: 2008 (the problems of the 2008 contest can be found here)
- MCM student competition: 2007 (the problems of the 2007 contest can be found here)
- MCM student competition: 2006 (the problems of the 2006 contest can be found here)
- MCM student competition: 2005 (the problems of the 2005 contest can be found here)
- MCM student competition: 2004 (the problems of the 2004 contest can be found here)
- MCM student competition: 2003 (the problems of the 2003 contest can be found here)
- MCM student competition: 2002 (the problems of the 2002 contest can be found here)
- MCM student competition: 2001 (the problems of the 2001 contest can be found here)
- MCM student competition: 2000 (the problems of the 2000 contest can be found here)
MCM student competition: 1999
(the problems of the 1999 contest can be found here)
The team taking part in 1999 consisted of Adele Geldenhuys, Werner Gründlingh and Marcel Villet. They chose Problem B and were placed in the Successful Participant category. Team advisor: Prof. Jan van Vuuren