MCM, 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 over 500 institutions around the world. Features of the contest include:
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The selection and adjudication of realistic problems chosen with the advice of experts in industry and government. |
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A weekend for teams to prepare solution papers within a clearly defined format. |
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The ability of participants to draw on outside resources including computers and texts. |
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An emphasis on clarity of exposition in judging, with the best papers published in professional journals. |
University faculty members can be part of MCM by serving as a team advisor. The advisors help recruit, organise and prepare a team of undergraduates for the contest. Team solutions are adjudicated and placed in a hierarchy of four categories: "Successful Participant", "Honourable Mention", "Meritorious Winner", and "Outstanding Winner". In 2010, two additional categories were added: "Finalist" just below "Outstanding Winner", and "Unsuccessful Participant".
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Major funding for MCM is provided by the National Security Agency. |
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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. Andre 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 1999-2011 are outlined below.
Determine the shape of a snowboard course (known as a “halfpipe”) to maximize the production of vertical air by a skilled snowboarder. Vertical air is the maximum vertical distance above the edge of the halfpipe. Tailor the shape to optimize other possible requirements, such as maximum twist in the air. What tradeoffs may be required to develop a “practical” course?
The VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by “repeaters”, which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies. For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available. How does your solution change if there are 10,000 users? Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.
[See the complete problem statements at the MCM Web Page.]
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| Team 1: Rijnard van Tonder, Thomas Weighill, Gerdus Benade | Team 2: Ruaan Viljoen, Wouter Bam, Robert Hagsphil |
Team 2 consisted of BSc students Robert Hagsphil and Ruaan Viljoen, and BEng student Wouter Bam. They also chose Problem B and were placed in the Honourable Mention category.