NewtonsCradle1.png NewtonsCradle2.png

MCM student competition

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 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.
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".
 
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: 2012

Our 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.
Team 1 consisted of Wiehan Agenbag, Gerard Louw and Jansen du Plessis. They chose to work on Problem B and were placed in the Meritorious Winner category.
Team advisor: Dr Willie Brink
 
 
Team 2 consisted of André Dreyer, Lize Cillié and Ricus Gräbe. They also chose Problem B and were placed in the Successful Participant category.
Team advisor: Dr Willie Brink
 
 
PROBLEM A: The Leaves of a Tree
"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.

Previous years

  • MCM student competition: 2011  (the problems of the 2011 contest can be found here)
    Team 1 consisted of Rijnard van Tonder, Thomas Weighill and Gerdus Benade. They chose to work on Problem B and were placed in the Meritorious Winner category.
    Team advisor: Dr Willie Brink
    Team 2 consisted of Wouter Bam, Robert Hagspihl and Ruaan Viljoen. They also chose Problem B and were placed in the Honourable Mention category.
    Team advisor: Dr Willie Brink
  • MCM student competition: 2010  (the problems of the 2010 contest can be found here)
    Team 1 consisted of Jan Buys, Alex Smit and Renier van Rooyen. They chose Problem A and were placed in the Meritorious Winner category.
     
    Team 2 consisted of Hilgard Bell, Marcel Dunaiski and Nereus Joubert. They chose Problem B and were placed in the Successful Participant category.
     
    Advisor for both teams: Prof. André Weideman
  • MCM student competition: 2009  (the problems of the 2009 contest can be found here)
    Team 1 consisted of Ryno Botha, Erhardt de Kock and Brendan Tighy. They chose Problem A and were placed in the Successful Participant category.
    Team advisor: Prof. André Weideman
    Team 2 consisted of Dirk Badenhorst, Daniek Joubert and Maryke Thom. They also chose Problem A and were also placed in the Successful Participant category.
    Team advisor: Prof. André Weideman
  • MCM student competition: 2008  (the problems of the 2008 contest can be found here)
    Team 1 consisted of Kirsten Lambert, Ralph Rudd and Bernard Schlünz. They chose Problem A and were placed in the Honourable Mention category.
    Team advisor: Prof. André Weideman
    Team 2 consisted of Dmitri Marais, Riaan Coetzee and Jason Matthews. They also chose Problem A and were placed in the Successful Participant category.
    Team advisor: Prof. André Weideman
  • MCM student competition: 2007  (the problems of the 2007 contest can be found here)
    Team 1 consisted of Andreas Hafver, Chris Rohwer and Louise Viljoen. They chose Problem B and were placed in the Outstanding Winner category. They also received the SIAM prize.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Dirk Basson, Jan Botha and Jaco van Zyl. They also chose Problem B and were placed in the Meritorious Winner category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2006  (the problems of the 2006 contest can be found here)
    Team 1 consisted of Morne Chamberlain, Retha Heymann and Corne Potgieter. They chose Problem A and were placed in the Meritorious Winner category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Benjamin Krige, Elsa du Plessis and Milton van Rooy. They also chose Problem A and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2005  (the problems of the 2005 contest can be found here)
    Team 1 consisted of Pascal Brandt, Carl Crous and Peter Eilers. They chose Problem B and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of JD de Caires e Freitas, Van Aarde Krynauw and Emmerentia Thiart. They also chose Problem B and were placed in the Successful Participant category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2004  (the problems of the 2004 contest can be found here)
    Team 1 consisted of Bernard Broens, Cecilia du Toit and Grant Cross. They chose Problem A and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Jean Marais, Christo Rautenbach and Jacobus Swanepoel. They also chose Problem A and were also placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2003  (the problems of the 2003 contest can be found here)
    Team 1 consisted of Maret Cloete, Evan Lezar and Deon Borman. They chose Problem A and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Albert Strasheim, Niel Thom and Conrad Visagie. They chose Problem B and were placed in the Successful Participant category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2002  (the problems of the 2002 contest can be found here)
    Team 1 consisted of Markus Kruger, Louis Brewis and Ingrid Mostert. They chose Problem B and were placed in the Successful Participant category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Renier Marchand, Luther Terblanche and Ashley Marcus. They chose Problem A and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2001  (the problems of the 2001 contest can be found here)
    Team 1 consisted of Francois Malan, Christopher Mumbeck and Deter de Wet. They chose Problem A and were placed in the Outstanding Winner category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Cobus Jacobs, Hendri Botha and Izak Snyman. They chose Problem B and were placed in the Honourable Mention category.
    Team advisor: Prof. Jan van Vuuren
  • MCM student competition: 2000  (the problems of the 2000 contest can be found here)
    Team 1 consisted of Cobus Carstens, Wynand Winterbach and Eon Zuurmond. They chose Problem B and were placed in the Successful Participant category.
    Team advisor: Prof. Jan van Vuuren
    Team 2 consisted of Stephen Benecke, Henri Hakl and Carl Scheffler. They chose Problem A and were also placed in the Successful Participant category.
    Team advisor: Prof. Jan van Vuuren
  • 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