Aaron Meurer, Ian Burch and Henry Horton were among the top 30 percent of teams that completed Problem B in this year’s event.

Aaron Meurer, Henry Horton and Ian Burch (from left) earned honorable mention accolades in the 2011 Mathematical Contest in Modeling. |
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The contest asks students to complete a complex modeling problem February 10 to 14. The Tech trio selected Problem B, which involved modeling VHF coverage over a 40 square-mile area.

Out of the 2,775 teams that participated, only 842 earned Honorable Mention. The international competition included only 347 teams from the

Problem B asked contestants to determine the minimum number of repeaters necessary to serve different population sizes and environmental conditions.

For a circular flat area of 40 miles radius, contestants were required to determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users, assuming 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 to reduce the potential of interference. Then, contestants were required to determine how their solution changes if there are 10,000 users. Finally, students were required to discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.

Meurer said the competition was intense; the three team members spent three full days working on the project.

“They want to see different ways you can solve the problem,” Meurer said. “There’s no one way to do it.”

The students did some research on VHF repeaters, their operation and their range. They then worked on dividing the geographical area into sectors and calculating how many repeaters would be needed, given one set of population density assumptions.

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.

This year’s contest ran from Thursday, Feb. 10, to Monday, Feb. 14. During that time, participants researched, modeled, and submitted a solution to one of two modeling problems. The 2011 contest was primarily an online contest. Teams registered, obtained contest materials, and downloaded the problem and data via the Internet.

The three math major are all seniors. Horton went to high school in

The Consortium for Mathematics and Its Applications, or COMAP, is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.

The competition included teams from

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*By Thomas Guengerich/*