Monmouth College student Corbin Peterson displays a canoe he helped construct during last month’s SOFIA (Summer Opportunities for Intellectual Activity) program on campus. Building the canoe was one of three SOFIA projects related to mathematics.
The first day of classes at Monmouth College was held on Aug. 23, but for nearly 50 students, school began three weeks earlier thanks to the college’s SOFIA (Summer Opportunities for Intellectual Activity) program.
Among those four dozen students were several with a strong interest in mathematics or computer science. They were involved in one of three projects within that department, led by faculty members Marjorie Bond, Howard Dwyer and Mike Sostarecz.
When the college’s new high-speed camera arrived last fall, Sostarecz immediately began conducting research with his students. So it was not surprising that his SOFIA project involved modeling with high-speed imagery. He worked with sophomore math majors Anders Nelson, an Honors Program participant from Galesburg, and Megan Lyle of Monmouth.
"Prior to the students arriving, I planned some experiments with projectiles, oscillations and tornadoes,” he said. “Once they started in, I invited them to come up with their own ideas.”
The students’ experience was not only confined to Monmouth College. During SOFIA, Sostarecz and Bond traveled to Lexington, Ky., for MathFest 2011, and they brought six of the department’s SOFIA students with them. That included freshman Gege Carr of Chicago, who worked with Dwyer, and the three students who were supervised by Bond – juniors Alexis Fulkerson of Macomb and Kimberly Short of Creve Coeur and freshman Mary Kate Guinea of Frankfort.
Sostarecz explained that the Mathematics Association of America (MAA) holds two national conferences each year, including one called MathFest. In addition to his role as chaperone, Sostarecz was also a presenter, delivering a longer version of the “Mathematical Modeling with High-Speed Imagery” talk that he gave earlier in the year at the Illinois sectional meeting.
“If SOFIA continues, I would hope that we have students present at the conference in 2012,” Sostarecz said.
Under Dwyer’s watch, Carr and sophomore Corbin Peterson of Monmouth constructed a 14-foot long canoe. Unlike many building projects, they came in under budget – so much so, in fact, that their first attempt will actually be part of a canoe fleet.
“We had a budget of $1,000, but $500 bought us enough supplies for four boats,” said Peterson.
When they presented their first canoe at the close of SOFIA, the boat was entirely white and awaiting its graphic design.
“It’s going to be half killer whale, half rainbow,” said Carr.
“We couldn’t agree,” added Peterson.
Where they did have to agree was in the many calculations for the vessel’s construction. An important one is the boat’s buoyancy, which they calculated to be 3.8 inches of displaced water with a load of 275 pounds.
“So, one big person or two small ones could use this kayak,” Peterson said.
Once the fleet is constructed – possibly during an upcoming workday for SOFIA students from all disciplines – Peterson said he hopes the kayaks can be used to “get city kids out to see nature.” Carr certainly qualifies, as she reported being introduced to the hum of cicadas during her SOFIA experience.
“The construction process went very smoothly,” said Dwyer of his students’ work. “It was remarkable to see how quickly some lumber and two sheets of thin plywood could be transformed into a rather attractive little boat. It will be interesting to see how closely the actual boat agrees with the computations.”
The final group of SOFIA math students spent their three weeks “Looking at Games of Chance Through a Multi-Discipline Lens.” They tackled the obvious calculations of probability in such games as poker, blackjack and roulette (there are, for instance, 2,598,960 possible card combinations in poker), but they also looked deeper into such games, examining them from historical, religious and social/psychological angles.
“It was a great experience,” said Short, who was able to combine her interests in classics and math by reporting on “Ancient Games of Chance.”
She learned, for example, that the Greeks played an early form of dice using the bones of sheep, and that soldiers played a version of craps during the war against Troy. Much like Prohibition centuries later, it was illegal to gamble in Rome, but that didn’t stop such games from being everyday occurrences, all the way up to the emperor Augustus. Ever wonder why Egyptian men would sign up to work on the pyramids? Short’s research showed that many were compulsive gamblers working to pay off debts.
“I also learned that lottery tickets helped pay for the American Revolution,” said Short, who included a photo of a 1776 ticket on her project poster.
Guinea was not surprised to learn that the more active Christians are within their church, the less they gamble. A typical religious view, she wrote, is that “gambling results in negative things,” but there is a conflicting view that offers support for lotteries held to raise money for schools or hospitals.
Fulkerson focused on why people gamble and what causes compulsive gamblers to go over the edge. Some of the solutions she posed for problems within the industry included better enforcement of the legal age of gambling, per day limits structured in the same way as individual table limits, and income taxes on gambling winnings.
“This project gave our students the opportunity to see how mathematics fits into the bigger picture of the world and its history,” said Bond, who helped her students run a Casino Night for other SOFIA students during the final week. “What we did here is a perfect example of what it means to study mathematics at a liberal arts college.”