For College of Natural Science (CNS) students Brandon Alberts and Jonathan Jonker, their research added up to outstanding presentation awards at the annual joint meeting of the American Mathematical Society and the Mathematical Association of America (AMS-MAA) last month in San Diego, Calif. They are both in the advanced track program in the Michigan State University (MSU) Department of Mathematics .
Alberts, a senior from Grand Blanc, Mich., submitted a poster entitled “Trirings and Trifields.”
“My work was done generalizing the well-known algebraic structures of groups, rings and fields,” he explained. “I studied structures that had three operations satisfying specific properties, called trirings and trifields. Interestingly, the complete classification of finite trifields gives a condition equivalent to the Mersenne Prime Conjecture, a currently open problem in mathematics.”
Alberts chose math as his major because he enjoys mathematics.
“It’s as much of a hobby as it is a major,” said Alberts, who decided to attend MSU for his undergraduate education because of the advanced track option and the flexibility that the Honors College gave him.
Rajesh Kulkarni, an associate professor in the Department of Mathematics, was Alberts’ adviser for the project.
Jonker, a junior from Grand Rapids, Mich., submitted a poster entitled “Generic Polynomials for Transitive Subgroups of Order 8 and 9.” His research was with inverse Galois theory.
“My poster was on the non-standard methods used to compute polynomials, which would completely capture all Galois extensions for a certain group,” Jonker said. “These polynomials can also give a measure of the complexity of the group. We proved how complex certain groups are on the basis of how complicated the computed polynomials were. Generic polynomials do not always exist, so finding them is one way of proving that they exist, which implies other information about the group related to the Noether problem and the inverse Galois problem.”
Like Alberts, Jonker chose to come to MSU because of the math department’s advanced track offering. Math was his best subject throughout high school and the one that he found the most interesting.
His research was done as part of a National Science Foundation-funded REU (research experiences for undergraduates) project at Louisiana State University (LSU) during the summer of 2012. His adviser for project was Jorge Morales, a professor in the math department at LSU.
Jonker is already learning the art of collaboration, an important component of university research. He collaborated with Bradley Brudick, a senior at Ohio State University, on the project.
Three other MSU students from the mathematics department also submitted research posters at the meeting — Dan Diroff, Erik Bates and Trevor Steil, all juniors in the advanced track program.
Jeanne Wald, undergraduate director and associate chair of the mathematics department, oversees the advanced track program. Wald praised all five students attending the conference as excellent examples of the caliber of student in the program.
“This program is designed to address the needs of students such as these – highly talented young people who desire a challenging, exciting program of study,” Wald said. “I couldn’t be more pleased with our current group of students.”
One of the main goals of the advanced track is to provide math students with more personalized mentoring on research and career opportunities.
“The awards for Alberts and Jonker are testament to the success of our approach and to the commitment by our faculty to mentoring,” said Yang Wang, professor and chair of the MSU Department of Mathematics. “We’ve seen a sharp increase in undergraduate research in recent years as a result of these efforts. I wouldn’t be surprised to see many more students like Alberts and Jonker in the future.”
The Mathematical Association of America is a professional society whose major focus is to advance the mathematical sciences, especially at the collegiate level. The American Mathematical Society is also a professional associate of mathematicians dedicated to research and scholarship, which it does with various publications and conferences. The joint MMA-AMS meeting is the largest mathematics meeting in the world.