Uni Students create Illinois Geometry Lab projects

On Thursday, Dec. 13, nine Uni students in three groups of three presented their projects at the Illinois Geometry Lab (IGL) Open House. The students were able to showcase the original mathematics research they had conducted over the summer.

“Getting to do original research was really fun especially since before the project I hadn’t thought it was possible at my level of math,” said senior Annemily Hoganson, who met with seniors Katherine Ahlgren and Raine Bernhard on finding sharp bounds for the Directed Postman Problem.

The groups met from June 4 to June 29, meeting with a mentor three times a week for those four weeks.

“My group’s mentor was amazing. She let us take the project in whatever direction we wanted but gave us great advice and taught us a lot about how to write about math,” said Hoganson.

“Our mentor worked closely with us, teaching us the linear algebra we needed and giving some guidance about what to try to do,” said senior Robert Nagel, who worked with seniors Kevin Grosman and Matthew Jin on semantic discovery via singular value decomposition.

The students were able to take advantage of a great opportunity to learn more about advanced topics in math than they could at Uni through their research.

“I learned how to write about math a lot more formally than we do in our classes at Uni. I also learned how to approach a problem by looking for a pattern and then something to prove,” said Hoganson.

“I learned some basics of graph theory. In addition much of the work we did was computational and learning about different ways to calculate things on mathematica. For example taking powers of a large matrix is difficult computationally so exploring shortcuts or graph theory might yield a quicker method,” said junior Ethan Muchnik, who worked with junior Ethan Ashbrook and senior Albert Lee on applying dynamics to fractals.

The three projects were also heavily coding-intensive.

“My favorite part was being able to create a useful program to solve a problem we faced,” said Nagel.

If you would like to learn more about these three projects, especially the math behind them, then check out these links:

Dynamics on Fractals: Ethan Ashbrook, Albert Lee, Ethan Muchnik (Mentor: Ivan Contreras)

Sharp Bounds for the Directed Postman Problem: Katherine Ahlgren, Raine Bernhard, Annemily Hoganson (Mentor: Dana Neidinger)

Semantic Discovery via SVD: Kevin Grosman, Matthew Jin, Robert Nagel (Mentor: Joseph Rennie)