The Mathematics Department has solicited some feedback from students about their summer experiences related to mathematics. Here, we share their comments with our other students.
Zalia Rojas participated in the PURE Math Summer Research Program and writes: "The summer of my junior year, I participated in the PURE Math Summer Research Program in Hilo, HI, along with 11 other students from across the U.S. The program included housing and meals, at the University of Hawai'i, and and we each received a $4,000 stipend. We studied the Abelian Sandpile Model the first two and a half weeks, learning about the math behind the model in class, and working in small groups on homework assignments in the evenings. After those first few weeks, we were divided into four groups to work on more specific research questions related to what we had learned so far. We found patterns, proved results, and presented our progress to the class every week. At the end of the program, students presented their findings at a research symposium. In between all the hard work, we had weekly soccer and ultimate frisbee games with the faculty, and weekend trips to beaches, a volcano, the local farmer's market, lava tubes, caves, waterfalls, and had plenty of other opportunities to explore the Big Island and spend time with the faculty and their families. I made friends and connections I'll never forget. I strongly encourage anyone interested to apply."
Colin White participated in a Math REU and writes: "I had a lot of fun participating in a math REU two summers ago. I was researching problems in dynamic systems with Professor Benedetto and three other Amherst students. It was tough work, but very rewarding: I learned a lot of new math and how to program. I liked researching so much that I decided to do another REU this summer! I would definitely recommend an REU to anyone looking for a challenge."
Michelle Ngo participated in The Columbia Summer Institute in Biostatistics (SIBS) program and writes "The program was an incredible experience and made this past summer one of the most memorable. Although this was the first year Columbia participated in SIBS, the school has been running another biostatistics summer program (BEST) for some time. We were enrolled in two classes at Columbia: introductory biostatistics and introductory SAS programming. Every Monday we also had a research seminar, where a faculty member would present his/her work in biostatistics, and we would occasionally get a few other guest speakers during the week. Additionally, each CSIBS participant was paired with a BEST participant to work on a research project under the guidance of a mentor. Since I've taken statistics before, the introductory biostatistics course wasn't difficult. The challenge was applying the math and making sure that it made sense, given a particular context and conditions. Learning SAS is comparable to learning any coding language, if not more intuitive, and was very useful for the research project.
While the classes were fun, the best part of this program had to be the people. I was able to meet and interact with so many inspiring and influential people that blew my mind away. The faculty and staff at Mailman all had unique perspectives and took different paths, so engaging with them helped me figure out my professional future plans. My fellow participants were also amazing, and since it was a relatively small group, we all bonded quite well. I really couldn't have asked for a better group of people to learn and explore NYC with, and would definitely recommend this program to anyone interested in public health or biostatistics."
Claire Castellano worked with Professor Corey Manack on a mathematics research project. Claire writes "I worked with Professor Manack for 6 weeks. Our first project of the summer was to create some simple Mathematica programs that would iterate a series of triangle constructions for both circumscribing and inscribing processes such that we could analyze how a triangle would change after many successive applications of the given construction. Although our initial plan was to see what we could conjecture about the nth iterate of such processes, and thus look into the dynamic geometry of such a system, as we investigated how the triangles were changing, we realized that different triple of angles could represent the same “shaped” triangle; at this point, we decided we must first clarify what notion of “same shape” we wanted to use before we could categorize our triangles and various constructions. As we began to investigate the shape of the triangle (as defined by its angles), and what space we could create to appropriately deal with all the possible-shaped triangles. We were able to extend the work of previous mathematicians to define a space that we referred to as our “Angle Space” that would accurately identify and relate points as triples of angles or “same shaped” triangles. We ultimately were able to exploit laws of linear algebra to further understand the relations we were making by using matrices and linear maps to describe the changes in triangles occurring in our Angle Space. During the summer we submitted an abstract describing our work to the Young Mathematicians conference. The abstract was accepted and, in August, we went to University of Ohio in Columbus for the three-day conference at which I was able to present our work from the summer as well as hear other presenters speak about their experiences with undergraduate research in math."
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