Math Horizons September 2016 : Page 25

a wonderful program that introduced me to the joys and frustrations of mathematical research. After the sum-mer, I presented my research at the University of South Carolina and JMM. The next academic year I worked with Joshua Cooper on a project in mathematical biology. I owe much of my success to my research experiences and the people who believed in me, even when I did not believe in myself. I am an example that anyone can conduct mathematical research if she or he puts forth adequate effort and has access to quality mentorship. Advice for students: You were selected from a pool of many applicants, so make the most of this opportunity and do not take it for granted. Math can be difficult, but you are in the early stages of your career, so learn all you can, and build your intuition. Remember that your mentor is there to help you. Listen to his or her advice about mathematics and life—your mentor was once in your position. Interact with the speakers and mathematicians you come in contact with. Learning from great minds helps foster a great mind. Advice for mentors: We are just starting out, and we sometimes (often) ask dumb questions—make sure to give constructive criticism. Our questions will get better as we learn. Get to know your students personally and stay in touch. The students look up to you, so treat them well and don’t be discouraging. Samantha VanSchalkwyk, Mount Holyoke College I started college as a shy student who worked indepen-dently to complete my schoolwork. But as I started taking more difficult mathematics classes, I found that working with a group was a more effective way to learn the material. This is why, after my junior year, I decided to attend an REU program at the Mathematical Sciences Research Institute in Berkeley, California. Seventeen other students and I studied arithmetic aspects of elementary functions. In particular, under the mentorship of Victor Moll from Tulane University, my group of three focused on discovering and proving properties of the Franel numbers. By the end of the program, a strong group dynamic had developed, and I had learned how to interact with the other students and instructors. Each week our group presented our findings to all participants and solicited feedback. It was particularly helpful to hear their opin-ions on how to tackle our research problems. Advice for students: Working as part of a team doesn’t always go smoothly at first. It takes a while to get to know your group and learn how to use each other’s strengths to produce the best results. Do not get discouraged Samantha VanSchalkwyk. when it seems like others have a better background in the subject. Every student was selected to join the program because she or he was qualified and could contribute. Results take time. My research group didn’t get any worthwhile results for days. Asking questions is essen-tial. Your mentors are there to advise you on how to move forward with your research, and they should be used as a resource. Advice for mentors: Give students space to define their research topic. Once the research is under way, point them in a few directions in which they can continue their investigations. Students work in a variety of ways, based on their skills and interests. It’s important to keep doors open for them so that they can get results and succeed. Give them deadlines. They should have a reasonable amount of time to explore a topic without wasting time searching for something that might be impossible. Lastly, get to know the students. My mentor spoke with me about my future, and this greatly influenced my decision to go to graduate school. Q Herbert A. Medina is a professor of mathematics at Loyola Marymount University. Some of his most rewarding moments as a faculty member have come from witnessing undergraduates producing original mathematics. Email: Herbert.Medina@lmu.edu Angel R. Pineda is an associate professor at Manhattan College and often tells his undergraduate research students that he knows more because he is older, not smarter. Email: angel.pineda@manhattan.edu http://dx.doi.org/10.4169/mathhorizons.24.1.23 www.maa.org/mathhorizons : : Math Horizons : : September 2016 25

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