Math Horizons: Lucarelli Article
Title: A Student Visits Mathfest
Author: Vincent Lucarelli
As a freshman, I knew very little about the life of a professional mathematician. I only saw professors in my department teach and research. I did not know who was in the math community or the areas of current research outside the department either. Fortunately, my advisor knew the benefits of attending professional meetings and convinced me to attend Mathfest, the joint summer meeting of the Mathematics Association of America, MAA, and Pi Mu Epsilon, in Burlington, Vermont in 1995.
Full of anticipation, I arrived at school (Youngstown State in Ohio) early on a raining morning – too early to remember. Four other students and I quickly loaded the leaky school van and embarked on a longer-than-expected escapade through the Adirondacks. After making a few wrong turns and negotiating mountain roads in a driving rain storm, we found Vermont.
I had heard a little about events for students at the summer meeting from my professors; once there, I quickly found that there are many presentations, meeting, and workshops during the four days. Our first activity was an ice cream social where I got to meet other undergraduates from across the country who were interested in and enthusiastic about mathematics. Some schools send five or ten students and others send one. Meeting other people is easy, and even if you do not know anyone when you arrive, you will never be alone.
I found Mathfest so enjoyable that I attended the next three years in Seattle in ’96, Atlanta in ’97, and Toronto last year. I had never been to these cities, and the evenings provided an excellent time to see the sights. Finding other students eager to have fun out on the town is not a problem.
Many of the students come to give a talk at the student sessions, but not all. Usually the student sessions are spread over two days. Besides awaiting their fifteen minutes of fame while presenting, students can enjoy many of the other activities. The Earle Raymond Hedrick lecture series is one of the annual events. Some of the lectures in the series are accessible to undergraduates; other parts are more advanced. A highlight of the invited addresses each year is the Pi Mu Epsilon J. Sutherland Frame lecture after the student banquet. Dr. Joseph Gallian from the University of Minnesota, Duluth gave the Frame lecture this past year in Toronto. He gave an unforgettable, and funny, presentation, “Breaking Drivers Lisence Codes.” The large crowd gave him a standing ovation.
The MAA sponsors student workshops and mini-courses on various topics. The artist/mathematician Helaman Ferguson drew one of the largest crowds in Toronto with his workshop, “Mathematics in Stone and Bronze.” Workshop participants reproduced one of his Klein bottle sculptures using bagels.
Besides the fun and the great lectures and presentations, the summer meeting provides an opportunity for undergraduates to talk about doing real mathematics. My first year, I worked closely with my advisor to prepare a presentation on the Brachistochrone problem posed by Bernoulli and solved by, among others, Newton. I was nervous that first time, but after I finished I realized how much I liked mathematics and telling others about it. The MAA and Pi Mu Epsilon pick several outstanding papers each year and present monetary awards at the Pi Mu Epsilon student banquet. Although I was not recognized that year in Burlington, the exposure to other undergraduates doing mathematics inspired me.
The meeting was in Seattle in 1996 and I wanted to participate. I needed a problem. Someone had mentioned that RSA public key encryption might be a suitable topic. I went off to the Internet and quickly learned that factoring large numbers was equivalent to breaking RSA. During a particularly dry psychology lecture one day, I had an idea about how to factor large numbers. Ober the following months, I developed a new method. An overview of RSU provided an perfect introduction to the factoring method I presented.
After Seattle, I prepared a historical account of the primality testing for the Atlanta meeting. This was at the end of my junior year, the time to apply to graduate schools. I am convinced the presentations at both the summer meetings and other regional meetings during the year made my applications more compelling. I was accepted by the University of Chicago, where I am currently pursuing my doctorate.
My final summer meeting as an undergraduate was in Toronto. I presented a portion of my senior project on elliptic curve factorization. I decided to present something that I loved, because that makes the best presentation, but the talk was too long and too advanced for a 15 minute student session.
All this experience has given me an idea of how to go about generating and presenting a good 15 minute presentation. Your first technical presentation to peers might be a little intimidating. Finding the topic and material might be a little frustrating, but knowing the topic well will provide you the confidence to make the presentation and not fear any questions from the audience.
Before you pick your topic, you should “know your audience,” but knowing you audience for a technical presentation is tricky. For the student sessions, assume a basic freshman knowledge and build on that idea. Pick a topic that either a freshman has likely heard about or one that you can introduce well in a minute. This does not mean you should not consider advanced topics, just that the harder the topic the harder you must work to make it accessible. Nothing is worse than confusing the audience.
Topics are plentiful. Ask your advisor or your favorite math professor, check the problem section in math journals, and search the Internet. Some of the best presentations result from an analysis of a specific problem or brain game. Do not be afraid to try and solve a hard applied problem, perhaps by making some simplifying assumptions. At the Atlanta meeting, a student presented his optimal soda can, a problem on which Coca-Cola had spent millions. Summer research topics from and REU are also popular, but be sure you do not try and use your final presentation at the summer meeting: you have a totally different audience that had not studied the topic all summer.
Once you have a topic idea, gather research. That is easy. The library, the Internet, and your advisor are great sources. Yes, you should have a faculty member oversee your work. He or she can help answer your questions, provide guidance, and help refine your work into an understandable and enjoyable presentation. Sometimes the simplest suggestion or hint will end your frustration.
Read what you have gathered and try to understand everything. Studying the details until they are automatic helps you formulate an intuitive presentation and gives you confidence. During this process maybe your focus will shift to a different idea. Follow your curiosity; it is much easier to study the material in depth if it is interesting to you.
If you plan to present a survey of the topic, you’re probably ready to being crafting a presentation. Original work requires more time and effort, but s more personally rewarding. Beginning in the fall for the summer meeting allows for some time to do original work.
Developing your presentation from the research is not difficult. Try to make successive simple links from an idea that your audience knows to the final results. A link should not require more than a minute or so of discussion. Transparencies are the classic medium for presentation, but a few brave people are using computer presentation software. In either case you need to present each link on a single viewing page, which I will call a slide.
Slides should not be crowded or messy. So not plan on reading the slide to the audience, they most likely can read. Instead, craft each slide to provide the most important information in that link. Overlays, as opposed to using overhead pens, are a good way to add a particular slide during a presentation. Do not count on a blackboard being available.
Remember your time limit. If you present an engaging topic, people will most likely ask questions. A minute or two for introduction and history, eight to ten minutes for the actual topic, and one to two minutes for a conclusion. Most proofs are not necessary and confuse the issue, but sometimes a single, interesting, edifying, beautiful proof could be the entire presentation. Visual representations such as graphs or flow diagrams are a wonderful aid; the audience can easily forget words, but visual cues help clarify complex ideas.
Do not assume your first draft is your final draft. Present your talk to your advisor, friends, and other faculty to get suggestions to test the clarity of your presentation. Take all the criticism you can get.
Practice your talk – a lot. It is better to get clarifications from people who want to help you rather than questions from a confused audience.
Some people dress formally for their presentation, dress or coat and tie, others are more casual. Still others dress is day-old clothes because their luggage was lost. By the way, fi you fly to the meeting, always include your presentation in carry-on luggage. You can deal with not having clean clothes at your talk, not having your slides could be a disaster.
Pi Mu Epsilon and MAA try to provide some financial support for student presenters to defray travel expenses, but funding is always tight and the policy can change. If your department does not send students, do not be afraid to ask for funding. Ask your advisor or department chair first; sometimes you have to go as far as your dean or provost, but somebody has money to support student activities.
Meeting people, sharing your work, hearing what your peers are doing, and learning new mathematics; that’s what professions mathematicians do at conferences. The MAA and Pi Mu Epsilon make a deliberate effort to give undergraduate students these same experiences at Mathfest. They succeed. Come to Providence this summer, July 31-August 2 to experience Mathfest for yourself.
Award-winning Students
At Mathfest 1998 in Toronto the MAA awarded prizes to ten student presenters. These prizes of $150 each are funded by the Exxon Education Foundation. The winners were:
Christos Athanasion, University of Massachussets-Lowell
Jeremy Dill, Pittsburg State University
Andrei Gnepp, Harvard University
Andrew Hetzel, University of Dayton
Yvonne Lai, Massachussetts Institute of Technology
Kuan Ju Liu, Harvard University
John Maki, University of Kentucky
Daniel Sheldon, Dartmouth College
Sean Simpson, Canisius College
David Windstrom, Montgomery Blair High School
Pi Mu Epsilon also organized a session of student paper presentations at Mathfest and awarded prizes for each of six presentations. The $100 prizes are funded by the American Mathematical Society. The winners were:
Joe Ferguson, Youngstown State University
Nathan Gibson, Worchester Polytechnic Institute
Stephen Hartke, University of Dayton
Kimball Martin, University of Maryland, Baltimore County
John Slanina, Youngstown State University
Stephen Bochanski and Harry Smith, St. Joseph's University
Call for Papers
Twelfth Annual MAA Undergraduate Students Paper Sessions
The Twelfth MAA Undergraduate Student Paper Sessions will take place at the MAA summer meeting in Providence, Rhode Island, July 31-August 31, 1999.
The program for the MAA summer meeting will include sessions for student papers. Partial support for travel by students presenting papers will be available on a limited basis (funded in part by a grant from the Exxon Education Foundation). Complete details on submission procedures and applications for travel support will be published in the April issue of FOCUS. This information will also be available on the MAA home page at http://www.maa.org/students/students_index.html. Students are advised to begin making plans now regarding participation. The deadline for student paper submissions is June 25, 1999.
Please direct all inquiries to Dr. Charles Diminnie via email at charles.diminnie@angelo.edu or by phone at 915-942-2317 ext 238.
The PhD Program in Mathematics at Dartmouth
The Dartmouth Teaching Fellowship.
The program requires that students develop both as research mathematicians and teachers. All regular students in the program are teaching fellows. Fellows begin as tutors, usually tutoring two or three evenings a week for twenty weeks each year during the first two years of study. After admission to candidacy for the PhD degree, students take a course on teaching mathematics and then teach one ten-week course per year. Dartmouth takes teaching seriously, and supports its teaching fellows strongly, especially as regards the careful selection of teaching assignments.,
Program features.
A flexibly timed system of certification, through exams or otherwise, of knowledge of algebra, analysis, topology, and a fourth area of mathematics, replaces formal qualifying exams. There is a wide choice of fields and outstanding people to work with. Interests include algebra, analysis, topology, applied math, combinatorics, geometry, logic, probability, number theory, and set theory.
For more information.
Write to the Graduate Program Secretary, Department of Mathematics, Dartmouth College, 6188 Bradley Hall, Hanover, New Hampshire 03755-3551 or e-mail mathphd@dartmouth.edu.