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He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.
A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research
Our goal was to have the students do enough research so that each could give her own talk at MathFest. For the first several weeks, we worked in the library together, trying to get our bearings and finding appropriate books and articles. We also started finding helpful sources on the Internet; more on this later.
Eventually, our weekly schedule evolved into the following one: Mondays were devoted to the students’ individual research topics. On Tuesdays the students gave presentations on Euler and his works using secondary sources. Wednesdays were our field trip days, and on Thursdays we worked with primary sources from Euler and his contemporaries.
Mondays: Individual research topics
On Mondays, each student gave a report on her previous week’s research and talked about what she would work on in the coming week. We all gave feedback and suggestions; often another student could answer a presenter’s question or direct her to a possible source. Eventually, as MathFest neared, this became our time to practice talks, first just for our little group, then with a few extra audience members (generally other professors, but not always math professors). Once the reports (or practice talks) were completed, we adjourned to the library or the computer lab to work independently. The students could also use this time to request help from the professors or each other.
Tuesdays: By and About Euler
On Tuesdays, the students each gave a presentation on Euler and his work, from sources assigned by the two faculty, including the previously-mentioned MAA books, [1,2,3,4,5], the online Euler Archive, and Ed Sandifer’s online MAA column How Euler Did It. The articles in these sources were generally bite-sized pieces of work from Euler that the author had streamlined and interpreted. Each student could pick any article from her resource, so long as it had not previously been presented. Her job was to read it, try her best to understand it, then present and explain it to the rest of us (who had not read it). If a student did not understand part of her article, then we would all puzzle it out together, generally with the presenter still at the board. This gave us a nice appreciation for the breadth and beauty of Euler’s work. Once all the presentations were finished for the day, the students traded sources and picked articles for the next week. This way, all four students had the opportunity to work with all of our resources.
Wednesdays: Field trips and speakers
Our original plan was to invite speakers to come to campus and make presentations and then spend some time discussing our project with us. But we quickly realized that our potential speakers were in much more interesting places than our college campus in Frederick, Maryland, and it would be more fun, and more helpful, to visit them in their own habitats.
It happened that William Dunham was giving a lecture on Euler as part of a public lecture series at the Johns Hopkins University Applied Physics Lab in Baltimore, MD, early in June. And so we used that event to kick off our summer project. After the talk we chatted with Prof. Dunham about our plans, and in fact we kept in touch with him throughout the summer for information and advice. Networking like this was invaluable to us in the course of the summer, and we never could predict who would be able to give us what information, so we learned to talk to everybody about everything. In many ways these trips were the most important part of our summer, as we discovered a great many helpful sources and information on them.
At the APL: Laura Printz, Lindsey Nagy, Bill Dunham, Chelsea Sprankle, Melissa Barrick
Our second field trip was to the MAA’s Carriage House Conference Center in Washington, D.C. There we began our day with a tour of MAA headquarters and met some of the staff. Then we gathered in a conference room and met with mathematics historian Victor Katz, who presented an overview of the process of doing research in the history of mathematics and gave us lots of good ideas for topics and resources.
Participants at the MAA: Kimber Tysdal, Lindsey Nagy, Laura Printz, Melissa Barrick, Chelsea Sprankle, Betty Mayfield
Mayfield, Betty and Kimberly Tysdal, "A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research," Loci (February 2009), DOI: 10.4169/loci003263
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