Christine Shannon, Margaret V. Haggin Professor of Mathematics and Computer Science at Centre College, shares some memories from her time at Purdue.
During my first year of graduate study in mathematics I had taken two courses in analysis and measure theory from Professor Robert Zink and two courses in complex analysis from Professor David Drasin. I was clearly being drawn to analysis instead of the applied mathematics I had planned to pursue. It was natural to continue with Functional Analysis in the second year and Professor Kaplan was the instructor assigned to the course. I think the book by Goffman and Pedrick was the designated text but I would say it was only for our reading pleasure. Unlike my professors of the previous year who had filled the board with theorems, proofs and examples, Kaplan only presented definitions, statements of theorems and occasional lemmas. It was the job of the students to write the proofs and present them at the next class to be discussed and scrutinized for correctness. For me as a student, the process was completely turned around. Instead of merely trying to understand and fill in details for proofs that were literally handed to me and then working exercises which used these theorems, I was expected to prove the theorems in a carefully designed order. It was clearly a slower process: I'm sure it was the third semester before we reached the material on topological vector lattices and the second dual of C(X) which was his research area. It was much later that I learned of the "Moore Method" and although I have never used a strict version of the technique in my teaching, I know colleagues who have and I have certainly designed worksheets where my students must construct a proof by following a sequence of steps that I define. It is hard to identify why I asked to be his student. I clearly enjoyed the material and after working through all those theorems largely on my own I had a very good understanding of the content. But I would not have wanted all my courses taught in that fashion. There is a good introduction to this method of teaching at http://legacyrlmoore.org/reference/quick_start-3.pdf and of course the Legacy of R. L. Moore website at http://legacyrlmoore.org/method.html.
It was good preparation for the research part of my graduate education as well. Kaplan was rather a hands-off advisor. He wanted me to find my own problem and when I finally wandered into a combination of topics including rings of functions theory as well as the second dual of C(X) – this time on a realcompact space – he was supportive and encouraging. My weekly meetings with him always had me doing the talking punctuated with occasional questions from him. Rarely did he make a suggestion about which way to go but he always listened and gave me his full attention, sometimes suggesting a paper to read. It was clear that I was responsible in this endeavor.
I am grateful to have had him as a teacher. I found the mathematics he was doing very engaging and his willingness to let me explore a lot of tangential topics in the quest for a research area opened up a lot of mathematics I had never before encountered. His calm, patient, and deliberate ways were good for me and though I was drawn more to teaching than to research, I never lost the desire to explore new ideas and to appreciate the beauty of an orderly development of mathematical concepts. It has given me great pleasure all my life and I may indeed have been influenced by the way I was guided to investigate mathematical topics and to prove the important results for myself.