An Appreciation of my teacher, M.M. Rao
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As a first year graduate student at Carnegie Tech, in 1963-64, 1 took Rao's year long course on Functional Analysis. There were a lot of good students around Tech at that time; included in Rao's class were second year students Neil Gretsky and Jerry Uhl. Rao's ambitious style was to cover one major result in each lecture, or three per week. And all major theorems had descriptive names, some standard ("Dominated Convergence Theorem") and some not ("Law of the Unconscious Statistician"). The use of those names made the results easier to remember; I think Rao got this idea from Michel Loeve's book (from which I learned probability theory). Our text was by Angus E. Taylor, but we didn't use it much. Rao taught mostly out of Dunford & Schwartz (Vol. 1) and Hille & Phillips. His organization of the topics was excellent. An unusually large amount of material was covered per class. So much so that details were often omitted (or, sometimes in our minds, incorrectly given). With great regularity Gretsky, Uhl and I would stay after class and work out the complete details of the arguments we had just seen. Sometimes we realized that Rao really had given all the details; after all we were merely beginners and not yet well versed in mathematics. We always found that all of his results had correct versions, occasionally slightly different from what one of us thought when the discussion began. But by the end of the year, I learned so much that, for the first time, I considered myself a mathematician. Gretsky, Uhl and I were somehow teaching assistants to Rao, helping to teach one another. At the time I didn't give Rao credit for orchestrating this, but I think he did, at least to a substantial extent. He conveyed his love of mathematical depth and understanding and his passion for intense mathematical discussions.