Retirement and Mathematics  


Retirement and Mathematics

So, one would think that retirement and aftermath would bring travel and the easy life -- finally. That is part of retirement, but I found myself trying to learn the undergraduate mathematics that I was suppose to know but don´t. Likely the others, retired like me, will admit to the same perversion. I started with Landau´s Grundlagen der Analysis. This is a classic and should be studied carefully by every undergraduate. Studying the Grundlagen brought back many found memories of Mr. Hoffman´s math 501, taught on the 4th floor of the Classroom Building in the classroom at the west end of the building. Math 501 was titled the Real Number System and in those days the first course every new graduate student had to complete. Of course every mathematician claims that they know the Grundlagen but I wonder how many have actually studied it? I know I fell into that category. Next I moved to Landau´s Integral and Differential Calculus. Again, a classic, but hardly comparable to modern Calculus texts. This volume has no pictures -- not one. The author assures the reader that he can draw pictures but will let the reader supply pictures if he wants. It has the first epsilon-delta proof that I had seen that if 0 < a < 1 then limit n --> infinity of a^n is 0. My practice in the classroom was to hand wave at that one. Next came Analytic Geometry and where else to go but George Salmon´s Conic Sections published in 1833. This subject is not taught in modern classrooms but should be since you can´t do Calculus unless you have some curves to work with. Modern texts do the just-in-time approach as the topics in Calculus unfold. Salmon does have a few pictures. As a freshman at OSU in 1958 I took Calculus from Thomas, Analytic Geometry and Calculus, 1st edition. I was told this was the first year OSU used a text with Calculus and Analytic Geometry integrated. At that time Calculus sequence was 2 five hour courses. Dr. Shreve taught my section of Math 205, the first Calculus course. I wonder if anyone remembers Dr. Shreve? Next I took up college algebra and located College Algebra by Bernard Fine published in 1905. Fine Hall at Princeton is named for him. Fine mentioned his debt to the college algebra text by George Chrystal - 2 volumes. I found copies of those volumes, both published in 1886. Comparing the texts by those two authors I found that the so called ¨dumbing down¨ process in text books started over 100 years ago in case someone thinks it started recently. Chrystal has a list of exercises to compute using Horner´s Method the irrational roots of a polynomial to 14 (yes that is 14) decimal places. Fine has the same exercises but lets the student off the hook for just 6 decimal places. In those days of course numerical computations were done with pencil, no mechanical devices for computing were available. So, just in case everyone I knew at OSU was wondering what I was doing in retirement (I know that they are not wondering) I bring all up to date. Wonder how the others are doing? George Butler, BS 63, MS 64, PhD 68