augustmarsblog

  Math by Default When I completed my high school education, I set my sights on college studies. That, in itself, was not a simple matter. My parents had to be convinced by a couple of my teachers that it was worth the cost, as it would be a considerable financial strain for them. And I was not entirely enthusiastic about it because those same teachers emphasized to me that college level courses would be much harder than those I had been taking. They seemed hopeful – not confident – that I could handle it. And they recommended some choices that I could make that would ease the burden the first year of the transition. Four years later, when I planned to continue my education at a graduate level, I had a similar experience. My professors warned me that the advanced courses would be much more difficult and recommended some means of making the transition easier. Now all of these advisers meant well, but I could not, or would not, take any o...

  Inabel One of the more interesting characters that I met during those hard years at Roanoke college was a girl named Inabel. She had a glaring physical defect. Her nose had a prominent hook, and on that hook there was a wart. In other words she was the living embodiment of a fairy tale witch. But her bright happy character was just the opposite of that of a witch. And she had a natural sense of humor that clearly overrode any anxiety she may have had about her appearance. The students who lived in Roanoke and did nor participate in dorm life were assigned a study room for those who did not have 8 o'clock classes, and it even extended to the 9 o'clock hour for those returning from an 8 o'clock class. These were hours of heavy study. We asked each other questions, some of which were anticipated test questions, and some real need-to-know questions as we struggled to keep our heads above water in the oner...

  Graduate School Now I had to make a crucial decision. I needed to qualify for some profession, and the only one that seemed within reach at this point was the teaching profession. I could easily, with a few evening classes, qualify for a teaching certificate. The major drawback was that teachers’ salaries at that time were pitiably inadequate, especially if one needed to support a family. I learned that a master’s degree would command a premium salary as a teacher, so I decided to make that effort. I wanted to understand advanced mathematics, and I had learned that the University of Virginia math department had a good reputation. But when I discussed that possibility with one of my undergraduate math professors, he warned me that the UVa graduate math curriculum was extremely difficult, as it focused on “pure, abstract” math, as opposed to applied math. His recommendation was that I apply instead to the Graduate School of Education with a concen...

  Dr. McShane But now I want to return to those first days of my introduction to graduate level mathematics, specifically to one course with the intimidating title, “Functions of a Real Variable”. The lecturer was Dr. E. J. McShane. He was the acting head of the department, in the absence of the permanent head who was on a sabbatical. I think that I may have made a slight impression on him by sitting on the front row in class, looking at him as he lectured, and attempting, with some success, to explain a theorem that he had assigned for study. But he definitely made an impression on me. He had enrolled all of the new graduate math students in this class. Apparently he wanted to give us a proper introduction to abstract mathematics, because he spent the first six weeks of the course teaching us logic in considerable depth – far beyond the basic logic of my high school course in Euclidean geometry. This logic utilized an extensive system of symbols that was appropria...

  The Man Who Loved Mathematics In my second year of graduate work, Dr. McShane proposed a master’s thesis subject for me, one involving a different approach to Stieltjes integration (You don’t need to know what that is). I thought that I had a general idea of what needed to be done, but for the sake of me I couldn’t seem to make any progress. To tell the truth, I couldn’t even get started on it. I sat in the Math library poring over papers on Stieltjes integration without understanding much of the material, especially insofar as it might apply to my problem. Eventually, either Fortune or Providence smiled on me – in the form of another student. Dave Lowdenslager was one of those academic types that chooses to live a life within the confines of Academia. He was single and under none of the pressures that most of us have: to get a degree and start into a professional situation with an income that would support a family. He was not at UVa during my first year of ...

  Introduction to Adulthood Through Temporary Employment Those were a few of my learning experiences in graduate school. Now, before I proceed to my career life, I should comment briefly on the various jobs that I worked at in order to earn money to pay for my education. These temporary positions only provided a fraction of my education expenses. In undergraduate college they didn’t even cover fully my tuition. My parents provided the balance. I also had the advantage of living at home, while commuting daily to college classes. After completing my undergraduate degree, they called it quits insofar as paying for education expenses directly, but they allowed me to live at home during the summers, and during the one-year work break that I had to take after my first year of graduate work in order to accumulate enough savings to pay for the second year. During that year I worked for the American Viscose Corporation at a rayon manufacturing plant within walking dista...

  My Brief Career as a Full Time Teacher After a few weeks I received a letter that shattered my hopes. My application had been rejected – not for lack of qualifications, but because of a security problem. Crestfallen, I quickly applied for an undergraduate teaching position. I had a couple of offers, largely because math instructors were hard to come by at that time. I began teaching at Randolph Macon College in late August. That brief teaching experience was enlightening in that I learned some math that I had not previously studied, and I learned some things about myself. The math was Statistics. I had never taken a course in Statistics, although I had studied some probability theory in my algebra classes. But this was a basic one-semester course geared toward Economics and Psychology majors. I had no problem teaching it to myself by staying one chapter ahead of the students. It seemed simple compared to the abstract math that I had recently been subje...

  Introduction to Research That post title is a little joke, because I wasn't introduced to research - I was thrust into it. My vision of entering into a research career was that I would undergo an orientation period that would involve lectures on the types of research that was being conducted at the Center, with tours of the wind tunnels and other facilities, and then work together with an experienced researcher for several years to develop my capabilities to do independent research. What actually happened was that Dr. Katzoff sat down with me, explained the problem, handed me some books on basic aerodynamics and some research papers relating to his problem, and sent me off to solve it. What a shock! Once more I had gotten in over my head. However, there was no reasonable option but just to dig in and do my best. I had two major problems to overcome: first, to learn the basics of fluid dynamics and aerodynamics; and second, to solve Dr. Katzoff’s problem. I spent as much...

  Success – Upside & Downside When I presented the solution to Dr. Katzoff, he was visibly pleased and impressed. He wrote up a technical paper on the problem and made me second author. I think that he felt as much relief as I did. The novice that had worked on the problem before being replaced by me had spent several months on it, and Dr. Katzoff had begun to fear that all of the time spent on it would go to waste. It felt great to have a publication to my credit, and it wasn’t too long before I had another. But this bit of research taught me an unexpected, and somewhat unpleasant, lesson. In the course of my studies of boundary effects on wind tunnel flows, I had come across two publications that analyzed the interaction of an acoustic wave with a slipstream, which occurs at the boundary of a steady flow through a stationary gas. The two authors had attacked the problem in very different ways but had arrived at the same result...

  Money My immediate concern when I entered on duty was financial, which translates to income. When I applied for a position at NACA, I had little hope for a significant increase in salary beyond my meager math instructor’s income. I had heard that the starting grade for engineers was GS-5, which at that time would represent only a slight improvement over my college instructor's salary. However, on reporting for duty I was pleasantly surprised to find that I would be ranked as a GS-7 because I had a graduate degree. Furthermore, a cost-of-living raise had recently been implemented, which added a second bump beyond the income I had expected. I felt a great sense of relief, as I now had a salary beyond the actual requirement for a very modest existence for a family of three. However, it still was not sufficient to permit me to set aside the kind of savings that would be required to purchase a home, establish a fund for my daughter’s future education, etc. That problem...

  Ray Wright By the time NASA was formed the era of the “Nacka Nuts” had pretty much ended. One of the few exceptions was my first branch head, Ray Wright. He was my direct supervisor, my branch head, although my initial research was conducted for Dr. Katzoff. Our branch offices were located in the building that also housed the offices of the engineers of the 8’ Transonic Tunnel Branch. The building faced Back River, a minor inlet of the Chesapeake Bay. At our building Back River was probably about a third of a mile across. Ray Wright lived on the opposite side, directly across from our building. Consequently, he rowed to work – which wouldn’t have been an exceptional decision if he had limited that practice to periods of reasonable weather. However, he doggedly stuck to it, summer and winter, rain or shine, the only exceptions being major storms, heavy surf (actually on one occasion in high wind and strong tide he rowed for more than an hour to get across the water)...

  The NACA Research Culture The personnel at LRC were classified according to their functions. There were the professional research engineers and the non-professionals. The engineers were of two types: experimentalists and theoreticians. The support personnel consisted of technical support (wind tunnel mechanics, machinists, typists, etc.) and infrastructure support. There were also a couple of non-research professional positions: technical librarians and “mathematicians”. These mathematicians were not, in any sense, like the mathematicians that taught math at UVA, nor were they like the theoretical physicists (which was to become my classification). They performed some of the computational tasks that were subsequently performed by electronic computers. Although the librarians and mathematicians often developed a certain familiarity with some of the technical terminology, they didn't have the scientific background for research...