I’ve been forced to broaden my horizons in my PhD pursuit. That’s because, although I’ve done coding since I was eighteen, I’ve had to acquire a deeper understanding for two things: linear algebra and numerical methods. It’s no understatement to say that both of these are at the core of the advances wrought by computerisation, whether we’re talking about statistical analysis or (in my case) simulation.
After my initial boffo performance, I turned to my Iranian friends for more help. So they let me use some of the books they found useful for study back in the “old country”. One of those was a sizeable book entitled Applied Numerical Methods by Brice Carnahan, H.A. Luther and James O. Wilkes. As was the case with their wedding video, the heart skipped a beat, because the middle author, Hubert A. Luther, was my Differential Equations teacher at Texas A&M, forty years ago this spring.
Applied Numerical Methods was, AFAIK, the first really comprehensive textbook which combined linear algebra, numerical methods, and coding (in their case, FORTRAN IV) in one text. Although some of the methodologies have been improved since it was published in 1969, and languages have certainly changed, it’s still a very useful book, although a little dense in spots. Many of the books on the subject that have come afterwards have learned from its mistakes, but still refer back to the original.
Dr. Luther taught me the last required math class in my pursuit of an engineering degree at Texas A&M. It wasn’t an easy class, even after three semesters of calculus (which I did reasonably well at). Although he was originally from Pennsylvania, he acclimated himself to the Lone Star State with western shirt, belt and string tie, the only professor I can remember who did so. The start to his course was especially rough; the textbook was terrible, he was a picky grader, the scores I got back were low. I thought I was facing the abyss…until another one of those “aha” moments came along.
We (the engineering students) were standing outside our Modern Physics class, which came before Differential Equations. I found out I wasn’t the only one having this problem. But one of my colleagues, a Nuclear Engineering student who went on to become my class’ wealthiest member, had a simple suggestion. Go visit his office, he said. He’s lonely (he was nearing retirement) and likes the company. Your grade will go up.
I wasn’t much for visiting my professors, but I was desperate enough to try anything. I made a couple of office visits. I’m not sure how helpful his advice was, but his grading became more lenient and I got through the course OK.
Today I’m on the other end of the visitation. I spend a lot of time in the office with no student visits. Part of the problem comes from scheduling, both theirs and mine. But I’ve found out something else about student visits: the students that come to see you really care about what they’re supposed to be doing in your class. Although there are still students who think it their duty to “tough it out” without asking questions, many others just want to get through in the quickest and least time-consuming way they can find.
I’m glad I took my classmate’s advice and made the office visits. But there are two other lessons I have learned since that time.
The first is that I wish I had taken a numerical methods course taught by Dr. Luther, it would have prepared me for what I’ve been doing both before and during the time of my PhD pursuit.
The second is that, when I started my MS degree twenty years later, I took a course over basically the same material taught by a Russian. I found out that there was a great deal I hadn’t learned from Dr. Luther, and that American math education leaves a lot to be desired of. So sometimes making the way easier up front comes back to get you in the end.