I Only Need ONE More Math Book…

Against my better judgment, I am stirring the moldy stew of my abandoned STEM education some more.

I’ve been watching videos made by a physics grad student. Today I watched one in which he listed the math courses he had taken. He always sounds extremely smart, and sometimes I have wondered if he was a much better student than I was, so I am curious to find out what he actually knows. I don’t want to think I was a complete idiot back when I was part of the shared agony of the physics community.

This morning I thought about something my undergrad advisor said. He told me I was “weak in math.” I don’t recall when he said that. Maybe he said it before I got it together, or maybe it was something he said to fill me with confidence right after I told him I had been accepted by the University of Texas.

I don’t know what “weak in math” meant to him, either. Maybe he thought John von Neumann was weak in math. After I recalled his remark, I remembered that four of my math professors had been pretty impressed with me. I wonder what they thought about people who were strong in math.

I remember messing with my PDE professor’s mind. He gave us a problem to solve, and I used a contour integral. I didn’t know he wanted us to use another method. He was pretty surprised. At first, he just said I was wrong. Then I talked to him about it. He took my work home, looked at it, and returned the next day and confirmed that I was right. It wasn’t obvious to him right away. He was impressed. That was one of my math glory moments.

But maybe I really was weak in math, and the math professors were so used to people so incompetent, I just looked good.

I looked at the video, and I was surprised to find out that the video guy had taken fewer math courses than I had. He didn’t take a complex analysis course. I didn’t even know it was possible to get a physics degree without complex variables.

I guess it was, though, because this guy did it, and when my advisor told me to take the course, he spoke as though it were optional.

Let’s see.

Calc I
Calc II
Multivariable Calc
ODE
PDE
Complex Analysis
Mathematical Methods for Physicists
Linear Algebra
Real Analysis

That’s all I remember. The course for physicists was taught by a physicist. Very useful. They used Arfken’s book, which wasn’t bad at all.

I don’t think I took a statistics and probability course, because I don’t know anything about probability.

Needless to say, I also took a ton of physics courses, every single one involved calculus and other types of advanced math, and sometimes I had to learn math that wasn’t covered in my math courses.

When I was a grad student, my mechanics prof taught us differential geometry in about a week. Did anyone actually learn it? I doubt it. The name is deceptive. It’s not trigonometry. It’s calculus on weird spaces. It’s a very demanding subject to which entire courses are dedicated.

I never got a grip on it. Ordinarily, when professors slammed us with new math during physics lectures, we picked it up. Differential geometry was the only exception for me.

The class started with a full room, and at the end of the semester, there were five people, including Dr. Matzner, a quiet and pleasant man who had written the thin but scary textbook. I got an A, and I didn’t really use differential geometry. Sometimes I think I got an A for not dropping the course.

I had taken…let’s see…three mechanics courses as an undergrad, so presumably, I knew a couple of things before I showed up.

The graduate program was very hard. Most people dropped that particular mechanics class because it was so hard. We were expected to teach two labs and take three courses. Teaching assistants in other departments had to take three courses, so we did, too, even though one physics course is as hard as about 50 history courses. Liberal arts majors don’t like to hear that their work is easy, but BOY, is it easy.

UT gave us an escape hatch, which is ridiculous. We could use “the colloquium” as our third course. They pretended it was a physics course. I think the course name was 398T, but I’m probably wrong. The colloquium was a weekly informal lecture given by a guest. I recall watching a guy from the Electrosource battery company, telling us about his lead-and-fiberglass composite batteries.

The colloquium was a joke, but it was necessary, because otherwise we would have been so buried in work there would have been no time for things like bathing and eating, and participating in research would have been unthinkable.

UT was like a machine that made French fries. Student/potatoes went in one end, they were forced through the array of sharpened blades, and they fell out as fries at the other end. There was no pity or flexibility. Had intelligent people run the place, the requirements for physics students would have been different from those for people who were taking drama classes, learning how to be convincing trees, but you could not bend the rules at UT. Not when it was so much easier to bend students.

Here’s how sensitive UT was to students. I went to the gym once to look it over. They had a row of toilets against a wall. Not stalls. Toilets. There must have been 20 of them. French fries don’t need privacy! Man up and poop in front of your professors, your fellow students, and anyone else who walks in! Audie Murphy didn’t have a stall when he was fighting the Nazis!

Maybe they were trying to discourage gay trysts, for which bathroom stalls have traditionally been prime venues, although having no privacy at all certainly encouraged voyeurism.

Anyway, I did not learn much about differential geometry, and it has always bothered me. I am sorely tempted to get a book and see what I can do with the subject.

If anyone else is interested in this brand of self-torture, I think I’ve found the correct book. A guy named John Lee wrote a text called Introduction to Smooth Manifolds, and it’s supposed to be “wordy,” “readable,” and “suitable for self-study.” To a physicists, those are fighting words, because physicists are crazy, but to a student, they are dog whistles of hope.

People in STEM fields often criticize books that explain things, which is bizarre. Explanation is the primary purpose of a book. The only other purpose is reference, and reference is only useful to people WHO ALREADY KNOW THE MATERIAL. I’ve seen people insult books that explain things well yet don’t cover their subjects exhaustively. Hello? You’re not supposed to cover a subject exhaustively in one book or course. It’s okay to write two separate books.

I made it through graduate electrodynamics (with a weak B) but that certainly didn’t mean I knew everything in the horrible, exhaustive textbook. My professor didn’t know it all, either. If no one could possibly learn everything in the book, how was its exhaustiveness helpful to anyone, EXCEPT people who wanted a reference book?

“Reference” and “instruction.” Two totally different concepts a person with an IQ of 170 ought to be able to comprehend. But then these are verbal concepts, so maybe it’s not fair to expect STEM people to get it.

I think maybe STEM people should swing their heads in a circle for a few minutes every day, so some of the brains slosh over into the language/emotion/common sense areas.

If I get this book, I’ll probably read it for two days, put it down, and forget about it. Still tempting, though.

It’s a bad idea. There is no reason to buy it.

Still might, though.