Mathematical Background

As I was reading Jacques’s post about UT’s undergraduate math requirements for upper-division physics, I knew he would get at least one comment or trackback about the general watering down of standards, or some such. I was not disappointed.

The issue Jacques describes has nothing to do with watering down of standards. Four semesters of math is (or should be) sufficient to get through upper-division Quantum Mechanics. Linear Algebra issues aside, the difficulty of upper-division Quantum Mechanics stems from the conceptual issues, not the math. The problem, as Jacques points out, is a mismatch between the math curriculum and the physics curriculum.

The UT physics department could do one of three things to fix this problem.

  • Require all physics students to take, or test out of, both the Advanced Calculus class and the Linear Algebra class. Physics majors really ought to have both under their belts.

  • Forget about those two a la carte classes. Instead, require all upper-division majors to take a “Mathematical Methods for Physicists” class, designed to ensure that everyone has the right machinery to forge through their upper-division work.

  • Coordinate with the math department; adjust the mathematical core accordingly.

My alma mater used the third approach. The math, engineering, computer science, and natural science departments all coordinated closely on the base four-semester mathematics core. Individual departments could then layer additional requirements, but at least everyone had a common foundation, even the biologists and computer scientists. This solution worked great for a school with 700 undergrads, where all the professors knew each other personally, shared babysitters, and so on. It would probably work less well for UT.[1]

1. The main disadvantage of this “Grand Unified Core” approach is that it generates a great deal of whining from certain students over “taking math that I’ll never use!” Long ago, I used to sympathize with my oppressed computer science and biology brethren. But now… not so much. Over the last few years, I have run into senior developers who did not understand that ln (A + B) is not equal to ln A + ln B. And who when queried about this responded, “Look, I have a mathematical background, I really can’t explain it to you.” Professors of All and Sundry Technical Disciplines: please don’t let this happen to your graduating seniors. Thank you.

One thought on “Mathematical Background

  1. Every once in a while, I regret the fact that I didn’t get to take any math classes in my undergraduate days. …the last time was in Fall 1999….and I was able to get by with trigonometry.

    I could never figure out why all the lower division math classes at my university met 5 days a week at 8am. There was no way to take math and sleep late! I felt cheated.

    It made no sense because all lower division language classes met the same time…that’s why I don’t speak 3 languages and possiblly why I had to write it out the stuff about 1nA + 1nB to see what Evan meant.

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