January 30, 2005
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.
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Posted by Mathdope on Feb. 07, 2005 at 4:05 PM [#]