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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.

Posted by Evan Goer on Jan. 30, 2005 at 10:52 AM | Comments (1)