Linear Algebra Course

[physjb]

hi all,

Im a lower division student at a large public university and I had a question about which linear algebra course to take.

My school offers two different courses in linear algebra, one that is mainly computational linear algebra and the other is more proof oriented. The course description says that students thinking about graduate school in mathematics should take the proof based one. As a physics major, is it a good idea to take the proof based class over the computational course? What if I'm interested in doing theory?

Thanks in advance

[zxcv]

If the "computational" course is actually oriented toward numerical methods with linear algebra then it might be useful, but I suspect it is really more about explicit calculation than computational methods. In that case, I would take the proofs oriented course. It will be more difficult, but getting a sense of linear algebra proofs could be useful if you're interested in theory. You also want to be sure you get exposed to more advanced concepts like the spectral theorem that will be useful in quantum mechanics. Otherwise, you'll get plenty of experience doing explicit calculations in your physics courses.

[swepi]

Here are my two cents. First, consider how many other math courses you would like to take. If you plan on taking any sort of "advanced calculus", then the more theoretical course on linear algebra may be more helpful. Linear algebra is usually a mixture of theory and technique, so even the theoretical course should teach you how to row reduce a matrix. What ever course you take, you should come out of it understanding what the following terms mean: finite dimensional vector space, linear combination, linear transformation, orthogonal, orthonormal, scalar product space, hermitian operator, eigenvalue, and eigenvector.

Quantum mechanics is generally couched in the terminology of linear algebra. Keep in mind that Heisenberg invented "matrix mechanics" and the whole trouble with physical quantities (observables) that cannot be measured simultaneously is that they don't "commute".

This is not to say that the "computational" course would not be useful. Just make sure that you would run into enough theory to understand what the terms above mean.

I hope that helps, and don't hesitate to post again if it doesn't.