Courses Which Math Elective Best Prepares for Advanced Quantum Mechanics?

[TLeit]

I previously inquired about whether a Probability or Mathematical Statistics course would be a more useful base for learning more about advanced quantum mechanics and related subjects in the future, since I need to take one more math elective next semester for my major. From the two I decided Probability would be better, but I have since been recommended to a few other classes that also sound interesting. I have posted the descriptions below. Any advice on which courses would be best for learning about quantum mechanics and similar fields in the future would be greatly appreciated! I am currently still leaning towards taking Probability.

Numerical Analysis I: Nonlinear equations, interpolation and approximation, least squares, systems of linear equations, and error analysis.
Mathematical Modeling: Introduction to building mathematical models in an applied context, including principles of modeling; project(s) involve modeling open-ended real-world problems. Skills covered may include discrete dynamical systems, differential equations, stochastic models, and linear programming.
Digital Image Processing: Applications of Fourier analysis and wavelets to optics and image processing. Topics include: diffraction, wave optical theory of lenses and imaging, wavelets, and image processing.
Probability: Probability in discrete and continuous sample spaces; conditional probability; counting techniques; probability functions; binomial, Poisson, normal distributions; and transformations of variables.

 

[jedishrfu]

Why not mathematical modeling? Is this computer based? This course could be useful for future job opportunities.

It seems you could eventually use it to develop quantum mechanical models and view how they behave under various conditions.

Next I'd choose Numerical Analysis followed by probability and lastly digital image processing which seems the most specific and narrow of the four listed.

 

[mpresic]

Over 9 years, I worked with an instructor who taught numerical analysis. I completed graduate courses in both image processing, and mathematical modeling. I completed all these graduate courses while working professionally, and I did not take them as an undergraduate. I was fortunate to have a course in probability as an undergraduate, and I believe this was the most important course of the ones you listed in learning undergraduate and graduate level quantum mechanics.

While in graduate school (before my employment) I mentioned to my thesis advisor that I had an interest in digital signal processing and wanted a course on it. He gave me advice, that: sure it is good to have but how much will it contribute to your research area in theoretical solid state physics? I had to wait for my employment before my employer sponsored me to learn it.

All told, all these courses will contribute to your employability, but probability will be most useful to your learning quantum mech, or stat mech. You will also (probably) have opportunities to complete the other courses in the grad school or even your professional career, (possibly sponsored by your employer, if work related). All these courses are interesting, and will contribute to employability, but probability is most useful for QM or stat mech.

If however you want to hedge your bets, and believe you might seek a position immediately (employment) and need the most "applied" course, maybe(?) one of the other three courses could be more sellable to a hiring committee, but even then, I do not think you can foresee which course your committee might think is most important.

PS. I do not think probability will be as much fun as math modeling, but probability will be most useful for QM or stat mech. Also my courses in digital signal processing required probability as a prerequisite.

 

[TLeit]

Thank you for the advice! jedishrfu, I am not sure if the mathematical modeling class is computer-based or not, and I was leaning towards Probability because I have heard that probability and statistics are useful subjects to know for topics like quantum mechanics and statistical mechanics. mpresic, thank you so much for your advice! It is good to know that a probability course is helpful for learning quantum mechanics, and that I will likely have opportunities to complete the other courses in the future if needed.

 

[micromass]

1. Probability
2. Numerical Analysis
3. Modelling
4. Image Processing