Which Math Elective Best Prepares for Advanced Quantum Mechanics?

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In summary, based on the conversation, it is recommended to take a Probability course for learning about advanced quantum mechanics and related subjects in the future. Other courses such as Numerical Analysis, Mathematical Modeling, and Digital Image Processing may also be useful for employability and developing quantum mechanical models, but Probability is considered the most important for understanding quantum mechanics and statistical mechanics. It is also possible to take these other courses in the future if needed.
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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.
 
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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.
 
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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.
 
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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.
 
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1. Probability
2. Numerical Analysis
3. Modelling
4. Image Processing
 
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Related to Which Math Elective Best Prepares for Advanced Quantum Mechanics?

1. What math courses are typically required for a science major?

Most science majors will require courses in calculus, statistics, and sometimes linear algebra. Depending on the specific field of science, additional math courses such as differential equations or discrete mathematics may also be required.

2. Are there any math courses that are recommended for all science majors?

In addition to the required courses, it is often recommended for science majors to take courses in multivariable calculus and differential equations. These courses provide a strong foundation for understanding and analyzing complex scientific phenomena.

3. How important is it for a science major to have a strong understanding of math?

Math is a fundamental tool for understanding and analyzing scientific data. Having a strong foundation in math can greatly enhance a scientist's ability to interpret and communicate their findings.

4. Are there any online resources or study tools that can help with math courses for science majors?

Yes, there are many online resources and study tools available for math courses. Khan Academy, Wolfram Alpha, and Mathway are just a few examples of websites and apps that offer tutorials, practice problems, and step-by-step solutions for various math concepts.

5. What advice would you give to a science major struggling with their math courses?

First, don't be afraid to ask for help from your professor or a tutor. They can provide additional explanations and practice problems to help you understand the material better. Additionally, practicing regularly and seeking out additional resources such as online tutorials can greatly improve your understanding of math concepts. Don't give up and stay determined!

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