Need an extra course, any ideas?

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Discussion Overview

The discussion revolves around selecting an additional math course that would be beneficial for a physics major. Participants explore various math courses and their applicability to physics, considering the constraints of the participant's schedule and prior coursework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that topology can be useful in classical mechanics, particularly concepts like open balls and compactness.
  • Group theory from abstract algebra is noted as useful in solid state physics and particle physics due to symmetry groups.
  • Complex analysis is highlighted as generally useful and likely to reappear in graduate studies.
  • Numerical analysis is mentioned as a fun course that provides practical skills for research and employment.
  • Several participants recommend courses such as Probability Theory, Complex Variables, Combinatorics, Real Analysis, and Numerical Analysis for their broad applicability across STEM fields.
  • There is uncertainty regarding the necessity of Advanced Linear Algebra, with questions about whether one course is sufficient.

Areas of Agreement / Disagreement

Participants express multiple competing views on which math courses are most beneficial for physics, and there is no consensus on a single best choice. Some courses are recommended by multiple participants, while others are debated.

Contextual Notes

Participants note the importance of considering the participant's specific physics concentration and prior coursework when selecting courses. There is also mention of the potential challenges of taking topology without a background in real analysis.

Who May Find This Useful

Students majoring in physics or related fields who are considering additional math courses and seeking advice on course selection based on applicability to their studies.

malignant
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In the fall I currently only have 11 credits and no physics courses will fit in my schedule with the way the times are set up. I was going to either take a math or a computer science course(leaning towards math).

Besides PDEs/intro linear algebra course, which math courses would generally be the most useful in physics?

Some of the options I was looking at include:

Abstract Algebra
Advanced Linear Algebra(Edit: this is only offered in spring so I can't do this)
Probability Theory
Complex Variables
Combinatorics
Topology
Number Theory
Real Analysis
Numerical Analysis (I have 2 programming courses so this wouldn't be over my head)

My problem is I'm not too sure which ones will actually be useful and applicable to my physics courses.

Currently I have Calc1-3, ODEs, PDEs, some self-studied complex variables, and an introductory Linear Algebra course
 
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I found some of topology (but not the course itself) useful for some classical mechanics. Notions of open balls and compactness are nice. I took topology without real analysis, but I wouldn't recommend it; it was rougher on me than the other students who had seen a lot more proof-based math. Numerical analysis was definitely a fun course as a physics major.

Group theory (abstract algebra) is useful. In solid state you have symmetry groups and it's also used in particle physics. Complex analysis is just plain useful, and you'll see the material come up again in graduate school. I'd say to pick one of these two.

Another option, depending on how your school/department does these things, is an independent study in physics.
 
It's not clear how many years you have been in college already. Sooner or later, you should take the courses listed below:

Probability Theory
Complex Variables
Combinatorics
Real Analysis
Numerical Analysis

Depending on you physics concentration, you might want to squeeze in topology and group theory as suggested by JEB, but the courses listed above have pretty general application across the STEM spectrum.
 
SteamKing said:
Probability Theory
Complex Variables
Combinatorics
Real Analysis
Numerical Analysis

I noticed you didn't include Advanced Linear Algebra, is just one course on it good enough?
 
Numerical Analysis wouldn't be a bad idea. It'll give you skills that will be useful for research and possibly employment.
 
malignant said:
I noticed you didn't include Advanced Linear Algebra, is just one course on it good enough?

You said it didn't fit your schedule. Also, not sure that the course would contain.
 

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