Programs Which classes? Double major in physics and math? (again )

AI Thread Summary
The discussion revolves around a freshman physics major facing a scheduling conflict between two pairs of introductory classes: graph theory vs. continuum mechanics and statistical mechanics vs. numerical analysis of ODEs and PDEs. The individual expresses a preference for numerical analysis to enhance programming skills and employability, despite having fulfilled math requirements for their physics degree. Graph theory is recognized for its applications in various fields but is deemed less relevant to immediate career goals. Continuum mechanics is highlighted as a valuable course that builds on existing knowledge in mechanics, although it does not contribute to graduation requirements. The main dilemma is whether to prioritize classes that fulfill graduation requirements or those deemed more useful for future employability. Opinions vary, with some advocating for continuum mechanics due to its relevance in physics, while others suggest statistical mechanics for its foundational concepts in the field. Ultimately, the choice hinges on balancing personal interests, graduation requirements, and future career aspirations.
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Background: I'm a freshman physics major, and I noticed that I have a time conflict between these 2 pairs of introductory classes that I want to take, and they are only offered once in 2 years, so I will like some opinion on which I should take:

1. graph theory OR continuum mechanics
2. statistical mechanics OR numerical analysis of ODEs and PDEs

The graph theory class is using a book by Chartrand; the continuum mechanics class is taught without a reference text; the statistical mechanics class is taught from a book by ; the numerical analysis class is taught using a book by R. L. Burden;

My heart tells me to go for numerical analysis because I haven't had any computing classes yet, and this gives me good reason to touch up on my programming ability while doing coursework; and gives me a more employable skill than statistical mechanics.

The issue is, I've already taken more than enough mathematics classes for my physics degree requirements and even a minor in mathematics. There are more interesting math classes coming up ahead: graduate algebra etc. Call it bad planning but I really enjoy taking these extra math classes; at the same time, I'm told it's no point doing a double major in math since I'm planning to go to grad school for physics.

This is where graph theory comes in. I know that graph theory has many applications, in computer science, electrical engineering, and simply as a research area. But these don't seem relevant to my immediate interests/internships/jobs that I am applying for. However - I will need graph theory to graduate with a math major!

Which brings me to where continuum mechanics bothers me... It's being taught by a great professor, it is a very useful class, and I will be building on my background in mechanics, statics, heat transfer, thermodynamics, fluid mechanics, ODEs, PDEs etc. instead of having a standalone in graph theory. But it's another useful class which will not contribute to my graduation requirements!

To put it short:

- If I were to assume I'm going double in math and prioritize graduation requirements, I'd take graph theory + numerical analysis.
- If I stick to a pure physics major, and prioritize graduation requirements, I'd take ? and statistical mechanics.
- If I were to go for the more useful classes for employability first, I *think* continuum mechanics AND numerical analysis is the way to go.

Which combination would you choose?
 
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I would probably take Statistical Mechanics. Concepts from Stat Mech show up almost everywhere in physics, such as entropy.
 
:/ It's a tough choice. Any other thoughts on this?
 
If I were you I would take continuum mechanics. It's far more useful to a physicist, then graph theory could ever be. Of course, I'm a bit biased, I already took graph theory and I didn't like it, so I would prefer anything above it :biggrin:

As for the second choice, I really don't know. Both classes are quite interesting and could be very useful to you. It's a tough choice...
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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