What are the best math classes for physics majors?

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Discussion Overview

The discussion revolves around the selection of upper division math classes that would be beneficial for physics majors pursuing a math minor. Participants explore various mathematical topics and their relevance to physics, including theoretical and applied aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest vector field theory, partial differential equations, and numerical analysis as highly applicable to physics.
  • Others propose differential geometry, particularly in relation to general relativity, as a valuable course.
  • Several participants emphasize the importance of linear algebra, with a preference for proof-based courses.
  • Complex analysis is mentioned as essential if not covered in physics classes, with some advocating for both ordinary and partial differential equations.
  • Numerical methods are recommended for those interested in programming, while group theory is suggested for those leaning towards theoretical physics.
  • A participant shares a personal experience highlighting the significance of complex variables in their graduate studies, expressing regret over not taking it as an undergraduate.
  • Another participant reiterates the value of differential geometry for those interested in general relativity.

Areas of Agreement / Disagreement

Participants express a range of opinions on which math classes are most beneficial, with no consensus on a definitive list. Multiple competing views remain regarding the prioritization of specific courses.

Contextual Notes

Some responses assume prior completion of calculus and ordinary differential equations as part of the physics major requirements, which may limit the applicability of certain recommendations.

Romperstomper
I'm majoring in physics and getting a math minor. I have to take 3 upper division math classes to get the minor. I'm wondering which math classes I should look at taking that would be good for physics majors.

Thanks.
 
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I would think classes in vector field theory(think Stoke's theorem), partial differential equations, and numerical analysis/numerical methods would rank high under "applicability to physics" in general.

Alternatively, differential geometry may be appropriate as well (in the context of general relativity) and also upper-level linear algebra (in the context of quantum mechanics)
 
complex analysis if you don't cover it in a physics class. Otherwise, the best is probably differential equations (both ODE and PDE)
 
if you haven't taken linear algebra, take that. preferably a proof-based one.

can't go wrong with complex variables and more differential equations, either.
 
I would take linear algebra, ordinary DEs, and partial DEs.
 
PDEs, Dynamical Systems, Numericals
 
I assume you already have to take calculus (including multivariable) and ordinary differential equations as part of your physics major requirements. In that case I would pick linear algebra, complex variables, and either numerical methods (if you're into programming), partial differential equations, or group theory (if you're inclined towards theoretical physics).

When I started grad school, I soon found out that I really wished I had been able to take a complex variables course as an undergraduate. My small college didn't offer one. But my first semester included an E&M course taught by an instructor who was really into conformal mapping for solving electrostatics problems. And in other courses I encountered integration in the complex plane. I ended up taking complex variables as one of my two required "cognate courses" (courses outside the physics department).
 
jtbell said:
I assume you already have to take calculus (including multivariable) and ordinary differential equations as part of your physics major requirements. In that case I would pick linear algebra, complex variables, and either numerical methods (if you're into programming), partial differential equations, or group theory (if you're inclined towards theoretical physics).

When I started grad school, I soon found out that I really wished I had been able to take a complex variables course as an undergraduate. My small college didn't offer one. But my first semester included an E&M course taught by an instructor who was really into conformal mapping for solving electrostatics problems. And in other courses I encountered integration in the complex plane. I ended up taking complex variables as one of my two required "cognate courses" (courses outside the physics department).


i can honestly say that complex variables was my favorite math class I've ever taken.
 
differential geometry, if your so inclined to get into general relativity
 

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