Mathematics useful for Physics classes

AI Thread Summary
The discussion centers on identifying the most beneficial mathematics courses for a physics major to take alongside or prior to specific physics classes. Key mathematics topics highlighted include multivariable calculus, differential equations, and linear algebra as foundational courses. Advanced topics suggested for deeper understanding include complex analysis, boundary value problems, tensor analysis, group theory, and differential forms, particularly for advanced physics areas like quantum mechanics and thermodynamics. The importance of linear algebra in quantum mechanics and advanced algebra for quantum field theory (QFT) is emphasized. Additionally, the book "Mathematical Methods in the Physical Sciences" by Mary Boas is recommended as a crucial resource for undergraduate physics students to grasp necessary mathematical concepts. Overall, the focus is on aligning mathematics coursework with the demands of upcoming physics topics to enhance comprehension and application in theoretical fields.
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I'm not going to ask what mathematics are relevant to physics, I know the answer is all mathematics. I was hoping you guys could help me figure out which specific mathematics topics would be best to take concurrently or prior to certain physics topics, so that the order of my classes is most beneficial to my understanding (I'm a physics major, and I'm going to go a bit beyond a minor in math). I am going to be taking some 300-level differential equations and partial differential equations as well as vector analysis. I could go deeper into these topics or to more statistical/analysis topics, or more pure mathematics, or really anything you could think of including graduate level. I'm looking for the greatest connection to my upcoming physics classes however, which are (in approx. order):

-Computational Physics
-Intro to Condensed Matter Physics
-Thermodynamics
-Optics
-Mechanics
-Electricity and Magnetism 1&2
-Intro to Quantum Mechanics 1&2
-Elementary Particles

Any suggestions? Also, take into consideration that I'm considering a more theoretical field likely involving heavy QM and perhaps particle/high-energy physics. I've already gotten the suggestion that a more advanced linear algebra that describes it more fundamentally would greatly benefit QM, and advanced algebra would benefit QFT specifically. This is such a complicated question though that I want to get as much input as possible.
 
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For undergrad:
- multivariable calculus,
- differential equations
- linear algebra

then
- complex analysis
- boundary value problems

later
- tensor analysis
- group theory
- differential forms
 
E&M - vector analysis is useful to understand all the derivations
Quantum - all kinds of integrals, linear algebra/matrices, spherical harmonics, Dirac notation
Thermo - so far, a lot of partial derivatives
 
Check out the various threads that we have had on Mary Boas's text "Mathematical Methods in the Physical Sciences". For any undergraduate physics and engineering student, this should be a book to refer to, and at the basic level, the math that you will need to survive. For a physics majors, the chapter on Calculus of Variation alone is worth the price of the book!

Zz.
 
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