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I am taking a course in physics -- intro to modern physics and physics 2 -- next semester, and the average weighted score, of people who took it in my university, is very low. I am wondering, which branches of Mathematics should I concentrate the most in order to do well in physics because I am going to take a lot more physics classes in the future. Of course calculus, but how about linear algebra, abstract algebra and so on?

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What exactly does this physics course cover? – EuYu Nov 9 '12 at 1:24
Physics requires a lot of mathematics, for example, calculus, linear algebra, group theory, differential equation, complex analysis, plus more. Those are mathematics I used in physics. – Patrick Li Nov 9 '12 at 1:28
@EuYu by just reading over the syllabus some topics are: electromagnetism and applications, light, modern physics, special relativity, Quantum mechanics, Atomic and molecular physics. – diimension Nov 9 '12 at 1:31
@PatrickLi so basically I need to concentrate mostly on those subjects? – diimension Nov 9 '12 at 1:32
Typically, in a course covering so much material there will not be much depth. In that case I would say calculus, differential equations and linear algebra would be the most important. I highly doubt you will require complex analysis or group theory in an introductory course. A little vector calculus probably wouldn't hurt for electromagnetism. – EuYu Nov 9 '12 at 1:35
up vote 1 down vote accepted

If you take Calc III before Phys II, everything will make sense right away. In modern physics you should mainly encounter special relatively, quantum mechanics and statistical mechanics. Therefore a good understanding of ODEs, PDEs (especially how to set up boundary conditions), probability theory, discrete math (for stat mechanics), and some complex variables is essential. You might need linear and abstract algebra, but I doubt you will study Pauli matrices, Lie groups, etc. in intro modern physics class. One think for sure, you will do well in modern if you are good at integration and understand how to solve PDEs and set up boundary conditions. Special relatively just takes a while to get used to. Also, in quantum mechanics, you should encounter some tricky integrals, for example, Gaussian integrals, so knowing how to do them quickly should help. If you will not have time to take all of the aforementioned classes, I would recommend Theoretical Physics playlist on this YouTube channel. If you watch all the videos and understand each topic you should be fine.

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Thank you very much for that channel! In your opinion should I take PDE course, instead of an analysis course next semester, along with my physics course? – diimension Nov 9 '12 at 1:58
You mean real analysis? Rigorous calculus? No, take PDEs class. It will help with modern and other physics classes like quantum mechanics, calculus of variations and electromagnetism (not Phys II). – glebovg Nov 9 '12 at 2:01
Yes, real. I signed up for abstract algebra and real analysis 1. I am going to drop analysis for PDE now, thank you very much for your suggestion! – diimension Nov 9 '12 at 2:04
Understanding of algebra will help you in particle physics. Of course, a good understanding of analysis is helpful, but you will mainly prove theorems in analysis. Algebra will seem more applicable to physics, especially groups. – glebovg Nov 9 '12 at 2:07
You're welcome. – glebovg Nov 9 '12 at 2:59

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