real analysis
Re: real analysis
Being familiar with Hilbert spaces could potentially help you in QM.
But I wouldn't suggest it if your intent is solely to improve your physics.
But I wouldn't suggest it if your intent is solely to improve your physics.
Re: real analysis
I took 2 real analysis classes in undergrad and I thought it was lots of fun... but no it's not very helpful in physics. The concepts and theorems from those courses haven't applied to anything I've encountered in physics. Basic definitions like "inner product" might show up in analysis and physics but the uses are different. I've been wrong many times before so don't take my post as an official answer, but if look in any "math methods for physics" book, none of the topics will come from analysis... it's all DEQ's, linear algebra, special functions, vector calc etc. (perhaps "advanced analysis" or graduate level stuff subsumes DEQ theory and L.A. etc, but undergrad analysis is mainly about what the real number system is and developing Calc 13 more rigorously).
But complex variables are used a lot in graduate physics (contour integrals, residues)... so the complex analysis class I had was helpful. However, real is probably a prereq for complex and those math methods books would cover all the complex you need to know for physics anyway.
But complex variables are used a lot in graduate physics (contour integrals, residues)... so the complex analysis class I had was helpful. However, real is probably a prereq for complex and those math methods books would cover all the complex you need to know for physics anyway.
Re: real analysis
I don't think real is a prereq. for complex. It might be in some places, but probably not most. In any case, there's always applied complex analysis classes that focus more on the applications.

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Re: real analysis
Real Analysis classes can be great in helping you think in the exact same way physics requires you to think and it is perhaps the best class there is to master how to set up and solve problems and how to properly define terms and use definitions to help you think logically about a problem. An issue could just be time constraints: a difficult real analysis class could take anywhere from 2o to 60 hours a week of hw depending on the school. And while many great physics students are also heavily into theoretical math, there are also many great physicists who are not nearly as good at math and show their brilliance through understanding abstract ideas purely in physics. Though many would say that pure, abstract math completely owns physics, chemistry and engineering when it comes to how intellectually demanding it is.
Re: real analysis
Just want to mention that real analysis is not necessarily going to be a prereq for complex. For example at my undergrad school complex came before real in the sequence, although the material was mostly orthogonal between the two anyway.
If you want to do some analysis, complex is really much more pleasant than real imo.
Edit: Just realized I pretty much am only repeating twistor.
If you want to do some analysis, complex is really much more pleasant than real imo.
Edit: Just realized I pretty much am only repeating twistor.