Graduate Level Math Methods (Physics)

[cmos]

Out of curiosity, I was looking at core course requirements for the PhD in physics at several different schools. I noticed that some schools required a first semester math methods while others do not. Reading the course descriptions, I noticed some overlap between topics usually seen at the undergrad level (Fourier analysis, series solutions to DEs) as well as some more advanced topics (Green's functions, complex analysis).

I am curious if the majority of the physics grad students and degree holders on this forum were give a math methods course in their first year of grad study. If you did, did you think that this course was absolutely necessary before undertaking the rigors of the rest of the common physics core? Or was it more helpful but necessarily a requirement?

I am also curious what the common text(s) is for this type of course. Other comments are always welcomed!

 

[eri]

My grad school required two semesters of math methods, but what the courses contained varied wildly depending on who was teaching it. Arfken was the required text for the first semester, which in my case covered topics like Fourier analysis, Green's functions, and complex analysis, and the second semester we used Numerical Recipes and spent the whole semester going over how to do computational physics and statistical tests. On the whole, I've found the second semester to be much more useful for my area (astrophysics) than the first, although they always threw a complex analysis and Green's function problem on the quals.

 

[George Jones]

I didn't take any mathematical methods course as a grad student. I did, however, take two required semesters of mathematical methods, at the level of Arfken or higher, in my final year of undergrad. Arfken is pretty standard for an advanced mathematical methods course, but see

https://www.physicsforums.com/showthread.php?p=1760434#post1760434

In grad school, I took three semesters (abstract algebra/Lie groups and algebras/ representation theory) of graduate courses in pure mathematics (from the math department), but these were not required.

I'm how necessary it is to have a traditional mathematic methods course before the grad physics core. I thinks at least some topics in this course will be applied in core physics courses, so such a course is helpful.