Deciding between group theory vs. complex analysis

[TheCanadian]

Hi,

I have one spot remaining to take a pure math course, and I'm trying to decide between complex analysis and group theory. Although I've touched some of the basic of dealing with complex numbers in my physics/DE courses, they haven't gone in much depth into them beyond applications. On the other hand, my background in group theory is a bit weak (read: nonexistent). I am also a little uncertain on which area in physics (I'm a physics undergrad) I'd like to go into in the future, but I'm leaning towards topics in astronomy and possibly high-energy physics. Any insight you have on which course might be better to take in my situation would be greatly appreciated!

 

[ModestyKing]

There's a graduate-level course in the Physics department at my school that apparently has undergrads in it often enough; "Mathematical Methods for Physics". From the description and talks to the teacher, you learn both the basics of dealing with complex analysis and the basics of group theory. Is that course a possibility in your school? It would likely only be offered in the Fall, but maybe you can switch around a course to take this spring.

As for your current choice, I don't have the background to say - neither Astrophysics nor High-Energy stuff are my interests. From my uninformed opinion, High Energy physics would benefit more from group theory. I might be thinking of Quantum Field Theory stuff (which you need to know group theory for if I recall correctly).

 

[fresh_42]

Hi,
in my opinion, as someone coming from the algebraic front, complex analysis is for any physicist necessary to know as much as possible. Group theory in it's basics is quite easy. You can learn it from a book during holidays. When group theory becomes a bit more sophisticated it's not unlikely that you'll meet Lie groups. These carry a differential structure which is essential. So learning about complex analysis will help you a lot in understanding the upcoming algebraic structures.

 

[TheCanadian]

There's a graduate-level course in the Physics department at my school that apparently has undergrads in it often enough; "Mathematical Methods for Physics". From the description and talks to the teacher, you learn both the basics of dealing with complex analysis and the basics of group theory. Is that course a possibility in your school? It would likely only be offered in the Fall, but maybe you can switch around a course to take this spring.

As for your current choice, I don't have the background to say - neither Astrophysics nor High-Energy stuff are my interests. From my uninformed opinion, High Energy physics would benefit more from group theory. I might be thinking of Quantum Field Theory stuff (which you need to know group theory for if I recall correctly).

There is a course like that, but it unfortunately has not been offered recently (nor is it planned to) due to lack of interest.

 

[ModestyKing]

You must be talking about an undergrad course. I'm talking about a graduate-level course - all physics graduates should be required to take it their first year!

 

[fresh_42]

Hi,
in my opinion, as someone coming from the algebraic front, complex analysis is for any physicist necessary to know as much as possible. Group theory in it's basics is quite easy. You can learn it from a book during holidays. When group theory becomes a bit more sophisticated it's not unlikely that you'll meet Lie groups. These carry a differential structure which is essential. So learning about complex analysis will help you a lot in understanding the upcoming algebraic structures.

P.S. And nearly everything in physics is about manifolds, vectorfields, special algebras, Banach-spaces and so on. None of them are groups (beside the additive group of vectorspaces) but computations in / with them involve analysis! And mostly complex!

 

[TheCanadian]

You must be talking about an undergrad course. I'm talking about a graduate-level course - all physics graduates should be required to take it their first year!

Hmmm...I was actually referencing a graduate course...

P.S. And nearly everything in physics is about manifolds, vectorfields, special algebras, Banach-spaces and so on. None of them are groups (beside the additive group of vectorspaces) but computations in / with them involve analysis! And mostly complex!

There are two forms of complex analysis offered at my school: one is by applied math, and one is pure math. Would it be preferable to take one over the other? It seems like one is more application-base while the other dwells on proofs a lot...I am not in pure math but understanding the theory seems a lot more important to me. Would you advise against taking the pure math version of the course when the applied math version is available?

 

[fresh_42]

There are two forms of complex analysis offered at my school: one is by applied math, and one is pure math. Would it be preferable to take one over the other? It seems like one is more application-base while the other dwells on proofs a lot...I am not in pure math but understanding the theory seems a lot more important to me. Would you advise against taking the pure math version of the course when the applied math version is available?

Well I guess it's getting personal here. Physicist have a very special kind of computing stuff. As a mathematician it's hard to get used to. So if the course in applied analysis is held by a physicst I truly recommend to take it. On the other hand you need to know a lot pure analysis for astronomy or high energy physics. Alone reading here you permanently see the Lagrangian, derivatives in all its forms, differential operators, Ricci tensors, curvatures etc. All of those appear in astronomy and high energy physics. So sooner or later you will meet them. Complex analysis in it's theoretic form is really helpful as it is the base of all.

 

[mpresic]

Group Theory will be useful (especially in HEP), nevertheless I side with Complex Variables. Looking at graduate school shopper, it seems like grad schools in physics seems to want courses in complex variables as preparation more than group theory.

I know my grad school offered a separate course in group theory in the physics department that I completed. (Although It turns our my undergrad school offered Complex analysis as part of their Math methods graduate physics.) In short, you may not close any doors with either decision, but I still lean towards complex analysis over group theory.

 

[TheCanadian]

You must be talking about an undergrad course. I'm talking about a graduate-level course - all physics graduates should be required to take it their first year!

I looked into it further and although the course is listed online as a graduate level course, it is not being presently offered due to lack of interest. I believe this course on Mathematical Methods in Physics is only listed as an optional course, and not necessary for graduate program completion at my school.