Pure maths or applied maths as a second major to physics

In summary: But, you don't need to go that far; you could take a real analysis course instead.Real analysisReal analysis is a good foundation for understanding complex analysis. It covers things like contour integrals, functional analysis, and Euler's equation. It's a good choice if you want to study complex analysis or probability and statistics.+1
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I am currently in my second year of studying a bachelor in physics and applied maths. My aim is to one day do research in physics. I am particularly interested in subjects such as gauge theories, AdS/CFT and gravity. My question is whether it would be more beneficial to switch from studying physics and applied maths to physics and pure maths? The two courses only differ in third year. These are the differences

Applied Maths
  • Partial differential equations
  • Partial differential equations (numerical)
  • Dynamic systems
  • Optimisation

Pure Maths
  • Real analysis
  • Combinatorics
  • Complex analysis
  • Algebraic structures
 
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  • #2
A priori, it's more likely that applied math will fit into physics. But it ultimately depends on what you want to do. Depending on your university, you could possibly also do an interdisciplinary degree mixing the two if there's classes from each you want to take.
 
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It's a little difficult to be sure without carefully examining the syllabus for each class. The applied classes look OK. The differential equations are pretty much required IMHO. Is it possible to "mix and match?"

The one that "glimmers" there is complex analysis. There are lots of times you will want that in the research areas that you mention. You need things like contour integrals and dealing with Euler's equation and all that good stuff. Possibly real analysis goes with? Maybe keep the differential equations and grab those two analysis courses.

But definitely discuss this with the appropriate guidance person or professor. There may be reasons that this division would be a bad idea.
 
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  • #4
Complex analysis is also important for understanding Fourier analysis. I think that is important.
 
  • #5
Captain Kneecaps said:
I am currently in my second year of studying a bachelor in physics and applied maths. My aim is to one day do research in physics. I am particularly interested in subjects such as gauge theories, AdS/CFT and gravity. My question is whether it would be more beneficial to switch from studying physics and applied maths to physics and pure maths? The two courses only differ in third year. These are the differences

Applied Maths
  • Partial differential equations
  • Partial differential equations (numerical)
  • Dynamic systems
  • Optimisation

Pure Maths
  • Real analysis
  • Combinatorics
  • Complex analysis
  • Algebraic structures

In general the pure maths courses are not likely to provide you with much in the way of a toolbox. The complex analysis, of course, may include contour integration. But, it won't be the purpose of the course to teach you integration methods. The focus of the course may be very different.

Complex numbers, Fourier Analysis and contour integration are covered in mathematical methods books - such as Boas, for example. You don't have to do a pure maths course in complex analysis to study these.

There's something to be said for learning some real analysis, but it may be something that you could do as a personal vacation project. Rather than putting yourself under the pressure of trying to pass an exam in the whole subject. I would definitely advise taking a look at the subject first. You may be horrified by epsilon-delta proofs!

The course missing from your list is Linear Algebra. If there is a pure maths course worth doing as a physicist, I suggest it's linear algebra.
 
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PeroK said:
Complex numbers, Fourier Analysis and contour integration are covered in mathematical methods books - such as Boas, for example. You don't have to do a pure maths course in complex analysis to study these.

... The course missing from your list is Linear Algebra. If there is a pure maths course worth doing as a physicist, I suggest it's linear algebra.
I agree. A full pure math course in complex analysis is not very efficient in learning what you would need to know. Another course that I don't see is probability and statistics, which I think would be helpful.
 
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PeroK said:
In general the pure maths courses are not likely to provide you with much in the way of a toolbox. The complex analysis, of course, may include contour integration. But, it won't be the purpose of the course to teach you integration methods. The focus of the course may be very different.

Complex numbers, Fourier Analysis and contour integration are covered in mathematical methods books - such as Boas, for example. You don't have to do a pure maths course in complex analysis to study these.
FactChecker said:
A full pure math course in complex analysis is not very efficient in learning what you would need to know.
+1
When I was in school taking complex analysis - as taught in the math department - I had no idea what it was all about. Only when I took math methods in the physics department, did it become clear why I might need to use it.

Since then, though, I have learned that the "pure" complex analysis is a beautiful subject and no wonder the math guys loved it so much.
 
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  • #9
These decisions are less important once one realizes that the more important contribution in a good education is not the topic learned but learning how to learn by exposure to a broad array of math and physics topics. Either path should provide that. But in either path you will still likely have to (more or less) teach yourself lots and lots of new stuff in your career.
 
  • #10
Dr. Courtney said:
you will still likely have to (more or less) teach yourself lots and lots of new stuff in your career.
A very good point, often overlooked in these threads.
 

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