Math Courses For Condensed Matter Theory or Quantum Optics

[PManslaughter]

What extra math courses should an undergrad take (or self-study) if they want to go into Quantum Optics or Condensed Matter theory?

I've already taken calculus, linear algebra, ODEs, PDEs, and complex analysis (I will also be doing a second course on linear algebra in two months time).

 

[liideal]

I have not learned that,but I heared if you want learn Quantum Optics you should learn advanced quantum mechanics:the Quantum Field Theory first.

 

[Andy Resnick]

What extra math courses should an undergrad take (or self-study) if they want to go into Quantum Optics or Condensed Matter theory?

I've already taken calculus, linear algebra, ODEs, PDEs, and complex analysis (I will also be doing a second course on linear algebra in two months time).

I'm not sure what course this falls in, but I wish my Quantum Optics students has a stronger grounding in Fourier Transforms- not just transform pairs, but understanding the connection with convolutions, using it to solve PDEs, etc. If you can find a copy of Mandel and Wolf's "Optical Coherence and Quantum Optics", you will see what I mean.

 

[radium]

Many current research areas in condensed matter theory make a lot of use of topology and some abstract algebra concepts.

 

[PManslaughter]

Many current research areas in condensed matter theory make a lot of use of topology and some abstract algebra concepts.

Any (undergraduate) textbook recommendations for topology and abstract algebra?

 

[radium]

Math books would not be the best place to learn about how these topics can be applied to condensed matter. I would recommend the physics oriented math books by Nakahara and Stone and Goldbart. The way physicists approach math is much different than the way mathematicians do so honestly, I think after taking a few basic courses, maybe one or two in abstract algebra, analysis, or topology you should have the ability to learn the other things you need on your own. I have heard this from a lot of theoretical physicists including a very mathematically oriented condensed matter theorists and a string theorist.

The math you use is also highly dependent on what area of CMT you want to go into. The math I mentioned is used in the more mathematical/exotic topics. Some examples include field theoretic work (quantum phase transitions, dualities of particles and vortices) and exotic phases of matter which are topologically ordered with topological excitations (they can be classified via their mutual statistics which involves representation theory, braiding, etc). There are also symmetry protected topological states with are topologically nontrivial only if a certain symmetry is present.

On the very nonconventional side there is also AdS/CMT which requires the prerequisite math knowledge you would need to study GR. However, although these methods are used to study condensed matter problems, most of the people in this field are still coming from a HET background (although there are still a few from the other side).

 

[PManslaughter]

Math books would not be the best place to learn about how these topics can be applied to condensed matter. I would recommend the physics oriented math books by Nakahara and Stone and Goldbart. The way physicists approach math is much different than the way mathematicians do

The reason I'm asking is because I hate learning math on the fly in a physics course. It's taught in a very hand-wavy manner, making it harder to grasp the concept.
I'd much rather learn the required math from a math course (or math textbook), then learn how to apply it in physics.