Functional Analysis exchange year at Imperial

[George444fg]

Hey,

I would like to do an exchange year at Imperial. I would like to follow as a physicist the Functional Analysis course. However, I have not heard the best things about this peculiar course. What is the audience opinion on that?

 

[mcastillo356]

Hi, @George444fg no personal experience, but yes a personal impression: go ahead, Imperial is on top among international universities
Good Luck!

 

[Joshy]

I had a good experience at Imperial College and would recommend it if you can get in. I studied electronics engineering although I really enjoyed PhySoc and mingled with the students there too. The university has a lot of resources and I felt like the classes were taught well. I felt like it had a good faculty to student ratio so it was easier to conenct with the professors (even some research opportunities); I was also surrounded by a bunch of very talented students and built some good relationships to help each other (I would like to think I was helpful too ).

I don't know much about the class you're asking about probably because of my major, but I didn't hear any of my friends complain about it. Given the above... though... I personally wouldn't get caught up over one (or two) classes.

 

[S.G. Janssens]

peculiar course

Where I studied, students in theoretical physics would usually take an introductory FA course.

How "peculiar" it is from a physics student's point of view, I don't know. Probably the complaint is that it is abstract, requiring initial time investment before it can be applied to concrete problems. Whether or not that is a problem, is in the eye of the beholder.

On the other hand, FA is the language commonly used for the mathematical study of subjects such as partial differential equations, stochastic processes, or operator algebras. It can be taught in different ways, even at the introductory level.

So if you want more specific advice, you can post the course description and prerequisites here. Or even better: Discuss the course description with your student advisors.

In addition to that, as Joshy said: Don't get caught up over one class. Enjoy the exchange.

 

[WWGD]

Where I studied, students in theoretical physics would usually take an introductory FA course.

How "peculiar" it is from a physics student's point of view, I don't know. Probably the complaint is that it is abstract, requiring initial time investment before it can be applied to concrete problems. Whether or not that is a problem, is in the eye of the beholder.

On the other hand, FA is the language commonly used for the mathematical study of subjects such as partial differential equations, stochastic processes, or operator algebras. It can be taught in different ways, even at the introductory level.

So if you want more specific advice, you can post the course description and prerequisites here. Or even better: Discuss the course description with your student advisors.

In addition to that, as Joshy said: Don't get caught up over one class. Enjoy the exchange.

Just curious as to how FA is related to Stochastic Processes?

 

[S.G. Janssens]

Just curious as to how FA is related to Stochastic Processes?

There are many relations, and I am sure you know at least some of them. Some examples, in brief:

On the more general level of probability theory, there are $L^p(\Omega,\Sigma,\mu)$ spaces of $p$-integrable ($\mu$-equivalence classes of) functions on a probability space $(\Omega,\Sigma,\mu)$.

What probabilists usually call "weak convergence" or "convergence in distribution" is really a form of weak$\star$ convergence in a topological dual space.

More specifically, with certain continuous time Markov processes you can associate an infinitesimal generator. This gives a connection between the theory of stochastic processes and the functional analytic theory of operator semigroups, since properties of the process may be studied by studying the infinitesimal generator.

(By the way, I don't think FA is indispensable for studying stochastic processes, but it is indispensable for understanding a considerable part of the work done by others. The same applies to some extent to the connection between FA and PDEs. You can perfectly well do beautiful things in PDEs using classical "hard" analysis, but a lot of work does use the language of FA.)