Functional Analysis, Neuroscience, and Grad School

In summary, the speaker is interested in applying to grad schools for either functional analysis and its involvement in QFT or computational/theoretical neuroscience. They find pure math more enjoyable but are concerned about job prospects in their specific area of interest. They are considering going into computational neuroscience as it has more opportunities and involves some mathematics, and they mention specific programs and researchers that use math in their work. They are seeking advice on other fields that use a lot of mathematics and are in demand, as well as areas of pure math or theoretical physics that are not oversaturated. They also mention the importance of having broad interests when starting grad school.
  • #1
empleh
3
0
I'm going to be applying to grad schools next year (I have an undergrad degree in math and phyisics), and I have narrowed down my areas of interest to two fields: functional analysis and it's involvement in QFT; and computational/theoretical neuroscience. I find pure math more enjoyable, but I'm concerned about job prospects. The specific area of math I'm interested in doesn't seem to be that popular. Unless I'm blind, there appears to be very few mathematicians working in c* algebras and operator theory. There are many in Europe (in both math and physics) but not in America. Is there a reason for this? Is it career suicide to go into this field? I would think with the yang mills mass gap problem still unanswered, the field would be more populated.

The "safe" option is to scrap math and go into computational neuroscience. I've always been fascinated with the brain and see wonderful things happening once the brain is understood completely. Computational neuroscience has at least some mathematics involved in it, especially statistics. MIT has a statistical neuroscience group that works in this area. There is also people like William Bialek and Michael Berry at Princeton who use a lot of math in their theoretical models of the brain. One positive aspect of neuroscience is that getting into a grad program at a top school would be much much easier than in math. I can actually consider applying to MIT, Harvard, Caltech etc... which would be kind of refreshing.

Any advice? Are there any other fields out there that are "in demand" but use a lot of mathematics? Are there any areas of pure math that fit this description? Any areas of theoretical physics that are not overly saturated (quantum information?)?
 
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  • #2
Just curious, how have you decided that your mathematical interests are so narrow at this point? The advice I have read strongly says to try to have as broad interests as possible when starting grad school (within reason; obviously you may know you prefer analysis to algebra) so that one will not be overly constrained in choice of school and advisor.
 

FAQ: Functional Analysis, Neuroscience, and Grad School

What is functional analysis?

Functional analysis is a branch of mathematics that studies vector spaces and linear transformations. It is commonly used in fields such as physics, engineering, and economics to describe and analyze systems with multiple variables.

How does functional analysis relate to neuroscience?

Functional analysis is used in neuroscience to study the neural networks and systems that underlie brain function. It can help researchers understand how different brain regions interact and how neural activity gives rise to behavior and cognition.

What is the significance of functional analysis in grad school?

Functional analysis is an important tool for many fields of study, including neuroscience. As a graduate student, learning and applying functional analysis can help you better understand and analyze complex systems and data in your research.

What are some common applications of functional analysis in neuroscience?

Functional analysis is used in many areas of neuroscience, including studying brain networks, analyzing neural activity data, and developing computational models of brain function. It is also used in techniques such as functional magnetic resonance imaging (fMRI) to map brain activity.

Are there any specific courses or resources for learning functional analysis in grad school?

Yes, there are many courses and resources available for learning functional analysis in grad school, including textbooks, online courses, and workshops. Your university's math or neuroscience department may offer specific courses in functional analysis, or you can also find resources through professional organizations such as the Society for Neuroscience.

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