Deciding on a Specialty: When to Choose Your Math Dissertation Topic

[Robert1986]

This is a question for anyone who thinks he has an answer:

I'm a first year math grad student (well, I will be in August.) I think for the first year I will take Algebra I&II Analysis I&II, Advanced Linear Algebra, and Complex Analysis (note, this is over two semesters so three classes per semester, not 6 classes this first semester.)

My question is: when did you decide on what area of math (or physics or whatever, if it is similar) to write your dissertation in? In particular, did you know before grad school, or did you really find out what you wanted to do after you took some grad-level courses to see what math at that level is really like?

I think I will need to wait until after the first year to get an idea; is this normal?

 

[chiro]

Hey Robert1986.

I don't have nor are working on a PhD, but don't schools have specific programs and departments that focus on specific kinds of things? If so, wouldn't this imply that you need to have some kind of specific focus with regards to the area (not so much the actual project or narrow investigation focus, but at least the area being narrowed down)?

 

[Robert1986]

Hey Robert1986.

I don't have nor are working on a PhD, but don't schools have specific programs and departments that focus on specific kinds of things? If so, wouldn't this imply that you need to have some kind of specific focus with regards to the area (not so much the actual project or narrow investigation focus, but at least the area being narrowed down)?

Well, where I go - and I imagine this is similar for most places - there are a few Ph.D. programs. For example, we have the Math Ph.D. which is the most "traditional" but we also have a Ph.D. in Computational Science and Engineering (which is like applied math) and we have one in Algorithms, Combinatorics and Optimisation.


I'm the the Math Ph.D. Inside of that there isn't really any other "subgroup". For example, there is no "Algebra Ph.D." or "Math Ph.D. with a major in Analysis", etc.

 

[chiro]

Well, where I go - and I imagine this is similar for most places - there are a few Ph.D. programs. For example, we have the Math Ph.D. which is the most "traditional" but we also have a Ph.D. in Computational Science and Engineering (which is like applied math) and we have one in Algorithms, Combinatorics and Optimisation.

I'm the the Math Ph.D. Inside of that there isn't really any other "subgroup". For example, there is no "Algebra Ph.D." or "Math Ph.D. with a major in Analysis", etc.

What I was getting at though (I should of said this earlier), is that each department whether a pure, applied, computational or whatever will have people who have particular backgrounds.

Because you need a supervisor, and because they will guide you through your research including telling you stuff to go through as well as guiding the formulation of your final topic, it makes sense to know their own background, their interests, and their specialty.

This information narrows things down a lot more than just knowing whether it's pure, applied, computational and so on, and really should be something that you look at very carefully.

 

[Robert1986]

What I was getting at though (I should of said this earlier), is that each department whether a pure, applied, computational or whatever will have people who have particular backgrounds.

Because you need a supervisor, and because they will guide you through your research including telling you stuff to go through as well as guiding the formulation of your final topic, it makes sense to know their own background, their interests, and their specialty.

This information narrows things down a lot more than just knowing whether it's pure, applied, computational and so on, and really should be something that you look at very carefully.

Yes, I agree. Certainly I would pick an advisor based, in part, on the areas he works in. In particular, I would choose an advisor who works in the same field as the field I would like to write my dissertation. I want to know when people typically decide what area to work in because I can't seem to land on a particular topic. I don't have to pick an advisor now (indeed, I can't really pick an advisor, now) but I can certainly ask different people about their fields to try to see what interests me most, if that's what you were getting at.

For example, when I study the Algebra book, I think "Man, why would anyone want to do anything but something in algebra?" But then when I study the Analysis book, I think "Holy, Cow, this is just amazing and I bet it gets better as I go on; Screw Algebra!" and then when I pick up some combinatorics paper I think "My goodness, I want to be able to work in this area, these proofs are so interesting, forget algebra an analysis!" and it goes on an on this way.

 

[chiro]

I think you'd be surprised at what can happen once things initially start a trajectory.

When people get into a routine and become comfortable with it, it's amazing how people are able to keep doing that kind of thing for a long time.

You might think now that you would never be able to settle down and focus on one thing, but you would be surprised at what can happen when you have a supervisor that you respect make a decision, and when you have both external and internal pressures really getting you to do what has to be done.

Keep this in mind when thinking about the thought of never being able to 'settle down' and 'stick to the focus'.

 

[Robert1986]

I think you'd be surprised at what can happen once things initially start a trajectory.

When people get into a routine and become comfortable with it, it's amazing how people are able to keep doing that kind of thing for a long time.

You might think now that you would never be able to settle down and focus on one thing, but you would be surprised at what can happen when you have a supervisor that you respect make a decision, and when you have both external and internal pressures really getting you to do what has to be done.

Keep this in mind when thinking about the thought of never being able to 'settle down' and 'stick to the focus'.

Oh Ok, I see what you're saying now. Thanks for the advice.