I like topology- what can I do with it?

[ianthe]

Hi all, so I'm finishing my third year as a pure math major and what interests me most is topology. I am thinking I want to go to grad school, but don't know what I would study there.

So my question is, what sort of things are there to study/research about topology, how does it relate to other fields, and what sort of jobs are there that might use it?

Sorry I'm really naive about all this, I've only taken a couple classes on it and I think it's cool, and I'm trying to figure out "what I want to do with my life," and maybe this is where to start asking questions.

Thanks.

 

[matt grime]

Well, what do you mean by 'topology'? Point set topology (like compact spaces, cofinite topology) or honest to goodness algebraic topology like simplicial homology? I guess the former, not that it matters.

In any case, the subject is just an indispensable tool in many parts of mathematics and physics, though I seriously cannot think of a 'job' that uses topology explicitly. I don't tihnk you should choose your career based upon maths course preferences like that; it isn't like one single course will lead into a career; they are all inextricably linked.

 

[JasonRox]

Well, what do you mean by 'topology'? Point set topology (like compact spaces, cofinite topology) or honest to goodness algebraic topology like simplicial homology? I guess the former, not that it matters.

In any case, the subject is just an indispensable tool in many parts of mathematics and physics, though I seriously cannot think of a 'job' that uses topology explicitly. I don't tihnk you should choose your career based upon maths course preferences like that; it isn't like one single course will lead into a career; they are all inextricably linked.

I do agree with you, but you have to make a decision on where to go for graduate school sooner or later. You can't wait forever. He's already going into 4th year so his time to choose is coming up.

 

[ianthe]

Well, what do you mean by 'topology'? Point set topology (like compact spaces, cofinite topology) or honest to goodness algebraic topology like simplicial homology? I guess the former, not that it matters.

Well I don't exactly know what the differences are, I just know my textbook is divided into "general topology" and "algebraic topology," so is this a very clear distinction then? I guess what I am wondering is what are the different sort of things to study about it. I am looking for something that will maybe peak my interest so that I can say "oh, that is what I want to study in grad school."

But, people don't go to grad school just wanting to study "math" do they? What about just "topology," is that specific enough, maybe I don't need to specify any further? How much do people know of what exactly they want to study before going to grad school? This is something I would really like to know.

Hmm, maybe I should ask my academic advisor these things, except that he is very untalkative and I would have to painfully drag everything out of him.

 

[JasonRox]

Well I don't exactly know what the differences are, I just know my textbook is divided into "general topology" and "algebraic topology," so is this a very clear distinction then? I guess what I am wondering is what are the different sort of things to study about it. I am looking for something that will maybe peak my interest so that I can say "oh, that is what I want to study in grad school."

But, people don't go to grad school just wanting to study "math" do they? What about just "topology," is that specific enough, maybe I don't need to specify any further? How much do people know of what exactly they want to study before going to grad school? This is something I would really like to know.

Hmm, maybe I should ask my academic advisor these things, except that he is very untalkative and I would have to painfully drag everything out of him.

You definitely need to get more specific than just "Topology".
That's equivalent to saying you want to study just "Mathematics". They are both very large.

 

[matt grime]

The vast majority of US grad schools are not set up so that you have to choose any specific area for research when you arrive; that is one of their main benefits. Obviously, the choices of direction you can take at a later date are restricted by the staff they have, but they are generally not so small as to effectively force you to pick one specific area by applying there, and if they are (in the US) they aren't worth going to in the first place.