Which path should I choose: Mathematician or Theoretical Computer Scientist?

[Oryctolagus]

Which scientist am I!?

I've searched my tail off for someone with my problem to no avail, and, noticing this community seemed to be full of decent people with whom I could get along, decided to give it up and just ask. Please excuse the life story.

I attend a fairly lame public college that I would be embarrassed to say the name of that houses surprisingly high ranking departments in CS, Math, Business, and Nursing. I started in the Summer of 2011 (taking a precalc/trig mash-up course in preparation) and had fun with my CS major status for most of the Fall 2011 semester. That's when I discovered Alan Turing. His name was showing up everywhere, and my instructor only mentioned him in passing, so I decided to look him up. Then I read a book about "On Computable Numbers" and suddenly felt like an idiot. I didn't know what I wanted to do with myself, I was aiming to be a pencil pusher like my dad, just not in a cubicle. That's what I was going to school for. But now computer science looks like a science, and imagining myself following my great grandfather's footsteps (last Ph. D. in our family; research chemist for Corning) got me all giddy.

So one day I'm looking at the required classes for a CS degree in the bulletin and I start to see a pattern: Software engineering. Databases? Operating Systems? Computers in Freakin Society? Where's the science in that? Where's the meat? So I looked into a second degree in math, but if I'm going to grad school why the hell would I want to spend more than 4 years getting my BS? In the end I ran into the breakdown of the Math major in the bulletin and, wondering how I missed it all this time, found that it has room for 31 (thirty-one, (10)(3) + 1) hours of chosen electives. Turns out that's enough to take all the computer science classes I want without having to take any extra hours. So now I'm a math major, and I had a helluva time explaining to my dad about how I'm going to make money with it.

So I slapped together a 4 year plan to go with it including every class with the word "algorithm", "discrete", or "computing" in it, to be sure. I'm really, really excited about knowing the grassroots of computation, and being able to solve problems. It seems like I'm leaning towards algorithms, as I enjoy pseudo programming (which hasn't been covered) better than Python (bleh). My passion is learning, and, knowing that an academic life circulates around that pursuit, I will work my *** off to put my self in a position of perpetual learning.

My question to you, should you choose to accept it, is that of what I am. I enjoy programming, and I love optimization, and algorithms, and doing huge math problems. Am I aspiring to be a mathematician whose life's work is in computation, or a theoretical computer scientist? I don't know whether to shop for cs or math grad schools.

 

[micromass]

If you're going into math, then you should go into logic. Logic deals with the things you want: computability, recursion, etc. Try to take as many logic classes as you can. The first logic class should be fairly boring: truth tables, etc. But the subsequent classes should be a lot better.

Discrete math would also be an option.

You can either go for theoretical computer science or mathematician. Both fields are able to do good research. Maybe you should also look at the other courses?? Pure athematicians will also take abstract algebra and real analysis, etc. Applied mathematicians do things like numerical analysis, statistics, etc. Computer Scientists also take programming or AI,...
So look at the other courses and see what you like most. Either three fields are good for ending up in what you want.