Should I Choose Math, Computer Science, or an Interdisciplinary Grad Program?

In summary, if you have a strong interest in a particular area of mathematics and you develop a good relationship with a professor, it can boost your chances of getting accepted into a graduate program in that area.
  • #1
Bourbaki1123
326
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I am currently a junior undergraduate and I am interested in too many areas, or I don't know how to reconcile my interests. I have a lot of interest in algebra and algebraic geometry but also mathematical logic and theoretical computer science. I am taking independent study courses for Algebraic Geometry and I will have a minor in computer science plus I will have taken Theory of Computation, graduate level mathematical logic, independent study in theory of recursion(hopefully) and independent study in advanced set theory.

I have developed a pretty strong interest in theory of recursion and I want to look into algebraic methods in computer science (I see that there are apparently a lot of applications of abstract algebra to computer science). I also am interested in automated theorem proving(to a lesser extent), and set theory (by grad school I will probably have covered forcing and the ideas surrounding large cardinals, though I am not at that level yet).

I have read the first few chapters of J. Donald Monk's book Mathematical Logic, and a good part of Smullyan's book on Gödel's Incompleteness theorem. I plan on beginning Smulyan's book on Theory of Recursion soon. As far as general mathematical logic, I am familiar with the basic ideas of proof and model theory and the completeness theorem and the Löenheim-Skolem theorem.

I suppose my interests could be broadly divided between algebra/algebraic geometry and mathematical logic with a focus on computer science.

So should I go math, or computer science or something in between? What kind of programs might suit me (ignoring the difficulty of getting in, I'll worry about that myself)? Any assistance will be greatly appreciated.
 
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  • #2
Bourbaki1123 said:
So should I go math, or computer science or something in between? What kind of programs might suit me (ignoring the difficulty of getting in, I'll worry about that myself)? Any assistance will be greatly appreciated.

For graduate work, you need to think in terms of professors rather than in terms of subjects. Go to the library, pull up papers that seem to be related to the fields and topics that you are interested in, and then see where those professors are, and apply to those programs (and mention that you did this in your statement of purpose.)

One thing that is very different between different schools is which departments talk to each other, and which departments don't talk to each other. You are probably looking for a school in which the math and CS professors have offices next to each other, take each other out to lunch, co-author papers together, have joint seminars, etc. etc. It's pretty much impossible to figure this out from the department name, but it usually becomes obvious if you look at the research output and the schools web pages.
 
  • #3
You're in luck Algebra and Logic complement each other.

P.S
Smullyan's great, I stopped somewhere in my reading of incompletness' textbook, hope to reread it someday.
 
  • #4
Thanks for the advice. I know Carnegie mellon seems to have a great correspondence and they even have a phd track for pure and applied logic that has people from math, philosophy and computer science. It seems pretty promising, especially coming in as a math candidate since it seems a lot less competitive than going in for computer science (you can do the program as a philosophy(I think), math or computer science candidate). there are definitely a couple people there I would like to work with.

Question:How much would it affect my chances of getting into a grad program if I find a professor who I can keep in correspondence with whose work is interesting to me? It seems as though building a relationship with a professor ahead of time would boost my chances plus it might get me the adviser I want. Does anyone know about this?
 

FAQ: Should I Choose Math, Computer Science, or an Interdisciplinary Grad Program?

1. What are the benefits of pursuing multiple interests in graduate school?

There are several benefits to pursuing multiple interests in graduate school. First, it allows you to explore different fields and find what truly interests you. This can help you make a more informed decision about your future career. Additionally, having a diverse range of skills and knowledge can make you a more well-rounded and competitive candidate in the job market. Lastly, pursuing multiple interests can also prevent burnout and keep your studies more engaging and enjoyable.

2. How can I balance multiple interests while in graduate school?

Balancing multiple interests while in graduate school requires good time management and prioritization skills. It's important to create a schedule and stick to it, while also allowing yourself some flexibility. Additionally, make sure to communicate with your advisors and professors about your interests and workload so they can provide guidance and support. It's also important to take breaks and practice self-care to avoid burnout.

3. Are there any challenges to pursuing multiple interests in graduate school?

Yes, there can be challenges to pursuing multiple interests in graduate school. It can be difficult to balance the workload and demands of different fields, and it may take longer to complete your degree. There may also be challenges in finding advisors and mentors who can support your diverse interests. Additionally, funding and resources may be limited for certain fields, making it challenging to fully pursue all of your interests.

4. How can I incorporate my multiple interests into my graduate research?

There are a few ways to incorporate your multiple interests into your graduate research. One option is to find a program or advisor who specializes in interdisciplinary research and can support your diverse interests. You can also look for collaborations and partnerships with researchers in other fields to bring a multidisciplinary approach to your research. Additionally, you can focus on a specific topic or problem that combines elements from your various interests.

5. Will having multiple interests affect my career prospects after graduate school?

In most cases, having multiple interests will not negatively affect your career prospects after graduate school. In fact, it can often be seen as a strength, as it shows your versatility and ability to handle different tasks and challenges. However, it's important to be strategic in how you present and market your diverse interests, and to showcase how they can benefit your potential employers. Networking and building connections can also be helpful in finding job opportunities that align with your interests.

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