I am a second-year Computer Science undergraduate.
I have been steadily getting into mathematics - after taking the basics in my first year and taking a course in set theory my second year I realized that if I want to get into a good graduate program in mathematics I would need to have had some research experience (and possibly a published paper).
That is why I asked my set theory professor if there is a way I could work on some open problem this summer (with him advising me). He was very polite and helpful and did offer me two topics on which he was working now - one was related to unification in modal logic, and the other related to definability in modal logic. Unfortunately, I am just now taking a course on logic - and that is classical first order logic (and we probably won't have much time to get too into deep results). That's why I've come here to ask for advice:
Is it a wise idea to embark on such a "research" ( my professor did offer some basic materials and papers to look up ) without prior experience in this specific field?
(My concern is that because I am feeling desperate to have a undergrad research experience , I will make the mistake to accept any kind of field for that.)
Obviously, since I have just been introduced to Modal Logic, the results of my hypothetical research experience will not be too fruitful ( or at least this is a high probability ), but if I develop a good work ethic then I will probably have the opportunity to continue this research for another two years under the supervision of my professors - is that a potential reason to do this research?
- Another concern I have is that If I spend more time on this topic I may end up with lower grades in my classes. And since this is not an official undergraduate research experience program, I may not have an legitimate excuse when applying to a grad school.
To restate my question in perhaps less vague way: If I am not very familiar with a research topic my professor offered me, should I skip it until I get good enough in the topics I am studying now, or should I embrace it and work hard enough to advance in the given topic (possibly long enough to produce at least one article)?
- My professor knows well that I haven't learnt Modal Logic before - so far we've had some brief meetings in which he gave some exposition on Modal Logic and specifically some insight into his paper.
- I am not switching from CS to Math per se, but right now I think that I would prefer to pursue a research career in mathematics primarily, and hopefully with some applications in CS. I will finish my CS undergraduate, and hopefully I will be able to enter a good Masters or Phd program in Mathematics.
- I am neither from UK, nor US. I am from Bulgaria, and I am not sure how the university system here compares to the UK, or US ones, but I wanted to get a more general answer on whether attempting such a research is better (given a certain urgence in having a paper published) than waiting out until I get more proficient in some area and attempting research in it.