Help for Research Advise | PF Community

[l'Hôpital]

Hey PF Community, the post is a bit longwinded so I apologize in advance!

Towards the very end of the Fall semester, I had asked a professor (sort of in a casual tone) if I could do research with him (he works with dynamical systems and mechanics). He replied negatively since my coursework was not exactly the level he felt was required for such things. In particular, I've yet to take an Analysis or Algebra course (I'm a math major, sophomore in the Fall). Granted, I've taken my college's equivalent of "Intro to Proofs" and was currently taking a year-long proof-y Multivariable Class (using Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach as well as the professor for the class being the same professor I want to research with) in addition to reading a few things in Baby Rudin, but I suppose that's not quite up-to-par as taking Analysis and Algebra.

Regardless, in the Spring semester, I basically asked him again after class during office hours (which no one ever uses). I had planned that he would reject me and perhaps send me to a prof would be more likely to accept, but I had been mistaken. I'm not sure if he took pity on me or something but he decided that maybe there was something we could do. Excited, I basically told him I'd do whatever he'd tell me, be his winged monkey, etc. So, he gave me a book to read, and said he'd think of something. So I read most of the book, leaving out a few chapters here and there, and I went on to talk to him. By then, a good deal of the spring had past and we basically decided to just move the project thing to the Fall (since he wouldn't be at the University in the summer). Eager to work on the project, I asked him what other books I should look into, and he recommended another one.

Later in the summer, I contacted him with an update and whatnot, and he gave more details as to the actual project, claiming it would deal with the Sitnikov problem, and told me what main concepts I should be learning from the second book. In addition, he attached some related PDFs so I could get a feel for what others have done in the problem. At the time, my thought process was that I should continue reading the book so that when I get to the PDFs, I'd be ready. My results were eh. In some of the papers, I just felt completely lost. In others, I can follow it if I sat down and spend a few hours on it, but I feel like I could never ever produce such a thing at this point in time (I was unable answer some of the question from Hirsch and Smale's book, for example). This mostly stems from a feeling that I don't know enough strong theorems from Analysis and/or Algebra or that if I do I'm not comfortable enough with them to use them as they do in some of these proofs. Lastly, in some cases, it's a matter of diction (what is a superquadratic point?) that Google (as well as indices of the sources I have) won't clarify for me.

So, I'm sort of starting to see why my professor had originally rejected my request for researching with him on the grounds of lack of math expertise. Then again, I'm not exactly sure what I'll even do with him as far as research goes. Am I supposed to come up with the theorems? I can't see myself coming up with theorems to even try to proof, much less actually proving the theorems.

So, I guess I need some guidance. I hold this professor in extremely-high regard. On one hand, I want to do the research and not appear like I'm just being lazy by pulling back, but on the other I'm afraid that I may not actually be ready and that I'll fail him and look like an idiot anyways. What should I do?

 

[diggy]

I don't think he will be disappointed in you as a sophomore to not be able to crank out papers.

Keep working through his recommendations, and see if he would be willing to set up a short meeting every week or every other week. In the meeting try to discuss what you are learning, and some of the technical points that you may have difficulty with (like superquardratic points).

You are effectively using him, but don't feel bad about it in the least, that is his job - to teach you! And most likely he is happy to have you share his interest, even if it is not at the same level.

If he really doesn't seem interested, that is ok too. You seem to be very self motivated, and that will pay off well in the long run -- keep plugging away.

 

[saim_]

I would never miss such an opportunity. Of course research is hard, especially for an undergrad who has not done many truly challenging problems and does not have a good all-round knowledge of his field. Talking from experience, I'll be an engineering sophomore in fall. We have done the basic physics and math courses (physics uptil electromagnetism and math uptil multivariable calc) and I think I have good understanding of these courses but I still find it very hard to read even pedagogical type of research papers in physics which are supposedly for undergrads with just these pre-reqs. Research papers usually cannot be read casually, at least not for undergrads, as they are a result of complex thinking about a significantly complicated problem.

To brush up on Analysis and Algebra watch the following courses, both based on classic texts, one on Rudin's first five chapters and the other on Artin's Algebra:
http://www.extension.harvard.edu/openlearning/math222/
http://www.youtube.com/user/HarveyMuddCollegeEDU

 

[sweetpotato]

I got my first taste of (electrical engineering) research this summer and had to "read" a lot of journal papers. I more or less fully understood 2 of them, and it took me ~3 hours each. The rest, I basically understood the abstract and the conclusion. You probably won't need to understand ALL the information in the papers to do your research. As you actually get into your research, you'll figure out what you have to understand and what you don't. Then you can look at the papers again and concentrate on what you need to know for your specific project. Ask your professor any questions that you weren't able to figure out yourself. Use books and the internet.