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I wanna start doing my own research... I've grown somewhat restless about the regular undergraduate training - study something, solve the problems, rinse and repeat. I feel like I've had enough training up until now to start doing some thinking on my own. Do you have any suggestions as how to start? For example, is there anywhere I can find what topics would be good topics to research? Or could I just start playing around with where I feel I might find something and take it from there.

Hope you can help.

Numbersandsoon
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    Which are the areas of science you prefer ? To do research is (and must be) a passion. Trust me, I started in reseach 53 years ago and I am still doing resaerch 15 hours a day. I am really willing to help. Let us start discussing if you want. – Claude Leibovici Dec 03 '13 at 16:34
  • http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html and http://oeis.org/ plus some computational software, but you might have tried these already. – Mats Granvik Dec 03 '13 at 16:34
  • @ClaudeLeibovici: Sure!! Let us discuss. Here? I really like math. Right now I'm into abstract algebra and number theory. I've been playing around with some measure theory lately and this also intrigues me. – Numbersandsoon Dec 03 '13 at 16:42
  • Some universities offer undergraduate research experience. Do you have anything like that? – Stephen Montgomery-Smith Dec 03 '13 at 17:24
  • @BoSchmidt. Your prefered area is beautiful but really very far away from my small knowledge. What James Mitchell suggests is a very good manner. But i suppose that you already have some problems in mind. Good luck and best wishes from the oooold man. – Claude Leibovici Dec 03 '13 at 18:03
  • @ClaudeLeibovici: Thank you! If I get into numerical simulation I'll get back to you :-) – Numbersandsoon Dec 03 '13 at 18:24
  • First, in solving small problems you should be thinking on your own (if you didn't, how did you solve them?). Second, I don't want to discourage you, but research is study something, solve the problems, publish, repeat. Third, there is nobody to stop you from thinking on your own and actually a question like this might contribute to not thinking on your own. Finally, I would encourage you to ask others about open problems in areas that are of interest to you, however, getting too much advice will may make you feel as if you were back to the square one. Think on your own! – dtldarek Dec 03 '13 at 18:30
  • @dtldarek: Nothing beats experience. All I was asking for was if other would like to share theirs. I don't see a problem with that.
    1. Solving those kinds of problems is not what I'm talking about. You're handed a very specific problem, find a solution. I was thinking of myself finding a problem, but being guided to an area with lots of possibilities.
    2. I would like to decide this for myself once I get into research.
    3. Totally.
    4. Is that not what I'm doing here? Too much of anything is never good, but guidance could be of help.
     – Numbersandsoon Dec 03 '13 at 19:00
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    @BoSchmidt I just wanted to make sure you are aware of aforementioned issues, and I'm glad that you are. Good luck on your endeavor! – dtldarek Dec 03 '13 at 19:06
  • @BoSchmidt. If you consider numerical simulation or numerical methods, jus contact me at any time. My e-mail address is in my profile. – Claude Leibovici Dec 04 '13 at 07:30

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I would approach one of your professors and ask them about it. Try a professor who you know and whose class you enjoyed. They might be able to suggest some problems, or you might even discover that there are undergraduate research programs at your school. Choosing appropriate research problems is a fine art and your professors should be able to help you with it. It is altogether too easy to choose problems which are too easy (maybe with known or trivial solutions), or too hard (like the Riemann hypothesis). It can be difficult to find a problem which is substantial enough to be interesting but not so hard that you can't make any progress at all. There is really no substitute for having an expert, like one of your professors, to guide you in choosing and solving a problem.

James Mitchell
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