Undergraduate research in computer science

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I'm an undergraduate student studying computer science.I am interested in doing some research in discrete mathematics or theoretical computer science.Can anyone tell some interesting research topics or open problems on which i can work on?
 
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There is this blog of a theoretical computer scientist, http://weblog.fortnow.com/, which has some interesting information and also links to other resources in theoretical computer science.
 
P vs. NP.

Barring that, ask a professor! There's plenty of things that a reasonably bright undergraduate can solve but you're going to want someone with experience and a big-picture knowledge of the field to guide you, and you won't find that online.
 
Start small.
ask around your dept. if anyone has projects they could use some help with, whatever help that may be. From there you can work your way up
Don't expect to delve right into solving open problems.
As Will said, find an adviser, make friends with one of your professors and see if they could use your help on their research.
 
You may also consider attending some seminar devoted to the subject, and even prepare a talk! For example I, despite being only 2nd year, attended a seminar about Logic and Computation Theory aimed at people doing their M.Sc. and was even allowed to make a talk about tree automata. If there are research seminars or something like that available, talk to the professors and ask if they will let you attend. Another good idea is to visit a prof during his office hours and simply ask him about his own reasearch.