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I'm currently in second year of undergraduate Mathematics. The courses that I've undertaken in the past include Group Theory and Ring theory. Can anyone suggest a project topic that I can undertake in Algebra?

Thank you.

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For some kind of term paper? Or do you want an actual research topic? If it's the latter, then this is probably not a good place to ask! Talk to your departmental advisors. –  Dylan Moreland Nov 14 '11 at 3:15
    
Perhaps you could elaborate a bit more; how long were the classes in group/ring theory? how much did you cover/what text did you use? A little more knowledge of your background would prove helpful. –  Tyler Nov 14 '11 at 3:15
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I am not exactly sure what you mean by a project, but there are nice areas of algebra that you can learn more about. For example, your current background seems to be right for learning Galois Theory. It is surprising how useful it is to have a good understanding of Galois Theory. If this is something that you are going to learn in a course anyway, then you could read some Commutative Algebra and Algebraic Geometry, with some emphasis on computer application through Cox, Little, O'Shea's wonderful book "Ideal, Varieties and Algorithms". –  Rankeya Nov 14 '11 at 5:12
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If you want to do some research project, it would be more helpful to speak to your professor. I am not exactly sure whether Indian universities have projects for undergrads to work on. Though, if I were you, I would first learn some more algebra, before embarking on some serious research. At this stage, I do not really see you doing a project where you do a lot of serious mathematics. You will likely be spending more time writing some sort of code for computational type problems. And depending on your taste, this is something that you might or might not enjoy doing. –  Rankeya Nov 14 '11 at 5:18
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To be fair, sometimes projects for undergrads (especially over the summer) really turn out to be a lot of fun, where you can learn interesting math. But, I have not had a good experience with these projects, as they usually turn out to be heavily computational in nature. So, my response is biased. –  Rankeya Nov 14 '11 at 5:37
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closed as too localized by J. M., Amzoti, Martin, Chris Godsil, AWertheim Jun 18 '13 at 4:03

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