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i don't know whether it will be appropriate to ask this question here or not but i need help. we have to a project in either pure or applied mathematics. my supervisor told me that it should not be something like a reading course but should contain some new topics. i have covered upto field extensions in abstract algebra and have read some point-set topology (upto chapter 4 from Munkres' topology). i also have studied differential geometry which includes global and local differential geometry of curves and local differential geometry of surfaces. now, i am seeking some potential topic for my project which may be on the interface between algebra and topology or differential geometry and topology but am unable to find. so , i request you to please suggest some topics for my project.

thanks.

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I am not sure any of us can answer as this is for your department and school and there may be rules we don't know about. A suggestion, can the professors at your school suggest areas of interest that could be used for project? For example Math Department Undergrad Research Project Ideas shows such a list of ideas. Maybe, professors at your school could provide a list like this within your particular area. Additionally, search for ideas and you can find stuff like math.vt.edu/ugResearchProjects.php Regards – Amzoti Jan 29 at 15:13
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I have to agree with @Amzoti. However, the things you mention more or less scream "homotopy theory" or "(de Rham) (co-)homology" in my direction. However, the not being a reading course is a really vague description, I'm afraid. – HSN Jan 29 at 15:17
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You might also want to ask your supervisor if there is a "repository" (collection or even a list/descriptions) of former undergraduate projects completed by students. That might spark some ideas of your own, and at the very least, will help clarify what is expected of you with respect to the project you need to complete. – amWhy Jan 29 at 15:17
well, thanks for the advice. yeah, he has suggested some topics like topological groups ,rings of continuous functions ,groups of isometries and smooth partitions of unity but i have already studied groups of isometries so i just want to do something new. as for others i see them as important topics for reading course and i think that they will be large enough to be project. – wanderer Jan 29 at 15:36
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I vote not to close, but flagged for CW – Brett Frankel Jan 29 at 16:25
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closed as too localized by Jason Bourne, rschwieb, Jonathan Christensen, Calvin Lin, Asaf Karagila Jan 30 at 18:22

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1 Answer

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To take on a project like this, consider the following points:

  1. You will be working on the problem for a longish period, most of the time. If it isn't something that really interests you, you'll soon want to throw it all into the nearest thrashcan
  2. Whatever the topic, see if there are people nearby that share interest in it. You will need somebody to talk to when you get stuck
  3. Check your supervisor's interest areas. If your problem doesn't interest them, you'll get little attention there...

Also take a look at this question, much of what is said there is equally applicable to your situation.

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