Undergraduate Research Problems

Question

I'm a third year undergrad with this summer off so would appreciate some material to look at.

I took courses in Galois theory, Topology, Complex analysis, ...

My main interest is in Analysis / topology.

I know this is a vague question, but I have begun the holiday - so am in a different country to my professors - who I won't see until the end of Summer.

edit: hopefully a question that can be solved by next summer (or semester - I have not used that term before, though I am guessing it means acedmic year).

Answer 1

I wrote an article which is in the last issue of the Harvard College Math Review (a math journal for undergraduates) about an open problem in set theoretic topology that might be a good project for an undergraduate. It is called The Toronto Space Problem. I also asked a question about it in Mathoverflow.com. I think there are some references there.

Answer 2

You can take a look at the following books which were especially written on the open problems in Topology

Open problems in topology - J. Van Mill, George M. Reed Google Books Link

Open problems in topology II Volume 2 - Elliot Pearl Google Books link

I hope you will find some interesting problems here.