This may be not appropriate to ask this kind of question here. But please feel freely helping me.
In our Maths faculty, there is not a program like Undergraduate Research Program(URP), however, the students can ask the professors for the problems, and they should do on their own and present it on April or May every year.
My case is quite sophisticated. My professor said that I should choose my own problem and he will help me to work(it's in contrast with others usual cases). But I do not know how to find such kind of problem(those are appropriate for undergraduate research).
I got quite solid background on Abstract Algebra, I have almost finished Commutative Algebra by Atiyah-MacDonald, and I am now studying Homological Algebra, Representation Theory, and Algebraic Geometry. 2 professors in my country suggest me finding the problem connecting Graph theory and Algebra, or Algebraic Combinatorics( like Combinatorial Commutative Algebra). I have to choose this kind of question, but there are many books, papers, and I do not know how to start finding my own problem.I hope that you can suggest me some problems.
Another problem is, do the problem and result of URP have to be new? I heard on MO(sorry I do not remember the link) that the undegraduate thesis need not be new, just like reading some problem and present it in your own way.
So what is the different between an undergraduate research problem and an undergraduate thesis problem ?
Thank you for reading my story.