I am thinking of doing some research (Real Analysis preferably) under a professor this year and I need ideas for interesting topics that might be accessible to an undergraduate.
Does anyone have any starting points for me?
I have taken Calculus, Multivariable Calculus, Differential Equations, Honors Linear Algebra I, Honors Abstract Algebra I, Honors Real Analysis I, as well as two proof-writing classes. You may assume that I am willing to learn any accessible material to fill in gaps in my knowledge. I have a preference for Analysis, though I am open to suggestions in other areas.
My initial idea was (Compact = Closed + Bounded + (?)), but in trying to write my proposal for the research (only two pages!) I found it hard to put into words exactly how I was going to go about the research, or how I would focus my efforts.
Please if you have any suggestions for either the topic of research, or where I could go to find the topic (obviously I am taking input from my professors already), let me know.