Next semester I have to start my Bachelor thesis in mathematics. I took a course on Measure and Integration theory last semester and am now taking Probability Theory and Functional Analysis 1 (first part of a two semester long course).
I am trying to find a subject for my Bachelor thesis that I can suggest to my supervisor. My problem is that I donot know what is accesible for me since I am only in my 5th semester of studying mathematics.
I would like to do either some theoretical stuff or something which includes programming (either both with maybe some original work from me?), in the area of Measure Theory, (basic?) Functional Analysis and/or Probability Theory.
Does anyone have an interestinn idea/subject/paper on what I can write my Bachelor thesis about?
Thanks a lot in advance. I am really struggling to find a interesting and accesible (to me) subject.
A few months ago I mentioned at the end of this mathoverflow answer a gap in the literature that I believe would be fairly straightforward to close as an undergraduate honors or masters thesis. I know a few more relevant references than what I posted, if you're interested.
This doesn't really involve programming, but perhaps programming could be incorporated by the inclusion of explicit algorithmic procedures and diagrams for the constructions, assuming existence is not proved by non-constructive means. (Actually, for this particular result, a non-constructive existence proof would probably be more interesting.)