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I'm considering writing a senior thesis this year and I'm trying to come up with a suitable topic before presenting my ideas to one of my professors. I'm leaning towards something to do with number theory and possibly cryptography, or perhaps something more algebraic. Honestly, I took a 6 year break in the middle of my degree and the only courses I've really taken since then were "Abstract Algebra" and "Number Theory and Cryptography," so perhaps that's the reason for my preference. (Though I will be taking both topology and analysis this fall, so perhaps something related to either of those topics might be beneficial?) In general, I definitely lean towards the algebraic side of mathematics vs say, analysis or geometry, though my experience with all of them is severely limited.

I've been browsing some of the papers I've been able to find online from various schools, but I honestly don't understand many of the topics. Really, I just don't feel as comfortable with upper level maths as I probably should for a senior, (probably in large part due to the gigantic break I took in the middle of my education...) But that's part of why I'd really like to write a thesis, so that I can understand some deeper mathematics, at least in a small way. The problem is just I feel so uneducated that researching ideas is proving somewhat difficult.

Anyway, before I get too long winded, I'm was just hoping some of you could point me in the right direction. I don't have a particularly strong relationship with any of my professors right now, so I don't want to bother them until I have a more formulated plan. So if anyone has any advice about where to start looking for suitable topics or any advice on which specific topics to consider, that would be awesome. I'm really excited to start researching but right now I'm just a smidge overwhelmed. Thanks!