Senior Thesis in Math: What Am I Supposed to Do?

[johnqwertyful]

I'm doing a senior thesis and I'm a little worried. It seems like it's just expository. The concepts have been hard enough for me to grasp (a lot of graduate math. I've taken some graduate classes. But more), especially with all my other classes. I have this quarter and next quarter to do it, which sounds like a lot but isn't really

Am I supposed to prove something new? It sounds like the goal is just to arrange things other people have done in a clear and concise way. Is that what I'm supposed to do? Is that okay?

I'm working on the connection between PDEs and Brownian motion. Starting off with Feynman's path integral formulation of quantum mechanics (which is basically to me, copy a long derivation. It IS a cool derivation (and cooler result) and I am learning from doing so), then introducing Brownian motion through Einstein or Smoluchowski derivation of Heat equation using Brownian motion (again, copy a few long derivations). Then introduce Feynman Kac formula, and talk about Wick rotation to tie the Heat and Shrodinger equations together.

It just seems like everything I'm writing has been done somewhere else, I'm just copying derivations basically. I mean I'm making them my own, and trying to understand them. But is that okay? I mean I'm only an undergrad, and these things are very hard to understand for me. Am I supposed to prove a new theorem? What is there to prove? If professional mathematicians can't prove the theorem, how the hell am I supposed to?

Is the point to just copy everything done before? Maybe tie things together, arrange it in a way?

 

[jedishrfu]

Perhaps the purpose of the project is to teach the reader how to derive the connection. So you may need to explain keypoints of the derivation some of which might not have been explained in the derivations you are sourcing.

 

[johnqwertyful]

If I just learn how to derive all these connections, I learned a lot But I didn't really contribute anything. Is that the point? Is a senior thesis just for me to learn stuff? I thought it was to contribute or prove some new theorem or something. I mean, I'm 21 and have a little bit less than an undergraduate education of math, how CAN I prove anything new?

 

[johnqwertyful]

I've been looking online a lot, it seems most senior thesis are expository. I guess that's not what I had in mind.

 

[jedishrfu]

if you were to prove something truly original and new then that would really be a PhD dissertation right?

I'd talk with your advisor about it and perhaps ask for an example of one so you know what to expect and so you can focus your energies appropriately.