Sometimes, I write things out when I want to I understand them. If you see any errors in these documents or have any comments, please send me an email at jpdsilva@umich.edu.

Proof of the classification theorem for modules over a PID (Dr. Shuyang Cheng) Professor DeBacker told me that the structure theorem for modules over a PID was one of the most important results I'd learn. Hence, I wrote up the proof I learned from Dr. Shuyang Cheng in Math 494, expanding any details I didn't understand.

Mechanism and Significance of Off-Target Effects in CRISPR-Cas9 This was my final paper for Honors 242 (Controversies in Scientific Discovery) with Professor Anna Mapp in 2017. CRISPR technology has moved very quickly since I wrote this paper: in particular, that there are several new strategies to ameliorate off-target effects (e.g. high-fidelity Cas9, nickases). Still, it is an interesting exposition of several potential pitfalls in gene editing.

Outreach

I tutor students in mathematics, both individually and through outreach programs, including Math Circle and Math Mondays in Ypsi.