Superirreducibility of Polynomials, Binomial Coefficient Asymptotics and Stories From My Classroom by Lara Du A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mathematics) in The University of Michigan 2020 Doctoral Committee: Professor Mattias Jonsson, Co-Chair Professor Trevor Wooley, Co-Chair Professor Ratindranath Akhoury Professor Jeffrey Lagarias Dr Elaine Lande Lara Du
[email protected] ORCID id: 0000-0001-6749-4867 c Lara Du 2020 ACKNOWLEDGEMENTS This work was partially supported by NSF grant DMS-1701577 and a Department of Mathematics Fellowship. I was extremely fortunate during my graduate school years to have had excellent mentors that helped me grow both as a mathematician and as a teacher. Mathematically, I benefitted from regular meetings with Professors Trevor Wooley, Mattias Jonsson and Jeff Lagarias, who have all advised me in some form during my PhD programme. Working with Trevor, I really found my place in the mathematical commu- nity: learning how to develop as an academic and have meaningful mathematical conver- sations while staying true to my own beliefs and roots. From Mattias, I learned to pursue the math that I found interesting, seeking out opportunities that were best for me and find- ing the conviction I needed to see them through. From Jeff, I learned to problem-solve, to adjust the research question I was asking if appropriate, to take things as slowly as I needed, but to never give up on seeking beautiful mathematical truths. Throughout graduate school, I’ve also benefitted enormously from collaboration with Gene Kopp, Jonathan Bober and Dan Fretwell and from the mathematical mentorship of Evangelia Gazaki.