Today I have something wonderful for budding mathematicians: directed readings. Recently at my university I became a member of the mathematics department’s directed reading program (DRP). The DRP is semester based and it pairs an undergraduate student (mentee) with a graduate student (mentor). The pair decides on a mathematical topic to pursue, specifically a reading within that topic, for the semester and meetings weekly to discuss the reading. Between meetings the mentee is expected to spend time with the reading and come up with questions. At the end of the semester the mentee delivers short presentation, about something discussed during the meetings, for the other students of the program. Part of what made the experience such a joy was that it only amounted to about 3 hours of work a week so it was easy to slide into my schedule. Here is a short overview of what I did during the program:
- Read Piatetski-Shapiro’s Complex Representations of for finite fields .
- Did some homework-equivalent exercises about representations.
- Gave a short presentation on proving groups of order are abelain using representations. An augmented version of the notes can be found here.
- Befriended a graduate student in the mathematics department.
If you have this program, or an equivalent, at your university I would definitely recommend trying it out for a semester. If you’re intrigued, but your department doesn’t offer this program don’t fret! I unknowingly did a directed reading at my university before the program was formally around during my freshman year. This started as a result of attending office hours with one of my TAs for an intro to proof class I was taking. I came to my TA with proofs I had done of some propositions we stated in class but had not yet proved. We eventually got to talking about if I wanted to do more of this kind of work in combinatorics, and being the excited student that I was (and still am), I agreed. We decided to read parts of Stanley’s Enumerative Combinatorics Volume 1 as well as some other selected readings, meet weekly, and have assigned weekly problem sets. This continued for about a year, including over the summer, and ended with some expositional research into using generating functions to compute the expectancy of fixed point permutations. In fact, I was able to give a talk about this research at my department’s undergraduate mathematics seminar in the spring of 2018. It was a wonderful experience, and something that jump-started my undergraduate career in mathematics.
So, look out for a DRP program at your university, and if there isn’t one go talk to your TAs! It’s never to early to jump-start your career in mathematics!