Today I have something wonderful to talk about 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 $GL(2,K)$ for finite fields $K$.
• Did some homework-equivalent exercises about representations.
• Gave a short presentation on proving groups of order $p^{2}$ are abelain using representations. An augmented version of the notes can be found here.
• Befriended a graduate student in the mathematics department.