# Directed Reading Program

## Johns Hopkins Chapter

### What is DRP?

The Directed Reading Program (DRP) is a program that pairs undergraduate students with graduate students for one-on-one independent studies over the course of a semester. The program was started at the University of Chicago but it is now running in several mathematics departments in the country.

The programme is largely free form and without theme inasmuch as content is concerned. To this end, both graduates and undergraduates commonly propose study material and directions. Nevertheless, for comparison and inspiration, a list of past projects and descriptions may be found below. We have also arranged with the university for a special, 1-credit course associated with the programme in which participants may elect to enrol, and selected mentees will have their chosen textbook (or similar resource) bought for them by the department.

For more information, feel free to contact the organisers at drp@math.jhu.edu or individually, Richard Brown, Apurva Nakade, Daniel Fuentes-Keuthan, and tslil clingman.

### What is expected of mentees and mentors?

The mentors are expected to meet with their undergraduate mentees for an hour every week. In addition to this, the undergraduates are expected to work independently for a few hours every week and prepare for the meetings with their mentors. The mentors are also supposed to help their mentees prepare their talks for the final presentation session-this includes helping them choose a topic, go over talk notes and practice the talk.

### Presentations

At the end of the semester there will be a presentation session. All members of the department and friends of speakers are welcome to join. There will be pizza!

# Fall 2018 Projects

*Differential Geometry and Lie Groups for Physicists*by Marián Fecko.

*Partial Differential Equations*by Lawrence Evans. We will begin with some classical partial differential equations, and then progress to a more general setting. This may include topics such as Sobolev spaces, second-order elliptic equations, or Hamilton-Jacobi equations, and may touch on various methods of finding solutions including Fourier analysis.

*Rational Points on Elliptic Curves*with a goal of understanding Mordell’s theorem.

*A Walk Through Combinatorics*, with supplementary reading from Wilf’s renowned

*Generatingfunctionology*.

*Lectures on the Hyperreals*, by Robert Goldblatt. We will begin by understanding the hyperreals and their correspondence with the reals through the transfer principle. We will then move towards reconstructing calculus and basic analysis through this lens. Finally, we hope to see some applications of nonstandard analysis such as Loeb measure and in Ramsey Theory.

*Algebra: Chapter 0*by Paolo Aluffi.

# Spring 2018 Projects

*Stable Homotopy and Generalized Homology*by J.F. Adams,

*A Primer on Homotopy Colimits*by Daniel Duggar, and

*Cubical Homotopy Theory*by Brian A. Munson and Ismar Volic. Once acquainted with these topics, we will move on to reading and understanding Thomas G. Goodwillie's paper,

*Calculus III: Taylor Series*.

*Noncommutative Algebra*by Benson Farb and R. Keith Dennis.