The Mathematics Directed Reading Program (DRP) at UCSC pairs experienced graduate students with motivated undergraduates to meet weekly and discuss a topic of their choice. This is a valuable opportunity for undergraduate students to learn material not offered in classes, and for graduate students to contribute their expertise and gain experience in outreach and mentoring.

At the end of the quarter, undergraduate students give a 15-20 minute talk about their work. We expect graduate students to help their mentees prepare for this talk – communicating knowledge is just as important as acquiring it!

Future plans for the program include securing further funding from external sources to broaden participation, as well as connecting with other DRPs in the Bay Area to provide more speaking opportunities for undergraduate math majors.

The DRP is funded through the UCSC Department of Mathematics as well as the DRP Network. The current organizers are: Graduate Students Deewang Bhamidipati, Nathan Marianovsky, and David Rubinstein.

Application

Application Process

Note: If the linked forms below are not accepting applications, we have finalized the list of DRP participants for the current quarter. Applications will be opened again at the end of the quarter, so please come back and reapply!

Graduate student mentors in the Directed Reading Program should be enthusiastic about sharing their love of math. Mentors should be prepared to meet with their mentee once per week for at least an hour, and attend the end-of-quarter presentation night.

Undergraduates should be excited to learn, be prepared to devote at least four hours per week to their project, and commit to giving a short talk about their work. Prerequisites for undergraduates are completion of Math 19A/B and 20A/B.

Guidelines

Choosing a Topic

A good DRP topic is something that is not covered in a typical undergraduate class. This topic should be chosen by the student with guidance from the mentor. Students should have some idea of what they are interested in, and mentors can help narrow things down to what might be feasible to learn in a quarter.

Expectations

For Undergraduate Students

Students are expected to meet with their mentors once per week for about an hour. Between meetings they should spend 4-5 hours on DRP-related work. At the end of the quarter they are expected to give a 15 minute talk.

Once a student begins a quarter of DRP, they are expected to complete the entire quarter. Students who drop early, without first obtaining permission from their mentor, will not be allowed to enroll in the program again.

For Graduate Mentors

Mentors are expected to meet with their students once per week for about an hour. It’s important that you let the DRP coordinator(s) know as soon as possible about any issues that arise. These issues might include a student repeatedly not preparing for meetings or deciding to leave the program. If a student misses two meetings in a row without forewarning, please email the DRP coordinator(s). Mentors are required to attend the talks at the end of the quarter.

Talks

At the end of the quarter, each student will give a 15 minute talk about something they learned. The talk does not need to (and indeed should not) cover everything the student learned during that time. For the sake of the audience, it’s best to do an overview with worked examples, or pick one thing to describe in detail, such as the proof of some theorem.

One of the goals of DRP is for students to get practice communicating mathematics, so the talks are just as important as the math that they learn. Students are encouraged to give practice talks to their mentors. The talks will be held either the last week of classes, or the week before. Dinner will be provided.

Purchasing Books

Up to $50 will be reimbursed for the purchase of a book for the student. Mentors should purchase books and then send the receipts to Gina Hernan in the Mathematics Office. All reimbursements will be processed at the end of the quarter.

Topics
The possible range of projects is completely open, and depends on the mutual interests and backgrounds of the mentor/mentee. The only prerequisites for undergraduates are completion of Math 19A/B and 20A/B. There is also the possibility of applied math/statistics or math education projects. Some suggestions from a subset of possible subject areas are:

Algebra

  • Modular Arithmetic/Fermat’s Little Theorem
  • Braid Groups
  • Quadratic Reciprocity

    • Analysis

  • The Contraction Mapping Theorem
  • The Lorenz System and dynamics
  • Poincare-Bendixson Theorem, Recurrence
  • The Cantor set and Lebesgue measure

    • Geometry/Topology

  • Maxwell’s Equations and Geometry
  • Matrix Groups/Lie groups and algebras
  • Projective Geometry
  • The Fundamental Group
  • Knot Polynomials

    • Applied Math

  • Persistent Homology
  • SIR Models in epidemiology
  • Signal Processing, Fourier Analysis
  • PageRank algorithm and Markov chains
  • The Capital Assets Pricing Model
  • Public-key cryptosystems

    • Students can also take ideas from past topics/ projects:

    Past Topics from UC Santa Cruz

    Past Topics from Other Directed Reading Programs

  • The University of California, Berkeley
  • University of Chicago
  • University of Connecticut
  • Indiana University
  • The University of Maryland
  • Massachusetts Institute for Technology
  • Rutgers University
  • The University of Texas at Austin
  • Yale University