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College of Liberal Arts and Sciences University of Florida

Directed Reading Program in Mathematics@UF

Welcome to the Directed Reading Program (DRP) in Mathematics at the University of Florida! This new initiative partners/groups undergraduate students with graduate mentors for semester-long independent reading projects in mathematics. Through this program, students explore topics outside the standard curriculum, build mentorships, and deepen their mathematical understanding.

What is the DRP?

The Directed Reading Program is a mentoring initiative designed to give motivated undergraduates an opportunity to explore advanced mathematics topics under the guidance of a graduate student mentor. Over the course of a semester, each student-mentor pair/group meets regularly to work through a math paper or book chapter(s), culminating in a brief presentation at the end of the term.

The original DRP was started by graduate students at the University of Chicago over a decade ago and has had immense success. It has since spread to many other math departments who are members of the DRP Network.

How It Works

  • Pairings/Groups: Undergraduate students submit a ranked choice of readings, and we connect them with the graduate students.
  • Meetings: Pairings/groups meet weekly (typically for 1 hour) to discuss the material, ask questions, and work through challenging ideas.
  • Final Presentation: At the end of the term, students give short (10–15 minute) presentations on their projects in a friendly, supportive setting.

We will do our best to match every applicant with an appropriate mentor though spots may be limited.

Goals of the Program

  • Support undergraduates in exploring math beyond coursework.
  • Provide mentorship and foster a collaborative learning environment.
  • Prepare students for research opportunities and graduate school.
  • Provide mathematics graduate students an opportunity for mentoring experience in their area of interest, as well as deepen their own understanding of their research area.
  • Strengthen the mathematical community at UF.

Who Can Participate?

Undergraduate Students

We welcome applications from all UF undergraduate majors although priority will be given to mathematics majors.

Graduate Mentors

Graduate students in mathematics can apply to serve as mentors. Mentors choose reading materials, meet weekly with their mentee(s), and guide them through the reading. Appropriate reading materials might include Math Monthly or other similarly accessible articles, foundational or introductory articles in the graduate student’s research field, or even book chapters. This is a great opportunity to build mentoring experience in a meaningful way.

Timeline – FALL 26

  • Undergraduate Mentee Applications: Close on  August 23, 2026  at 2pm.
  • Pairs/Groups Announced: by August 25, 2026.
  • Reading Period:  August 26-November 30, 2026.
  • Final Presentations:  Tuesday, December 1, 3-5pm, Room: TBA

How to Apply

Undergraduates: Complete this form by 2pm on August 23: https://forms.gle/W2SZivdtDsPJKqZ16

Note: To access  the form, you must login to Google forms with your @ufl.edu email: https://cloud.it.ufl.edu/collaboration-tools/g-suite/

Graduate Mentors: check your email!

 Fall 26 Readings

Please note that students will only be assigned to projects for which they meet the prerequisites.

 1. The Knot Book : An Elementary Introduction to the Mathematical Theory of Knots by Colin C. Adams
  • Description: This book is a great introduction to higher-level mathematics. I read parts of it in a similar directed reading and it actually really influenced my decision to pursue mathematics further. This book introduces students to topological questions (deformations, invariants, what a surface really is…) without overwhelming them with overly technical or complicated definitions. It is also a very flexible book, as some chapters can be very accessible (I first read them when I was in high school) while others are about more difficult concepts. I will thus be able to adapt to the students’ level and interests. I also think the topics are abstract enough to introduce students to the style of mathematical thinking they will need in more advanced math while still being about visual objects like knots and surfaces. Finally, one of the chapters is about applications of knot theory to chemistry and biology which some students with interest beyond math might really appreciate.
  • Prerequisites: MAC2311
  • Recommended background: MHF3202

2. Missed congruences of overpartitions, Authors : Hirakjyoti Das and Hemjyoti Nath

  • Description: Missed congruences of overpartitions, Authors : Hirakjyoti Das and Hemjyoti Nath
    This is a simple paper on overpartitions. The authors found new congruences that seem to be missing from earlier work. The paper ends with a conjecture. It may be hard to prove, but students can try using ideas from the paper. By reading it, they will learn about partitions, overpartitions, and ways to find congruences.
  • Prerequisites: Students should first learn the basics of partitions and generating functions. They may also read The Theory of Partitions by George Andrews.

3. An Introduction to Modular Forms: From Modular Groups to Ramanujan’s τ-function and q-Series. References: Chapters 1 to 5 from the book “Problems in the Theory of Modular Forms” by M. Ram Murty, M. Dewar, H. Graves

  • Description: Almost all phenomena in biology, chemistry, or physics are complex, non-linear systems that evolve over time. If you’re interested in understanding and explaining such phenomena for intellectual curiosity or innovative purposes, you may find it beneficial to learn more about these fascinating mathematical concepts. These fundamental concepts will equip you to comprehend, explain, and challenge various natural phenomena that follow non-linear patterns. The topics you’ll study include: Chaos Theory and its application in sending secret messages, Strange Attractors, the Lorenz Map, the Logistic Map, the Henon Map, Fractals, stability, fixed points, the Cantor Set, and orbits. This practical mathematical knowledge is incredibly valuable to a mathematician, offering a strong foundation for exploring and understanding the complexity of the natural world. We’ll first start from Chapter 2 and cover up to Chapter 5, and then we’ll look into Chapter 1). And if time permits, then we’ll look into Chapter-5 of the book “Modular Functions and Dirichlet Series in Number Theory” by Tom M. Apostol.
  • Prerequisites: MAS 4301 and MAA 4402

4.High-Dimensional Probability, R. Vershynin

  • Description: This nice book shows beautiful overlapping between Probability and Linear Algebra. There is also a good point of studying this topic if you want to continue career in industry (quant, data science) since solving problems from there prepares for brain teasers and there are options to do numerical projects with generated or real data.
  • Prerequisites: MAS4105 and MAP4102
  • Recommended background: Problem solving, basics of real analysis. Optional Python programming skills.

5. Weak Convergence Methods for Nonlinear Partial Differential Equations, Chapters 1-3

  • Description: In this reading group, students will explore the weak and weak-star topologies on function spaces and their use in the analysis of systems of non-linear partial differential equations arising in the study of nonlinear (steady-state) elasticity, electrodynamics, and fluid mechanics. Weak convergence is, as you may be able to guess, a very ‘weak’ sort of convergence — a sequence of functions converge weakly (in L^p) if and only if their averages on every bounded (nicely-behaved) set converge. This notion of convergence furnishes a notion of what it might mean for a sequence of functions describing ‘microscopic’ (or, more accurately, ‘mesoscopic’) states of a system to converge to a ‘macroscopic’ picture. Sequences of functions converging weakly may have energy escape to infinity or concentrate and disappear along a lower-dimensional subset. It is the goal of this reading group to study the weak convergence of sequences of functions and explore methods in which weak convergence can be used to model and solve problems in engineering and applied mathematics. In particular, students in this reading group will develop a familiarity with the direct method in the calculus of variations. If chapters 1-3 are finished before the semester is over, the reading group will cover either the div-curl lemma and its applications to div-curl systems of PDEs (e.g. Maxwell’s equations) or the vanishing viscosity method applied to the study of systems of conservation laws (e.g. the Euler equations of fluid mechanics).
  • Prerequisites: MAA4212
  • Recommended background: There is a preference for students who have taken MAA4226 or MAA4227 or have an engineering or physics background, i.e. a double major, minor, or special interest in one of these topics.

6. Lecture notes in Algebraic Geometry by Andreas Gathmann.

  • Description: These lecture notes provide an accessible introduction to algebraic geometry, highlighting the rich interplay between algebra and geometry. Students will learn the fundamental concepts of affine and projective varieties, regular functions, and morphisms, providing a foundation for further study in algebraic geometry and number theory. Moreover, students will gain an appreciation for the deep connections between algebra and geometry.
  • Prerequisites: MAS4302

7. Optimal Control Applied to Biological Models (Suzanne Lenhart, John T. Workman) [ Chapters: 1, 2,3, 4 and selected lab programs : Lab 1, 7, 8]

  • Description: Optimal control is a powerful mathematical tool used to determine the best strategies for dynamical systems. This reading aims to develop a deeper understanding of the mathematical foundations of optimal control theory and its applications to biological models.
  • Prerequisites: MAP2302
  • Recommended background: MAS 3114 or MAS4105 would be helpful but not necessary. An interest in working through selected computational examples from the textbook using MATLAB is preferred.

8.Set Theory: On the Structure of the Real Line.

  • Description: The materials selected will provide the reader with enough background to understand how to construct models of ZF where paradoxical sets exist and only fragments of the axiom of choice have been used. On the other hand, can we recover fragments of the axiom of choice assuming the existence of these paradoxical sets?
  • Prerequisites: MAA 4226.

For reading ideas, you may find it helpful to view readings from previous semesters:

Questions?

Email Konstantina Christodoulopoulou (kchristod@ufl.edu) or Sara Pollock (s.pollock@ufl.edu).