Guided Reading Program
The Guided Reading Program (GRP) pairs undergraduate students with graduate student mentors for fun, independent study projects of various sizes and scopes during the spring semester. The projects can take the form of reading and working through a mathematics text, reading research papers, or even doing research.
The goal of the GRP is to enable undergraduate students to study mathematics in greater depth than is possible in a classroom, to increase interaction between undergraduates and graduates, to give undergraduates an opportunity to practice explaining mathematical ideas in conversations and in presentations, and to give graduates an opportunity to share their passion for mathematics.
For questions about the program, please email mathdepartment@brandeis.edu.
Structure of the Program
Selected students are expected to meet with their grad mentor for at least one hour each week to discuss their progress, and put in at least four hours of independent work between meetings.
Undergraduate Students
Any sophomore, junior, or senior who has taken 15A (Linear Algebra) and 20A (Multi-Variable Calculus) is eligible to apply. First-years who have seen this material are considered on a case-by-case basis. Acceptance into the GRP is determined by previous coursework in mathematics (including final grades) and availability of grad mentors. No course credit is awarded. Students with heavy or challenging course loads should think carefully before committing to the GRP.
Graduate Mentors
Any graduate student who has passed the teaching apprenticeship program can apply to be a grad mentor. Each mentor is expected to guide their student through the study of a topic. This means helping the student come up with a study plan. This also means meeting with the student every week to answer questions, point out subtleties, explain the big picture, and have the student present material. Mentors are required to write a report about the experience, during official breaks. Mentors are modestly compensated for their work.
Spring 2026 Program
Three graduate student mentors are offering a total of three exciting projects.
Project descriptions, Spring 2026
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Graduate mentor: Rachmiel (Rocky) Klein
Description:
The integers sit in the rational numbers. The rational numbers sit in the real numbers. Do the real numbers sit in something else? This GRP is on constructing the surreal numbers, the "much larger" version of real numbers. We will start with defining the surreal numbers by reading a short and cheesy mathematical romance novelette (yes, you read that right), and then continue with some intro papers on surreal numbers, discussing ordinals along the way. Depending on time and interest, we may discuss how to do calculus on surreals. Rocky will be partially learning alongside the students, guiding the discussion.
Required Courses:
Intro to proofs required. Real analysis is strongly recommended.
Graduate mentor: Tudor Popescu
Description:
The goal of this project is to study one of the most active areas of mathematics at present, additive combinatorics, which lies at the intersection of combinatorics, number theory, and analysis. Generally, additive combinatorics seeks to answer how large a set with specific properties can be. For example, could you have a "large" set of real numbers that doesn't contain "long" arithmetic orgeometric progressions? Do "large" sets of natural numbers always contain a 3-term arithmetic progression? To answer these, we will study the sum-product conjecture (particularly Elekes' bound), Roth's theorem, Sidon sets, Plünnecke–Ruzsa inequality, and Freiman's theorem.
Required Course: A course on proofs is required. Prior knowledge of combinatorics or Fourier analysis is a plus, but not required.
Suggested Books:
Adam Sheffer's notes.
Graph Theory and Additive Combinatorics by Yufei Zhao
Additive Combinatorics and its Applications in Theoretical Computer Science by Shachar Lovett
Additive Combinatorics by Terence Tao and Van Vu
Polynomial Methods and Incidence Theory by Adam Sheffer
Graduate Mentor: Alan Hou
Description:
We will study linear representations of finite groups and basic representation theory of finite groups of Lie groups, etc. After establishing the general theory, we will discuss selected examples arising from groups of Lie type, with a focus on the representation theory of \mathrm{GL}_2(\mathbb{F}_q). This will provide students with a first glimpse of how abstract representation theory interacts with linear algebra and finite fields, and serves as preparation for further study in algebra, number theory, and related areas.
Required course:
Prerequisites include linear algebra and a basic background in abstract algebra (groups, rings, and fields, for example).
Suggested book:
The primary reference for the course will be lecture notes by Brandeis professor Justin Campbell, supplemented by additional examples and exercises as needed.