Classes

We teach five classes each quarter during the academic year, as well as some classes over the summer. All academic year classes are offered in both online and in-person versions; summer classes are purely online. There are two components to our classes: lectures and problem sessions, which meet on different evenings each week. All students will attend lectures online, and then students can take either the in-person or the online version of the problem session. We have five levels of classes, listed in increasing order of difficulty:

  • Our mathematical information class is a year-long sequence offered every year. In this class, students will learn algorithmic thinking, problem solving, and how to present and work with information in a mathematical context. Topics include different representation of numbers, ciphers, and puzzles, among other topics.
  • Our mathematical thinking class is a year-long sequence offered every year. In this class, students will move beyond algorithmic mathematics toward more sophisticated problem solving. Students will be exposed to a wide range of mathematical topics, from topology to group theory to game theory, and many more areas.
  • Our transition to proof-based mathematics class is a year-long sequence offered every year, focusing on number theory in the fall, combinatorics in the winter, and analysis in the spring. Students learn how to write good proofs, as well a wide selection of interesting topics within the relevant subjects each quarter.
  • Our fundamentals of higher mathematics class is the next level after transition to proofs. Here, students learn the most important topics that are used everywhere in mathematics: linear and abstract algebra, real analysis, and point-set topology. This is also a year-long sequence offered every year.
  • Finally, we have advanced classes. Topics vary from year to year and term to term; in the 2025–2026 academic year, we will be offering combinatorics in the fall, infinite series in the winter, and p-adic analysis in the spring. Students also write an expository paper on a topic of their choice related to the class material but not directly covered in it, and especially dedicated students may have the opportunity to work on open research problems.

In the summers, we offer an independent research and paper writing (IRPW) class. Here, each student selects a topic and studies it in depth, writing a 20-page paper and giving a presentation to the class. Students learn best practices for mathematical writing and presentation, and there are also talks from distinguished mathematicians describing some of their research.

Here are the past advanced classes:

Year Fall Winter Spring Summer 1 Summer 2
2025–2026 Combinatorics Infinite series p-adic analysis Independent research and paper writing
2024–2025 Combinatorial game theory Complex analysis 1 Complex analysis 2 Independent research and paper writing Differential geometry
2023–2024 Number theory Ergodic theory Analytic number theory Independent research and paper writing Cryptography
2022–2023 Theory of computation Gems of linear algebra Differential topology Independent research and paper writing Mathematics of Euler
2021–2022 Generating functions Proofs from the book 2 Differential geometry Independent research and paper writing p-adic analysis
2020–2021 Markov chains Complex analysis 1 Complex analysis 2 Combinatorics Combinatorial game theory
2019–2020 Cryptography Infinite series Abstract algebra Ring theory and algebraic geometry Proofs from the book 1
2018–2019 Number theory Ergodic theory Analytic number theory
2017–2018 Combinatorics Mathematics of Euler p-adic analysis
2016–2017 Combinatorial game theory Proofs from the book 1 Ring theory and algebraic geometry
2015–2016 Abstract algebra Cryptography Complex analysis

We are now accepting applications for the winter 2026 classes. Click here to apply! Applications for winter are due by November 23rd.