Euler Circle

See our winter class offerings and schedule

Are you a student who loves mathematics? Do you enjoy solving challenging problems, exploring unfamiliar ideas, and discovering new ways of thinking? Do you want to learn mathematics beyond what you encounter at school and in competitions? Would you like to work on challenging problems and make friends with mathematically-minded peers? If so, you have come to the right place!

Our classes

Euler Circle is a mathematics institute for precollegiate students who love mathematics. We offer mathematics classes ranging from introductory mathematical problem solving to classes at the level of upper-division college classes and beyond. Students can begin at whichever level is appropriate for their preparation and progress to increasingly sophisticated mathematics as they are ready.

The Euler Circle sequence begins with mathematical information, where students explore how information can be represented, stored, transmitted, and protected. Topics include different representations of numbers and their efficiencies, algorithms, puzzles, codes, and elementary cryptography. Students should be familiar with algebra, but there are no further prerequisites.
The next level is mathematical thinking, where students learn how to approach challenging problems while being exposed to snippets coming from a wide range of fields of mathematics, including number theory, combinatorics, set theory, topology, group theory, fractals, game theory, and more. Students should be comfortable with basic algebra and geometry.
The next level is transition to proofs, where students who already have problem-solving experience, whether from the mathematical thinking class, mathematics competitions, or elsewhere, learn how to write good proofs while also learning number theory, combinatorics, and analysis.
The next level is fundamentals of higher mathematics, which focuses on the core fields that are needed for all future mathematics: linear and abstract algebra, real analysis, and topology. This is the language that almost all advanced mathematics assumes, so it is crucial for students to have strong foundations in these fields.
Finally, we have a wide range of advanced classes, with topics varying from term to term. These classes are at the level of upper-division college classes or beyond. Classes include complex analysis, analytic number theory, ring theory and algebraic geometry, p-adic analysis, and differential topology, among many others. These classes have difficulty levels that are unbounded above: everyone will be challenged in these classes!

In each class, students solve many problems to gain familiarity with new material, and in the advanced classes each student writes an expository paper on a topic related to the class material.

The classes are set up in such a way as to provide a pathway to independent research. Many of our problem sets in the advanced classes include unsolved problems that students can explore once they have mastered the material presented in class. We offer small group meetings for students interested in working on the research problems once they have demonstrated the ability to work hard on challenging problems. See more on research in Euler Circle.

Why Euler Circle?

Much of the existing education for advanced students is aimed at preparing them for mathematical competitions. But mathematics doesn’t end with competitions. There is an enormous world of beautiful and fascinating mathematics out there that students rarely learn before college, if they encounter it at all. We believe that students should be able to learn as much mathematics as they are ready for, without being held back by age or grade level. We provide a pathway from introductory mathematical exploration to mathematics at the college level and beyond, giving students the opportunity to progress as far as their interests take them.

We love sharing the rest of mathematics with students who are curious about what else is out there—and the mathematics doesn’t disappoint!

Other subjects

Are you looking for Euler Circle-style education in other areas? See our umbrella program, Kaleidoscope Circles, which now also offers classes on physics in the Curie Circle and classes on AI in the Turing Circle. We plan to offer circles on other subjects eventually as well.

Teach at Euler Circle

Are you interested in teaching at Euler Circle? We’re always looking for exceptional TAs, instructors, and other collaborators. See our teaching page for more information.

Upcoming classes

Winter 2027 classes

Classes are available online to students around the world, with in-person options in Palo Alto, California.

View winter classes and schedules

Applications for winter 2027 classes are due November 22nd, 2026. After that, we will continue to accept applications while space remains on a rolling basis. Click here to apply!