Summer 2020 Online Program

Please note that some details below may be specific to our residential program, which has been transitioned to an online-only format for 2020 due to COVID-19. For more information about this summer’s program, please visit the Online Program page.

Program Overview

The SUMaC courses focus on pure mathematics—that is, mathematics that is motivated independently of ties to other sciences—nonetheless, important applications are introduced and pursued along the way. The SUMaC courses are not for credit or grade—they are designed for pure mathematical enrichment.
A group of participants attend a guest lecture.

Two Academic Tracks

SUMaC offers two courses, called Program I and Program II, with unique topics for each course. Participants are enrolled in just one course during the summer, and the two courses allow participants to potentially return for a second summer. The two courses take place simultaneously.
A participant speaks to a class, gesturing at formulas on the whiteboard.

Research Projects

Both courses feature the research project where participants pursue course topics in greater depth. This project is one of the highlights of SUMaC. For this activity, participants initially work in groups under the leadership of Teaching Assistants, and expand their research using journal articles, advanced textbooks, and other materials. At the end of the course, participants give presentations on their topics to their peers, providing participants with experience in the important activity of communicating mathematics.


SUMaC challenges students with topics far more advanced than what they normally see in their high schools. Each student attends one of two courses, both of which build on topics central to mathematics through their historical significance and their relevance to current lines of mathematical research. Students can indicate their preference between the two course options on their applications, and then the admissions committee will place students into their final admitted course.

Program I

Abstract Algebra & Number Theory
Research Topics: Field theory, error-correcting codes, cryptography, primality testing, eliptic curves, mathematics of the Rubik’s cube, classifying symmetries of patterns, Galois theory, applications of group theory in combinatorics, and other topics.

Program I topics are introduced through five motivating problems such as limitations of straight-edge and compass constructions, classification of patterns in two dimensions, error-correcting codes, cryptography, and the analysis of symmetry in structures. 

The mathematics central to solving these problems comes from the areas of abstract algebra and number theory. Abstract algebra originated in the early part of the 19th century through the study of polynomial equations. This branch of mathematics lies at the core of many areas of modern mathematical research. Number theory concerns properties of the integers, and has its origins in ancient mathematics. Number theory remains a very active field of study with interesting open problems and important applications in computer science.

Program II

Algebraic Topology
Research Topics: Moduli spaces, homotopy groups, cohomology, configuration spaces, Lie groups, Lie algebras, knot theory, hyperbolic geometry, and other topics.

Program II centers on algebraic topology, a major area of current mathematics research.

Topology is the study of the properties of shapes that remain unaffected by deformations. For example, a sphere made out of rubber can be deformed into the shape of a cube. While it may appear that a sphere and a cube don't have that much in common, it turns out that they are topologically equivalent and in a way that can be made precise mathematically. This course will explore different ways of analyzing topological properties of shapes using algebraic concepts, such as the notion of group.

Founders & Instructional Staff

Rick Sommer

Dr. Rick Sommer

Director & Program Instructor

Portrait of Rafe Mazzeo

Professor Rafe Mazzeo


Portrait of Ralph Cohen.

Professor Ralph Cohen


Photo of a column

Professor Simon Rubinstein-Salzedo

Program Instructor

Program Staff

Alivia Shorter

Alivia Shorter

Director of Diversity, Outreach, and STEM Programs

Portrait of Monique Ellis

Monique Ellis

Assistant Director of Diversity, Outreach, and STEM Programs

Guest Lecturers

Mykel Kochenderfer

Mykel Kochenderfer

Professor, Stanford Department of Aeronautics & Astronautics

Stacy Speyer

Stacy Speyer

Artist in Residence with the Exploratorium

Lucas Garron

Lucas Garron


Nitya Mani

Nitya Mani

Stanford and SUMaC alum, PhD Candidate at MIT

Brian Conrad

Brian Conrad

Professor, Stanford Department of Mathematics

Tadashi Tokieda

Tadashi Tokieda

Professor, Stanford Department of Mathematics


Learn more about the program's decades-long history on the Stanford campus, and get to know just a few SUMaC alumni that are doing innovative work in industry, research, and education.


In its first year, all SUMaC students came from Northern California, mainly the San Francisco Bay Area. In year two, students joined from throughout California. By 1997, SUMaC was attracting students from out of state. The first international students joined in 1998. Over the years, SUMaC has hosted students from more than 50 countries.

Fall 1994: Stanford University Mathematics Camp (SUMaC) began in Fall 1994 when Professors Rafe Mazzeo and Ralph Cohen obtained funding from the Howard Hughes Medical Institute to develop a new program in mathematics at Stanford intended for high school students. Dr. Rick Sommer soon joined the founding team.

1995-1996: SUMaC enrolled just 12 students in 1995, and then grew to 36 students in 1996. The founding team decided to keep enrollment at SUMaC to a maximum of 40 students in order to preserve key features of the SUMaC experience.

1997: The Program II course was offered for the first time in 1997 to a group of just four students returning from the previous year. In the coming years Program II grew to include approximately 40% of the SUMaC participants each year, and the Program II topics have varied from Complex Analysis to Topology.


Meet some of our outstanding alumni that are doing innovative work.