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About SUMaC

In this three-week online program, rising high school juniors and seniors engage in deep exploration of mathematics and develop as mathematicians.
Rubik's cube with Stanford Pre-Collegiate Studies logo

Online Academic Enrichment

SUMaC courses are not for credit or grade—they are designed for pure mathematical enrichment. Participants will explore mathematics beyond the typical high school curriculum.
Intensive Exploration
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.
Real-Time Online Instruction
Courses meet for two hours each day (Monday–Friday) for live, online classroom discussion with their instructor and peers. Students will also engage in daily problem sets, work with Stanford graduate students who serve as teaching assistants, and attend virtual guest lectures from mathematicians and others who use mathematics in their respective fields.
College-Level Workload
Similar to what they would experience in a college course, students can expect a heavy and engaging workload of assignments to work on outside of the live class meeting times.
Student Engagement
Active participation is key to creating an online community of engaged learners, and students are expected to participate in class and to collaborate with their peers, instructors, and teaching assistants.

Academic Tracks

SUMaC offers two courses, called Program I and Program II, with unique topics for each course. 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 admit students into their final course.

Courses meet daily, Monday–Friday, for live classroom instruction. The virtual class period will be held in both the morning (8:00–11:00am Pacific Time) and afternoon (5:00–8:00pm Pacific Time), and participants will be assigned to attend just one of the available meeting times. The exact class start times will be set closer to the program start.

Program I – Abstract Algebra & Number Theory

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

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.

Please note that Program II is only available during Session One this summer. See more details about the session dates below.

2022 Dates and Courses

SUMaC courses will be offered across two sessions this summer. Each session runs for three weeks, with classes meeting Monday–Friday.
Session One Dates
Monday, June 20 – Friday, July 8, 2022
Session One Courses
Program I, 8:00–11:00am Pacific Time
Program II, 5:00–8:00pm Pacific Time
Session Two Dates
Monday, July 18 – Friday, August 5, 2022
Session Two Courses
Program I, 8:00–11:00am Pacific Time
Program I, 5:00–8:00pm Pacific Time

Online Classroom Technology Requirements

Computer
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Participants will need to have daily access to a computer that is capable of running the latest versions of internet browsers, plug-ins, and software. Mobile devices are not recommended.
Internet Connection
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Students must have a reliable broadband internet connection that is robust enough to handle video conferencing with minimal difficulties. Our courses take place in an interactive environment which includes having all students on camera, chat, videos, and presentations. We highly recommend that students use a wired ethernet connection.
Webcam
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Participants should have a webcam to support daily participation in class.
Headphones & Microphone
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If you are using a laptop with a built-in microphone, we recommend that you use headphones during live class sessions to avoid echo or feedback. Using a headset with a microphone will help ensure that you have clear audio when participating in class.
Suitable Learning Environment
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Do your best to choose a comfortable, quiet, distraction-free learning space for the live class meeting times. Keep in mind that the setting should be appropriate for interacting with instructors and fellow students on camera.

Engaging Student Life

Stanford Pre-Collegiate Studies seeks to not only provide enriching academic experiences, but also to facilitate engaging learning communities that foster critical thinking, promote personal growth, and inspire lifelong learning outside of the classroom. Outside of the academic coursework, students will have opportunities to engage and build community with their peers through a variety of student life seminars, workshops, and activities, all of which will be available to SUMaC participants.
Hoover Tower on Stanford Campus

Build Connections Around the World

Meet participants from other countries while participating in exciting events like orientation, talent shows, student life workshops, and commencement.
Participants do yoga together outside.

Participate in Student Life Workshops

Take a series of student life workshops to complement your academic course, engaging in topics such as health and wellness, leadership, life and career planning, design thinking, cross-cultural communication, and more.

Daily Expectations

Participants have full daily schedules which incorporate the academic and social aspects of the program. Class time and student life activities are scheduled in an effort to accommodate multiple time zones. Each participant will have a unique schedule as they join our online community from their homes around the world.

In general, students can expect to have roughly 3-5 hours of academic work per weekday, in addition to the daily live class period. Outside of the scheduled class period, students are able to set their own schedule for when they work on class assignments and problem sets.
 

History

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.

Timeline

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. 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.

2020: In light of the COVID-19 pandemic, SUMaC was transitioned into an online program and successfully continued the tradition of engaging students in a deep, meaningful exploration of mathematics. The online model was designed to accommodate students across two sessions, so the program was able to expand to accommodate 60 students in total—30 in each session—without diminishing the key benefits and features of the small program. 

Alumni

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

Founders & Instructional Staff

Rick Sommer

Rick Sommer, Ph.D.

Co-Founder & Program Advisor

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Portrait of Rafe Mazzeo

Professor Rafe Mazzeo

Co-Founder

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Portrait of Ralph Cohen.

Professor Ralph Cohen

Co-Founder

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Photo of a column

Professor Simon Rubinstein-Salzedo

Program Instructor

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Stanford Pre-Collegiate Summer Institutes: Mathematics Courses

If you are not ready for Abstract Algebra & Number Theory or Algebraic Topology, we offer other math courses through Stanford Pre-Collegiate Summer Institutes. These courses are highlighted below. Please note: Stanford Pre-Collegiate Summer Institutes is another program that requires a different application from Stanford University Mathematics Camp. You can use the same application account to begin and submit applications for both programs.

Number Theory

Number theory, the study of properties of integers, has attracted the interest of mathematicians for over 4,000 years. This branch of mathematics continues to be an area of intrigue and active research. For some, the attraction is the possibility of solving a problem that has remained unsolved for hundreds of years; for others, it is the pure beauty of a branch of mathematics where the basic concepts are easy to understand, yet the techniques are deep and intricate. Number Theory is also important for its applications in cryptography, which is routinely applied to ensure the secure transmission of information over the Internet. In this course, students learn about unique factorization, the Euclidean Algorithm, congruence arithmetic, the Fermat/Euler Theorem, Diophantine Equations, Fibonacci Numbers, continued fractions, and quadratic reciprocity. Students will be given the opportunity to explore a subtopic of their choosing in greater depth as part of a culminating project of the course.

Discrete Mathematics

Discrete mathematics encompasses a broad range of mathematical fields centered on discrete (non-continuous) mathematical structures with an eye toward applications in applied and theoretical computer science. Topics include number theory, set theory, logic, graph theory, and combinatorics. Problems encountered in this field range from easy to very difficult, so this course provides an opportunity to hone mathematical problem-solving skills. Additionally, the course will help students develop proof-writing skills, and it will enable them to build a strong mathematical background for future study in computer science. The course will include applications in the analysis of computer algorithms.