Stanford Math Circle

Stanford University Stanford Math Circle

Stanford Math Circle The Stanford Math Circle is jointly sponsored by the Stanford Pre-Collegiate Studies Program and the Stanford University Department of Mathematics.


(March 5)

This Saturday, we're hosting a special math circle session for middle school (5th-8th grade) students and parents -- you don't have to be currently enrolled in the math circle to come! The session will be part engaging math talk and part an introduction to a new high school for mathematically talented students that will be opening in San Francisco in Fall 2105. There is more information, and a link to RSVP at the Proof School's website. (You don't have to RSVP to come, but it would be helpful to have a rough idea of how many people may be attending.)

The event will be on Saturday, March 8th from 2 to 3:30 PM, in the basement of the Stanford math building (room 380C in building 380).

(February 13)

  • Applications for the spring quarter of the Stanford Math Circles will open on Friday, February 14 and close on Friday March 7th. Students currently enrolled in the math circles who apply by March 7th are guaranteed admission for Spring. After that we will fill any open spaces with students from the wait list. The last day of winter quarter classes is Thursday, March 13. The first day of spring quarter classes is Thursday, April 3.

    To apply, click Apply to the Math Circle Programs (but the links won't be active before February 14) If you have previously applied, use your existing account with your student id and password, not a new account (If you don't remember your student number or password, please contact us at .)

  • Applications are also open for the various academic summer programs run by Stanford PreCollegiate Studies (SPCS), in particular, SUMAC the Stanford University Math Camp, which is for current 10th and 11th graders with exceptional mathematics talent and motivation and the SPCS Summer Institutes (formerly named EPGY Summer Institutes), intensive summer academic (not just math) camp programs for middle school and high school students. )

(Jan 2)

The Schedule for the winter quarter is now posted.

Applications are closed for the elementary and middle school circles, but the advanced circle can still accept applications for winter quarter. Applicants should normally be in grades 9-12, but younger students who have evidence of readiness (which could be scores on the AMC 10, AMC12, or Bay Area Math Olympiad) may also apply.

Contests in January and February:

The "AMC 10" and "AMC 12" are each 75 minute, 25 question math competitions in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Any student in grade 12 or younger may take the AMC 12; only students in grade 10 or younger may take the AMC 10. The contests are meant to be enjoyable, spurring interest in mathematics and offering challenging problems of a different nature than those you may encounter in a math class.

The Stanford Math Circle, in cooperation with the Stanford Math Department and the Stanford Pre-Collegiate Studies Program, will once again be offering the AMC 10/12 contests to Bay Area students who are not otherwise able to participate. Students who attend a school where the contests are offered must take them at their own school [most high schools, and even some middle schools, already give the AMC contests.

For 2014 the tests will be offered on Tuesday February 4 and Wednesday February 19. Students may participate in either test, or both -- it is possible to take the AMC 10 on one date and the AMC 12 on the other, assuming all other eligibility requirements are met. Please note that the "Registration" link at that web site linked above is for schools and test sites -- individual students do NOT register there. Students who do NOT attend a school where the contest is given may sign up to take the contest at Stanford here. If you are uncertain whether your school participates in the AMC 10 or 12, you may consult this link, which will tell you if they participated last year or if they have already signed up to participate this year. Please do this before signing up to take the contest at Stanford.

Another contest worth investigating is NACLO, the North American Computational Linguistics Olympiad, which will be on January 30th. This is the qualifying contest for a more advanced round, which is used to pick the US team for the International Linguistics Olympiad. There will be test sites at Stanford (run by the linguistics department) and San Jose State and possibly at some local high schools. Check the NACLO web site for more information.

"This olympiad is a contest in which high-school students solve linguistic puzzles. In solving the problems, students learn about the diversity and consistency of language, while exercising logic skills. No prior knowledge of linguistics or second languages is necessary. Professionals in linguistics, computational linguistics and language technologies use dozens of languages to create engaging problems that represent cutting edge issues in their fields. The competition has attracted top students to study and work in those same fields. It is truly an opportunity for young people to experience a taste of natural-language processing in the 21st century."

The Stanford Math Tournament will be held on February 15. Teams compete in groups of up to eight students, and work on short answers as well as proof-based questions in their team, and also take an individual contest with a choice of either individual subject tests or a general test.

The Bay Area Math Olympiad will be held on February 25. This is a long (4 hours) proof-based contest, with a version for students in 8th grade and younger, and another version for students in 9th-12th grade. We anticipate offering this contest at Stanford for students who are not able to participate at their own schools.

(Oct 2)

AMC 8 The AMC 8 is a fun mathematics competition, aimed primarily at middle schoool students, though some younger students may also enjoy the contest. We do expect that the Stanford Math Circle will again offer the AMC 8 contest to local students. You don't have to be a member of the math circle to participate, but you DO have to be in 8th grade or younger, and you *must* take it at your own school if it is offered therel. You can find a list of all the schools that participated last year [or have signed up already for this year] here.

While we have not yet received confirmation of what rooms we may use on campus, so we aren't sure how many students we will be able to accept, we do have a signup sheet here and will contact students on the list when we have more information.

BAMA The next session of the Bay Area Math Adventures (BAMA) series will be on Wednesday, October 16 at San Jose State University at 7:30 PM. Brian Conrey, of the American Institute of Mathematics will be speaking on the subject of "Non-transitive Dice". See the flyer for more information. (and I hear Ivars Peterson, mathematical author, will be the speaker at the November BAMA on FRIDAY, November 15 at Santa Clara University).

BAMA talks are free and open to the public. Reservations are not necessary, but it makes sense to arrive early to secure a good seat.

deLeeuw Lecture Actually, on the very same day -- Wednesday, October 16 --- Jean-Pierre Bourguignon (Director Emeritus, IHES /President Elect, European Research Council) will give the Karel deLeeuw Memorial Lecture at Stanford at 4:45 PM in Building 370, Room 370. The talk is entitled "Sound, shape, and harmony: a mathematician's perspective. See the flyer for more informaiton.

(September 3):

Applications for the Stanford Math Circles for the 2013-2014 school year are now open! Those applying before September 16 will be entered in a lottery for avai lable spaces; Applications received after that date will be accepted if space remains.

(August 15)

Hello All!

As you are aware, fall is coming up quickly and that means it’s almost time for registration! We have some changes in the works that will roll out this fall for the Elementary circle and a new program for Middle School students. Please see the details for changes to your program below.

Elementary Circle

  • Additional sections: we are adding additional sections of the Elementary program to accommodate more students. This will help alleviate some of the waitlist backup.
  • Full Year Registration: you will only need to fill out an application once to apply for all three quarters; you will still have to log in to your student page each quarter to pay fees, but you will no longer have to re-apply every three months.
  • Lottery system: we will be implementing a new lottery system to determine seats in the program; priority will be given to students who have NOT participated in the past. Combined with the additional sections, we believe this will help many more students share in the Math Circle experience!

Middle School Circle

  • 5th-8th Grade: students in grades 5-8 will be eligible for the Middle School program.
  • Format: The Middle School circle will be similar in structure to the Advanced circle with a series of guest mathematicians as instructors, but most instructors will lead several consecutive sessions.
  • Quarterly Registration: Participants will apply quarterly following the same steps as the Advanced program.

Advanced Circle

  • Quarterly Registration: Advanced circle registration will continue on a quarterly basis.

A new website and online registration system will be released in the coming weeks. You will receive an email once all changes go live. Please stay tuned for updates.

We look forward to seeing you all this fall! Please feel free to contact us in the meantime with any questions.

Best wishes,
Kellie Trauner
Program Assistant
Stanford Pre-Collegiate Studies

Older Announcements

(As of August 8th, 2013) We're not yet ready to receive applications for the Stanford Math Circles for 2013-2014, but we anticipate we'll be able to begin accepting them in a few weeks. I know many people are eagerly awaiting information about the new year and I wanted to give you an update.

Our application process will be changing somewhat for this year. Full details will be available later this month, but the most notable changes are:

  • We will be expanding the the elementary math circles, increasing the number of available sections! (class size per section will not increase).
  • We will, for the first time, have a middle school math circle, aimed at grades 5-8!
  • For the Elementary circles, applications will be for the full year, not for one quarter. The middle school and advanced circles will still require re-registration each quarter.

The International Math Olympiad was just two weeks ago, as was the International Linguistics Olympiad (which contains a lot of nice puzzles, too!) These are pretty tough, though I think the first IMO problem would be doable in the advanced circle -- still, it can be interesting to try them without a time limit, then review the official solutions. You can see the problems at and

Here are two (slightly) easier problem, still for the advanced circle:

  1. The vertices of a regular nonagon (9 sided polygon) are colored -- some of them are colored red, the rest are black. There are many [how many?] triangles that may be formed by connecting 3 of these vertices. Such a triangle is called "boring" [or, you could call it "monochromatic"] if all of its vertices are the same color. Prove that there must be two congruent boring triangles.
  2. Can you find 2013 different positive integers for which the sum of the RECIPROCALS of these integers is 2.013? Can you find 2013 different positive integers for which the sum of the reciprocals of these integers is 20.13?

The Stanford Math Circles are on summer break. We'll resume the week of September 23 (expected first day of sessions: Thursday, September 26). We expect to begin receiving applications for the Math Circles in August, at which time we should have more information on the number of sessoins available at each grade level, as well as the dates, times, and costs for the new school year.

Participation in the Elementary Circles are limited to enrolled students; Everyone is welcome to visit the advanced circle, but should be aware that:

  • The material is aimed at high school students with an interest in mathematics. Younger students are welcome to participate, but many sessions of the circle may assume familiarity with mathematical concepts to which they have not yet been exposed.
  • Anyone who thinks he or she might be interested may come to one or two sessions to try it out, but those who decide to participate regularly must register.

For applications to both programs see the "Apply" link to the left. (CURRENTLY INACTIVE DURING SUMMER 2013 until August). Note that the elementary circles have a waiting list, and we cannot guarantee how long it may be before a space is available for your student.

There is a google groups mailing list for the Stanford Math Circle: roughly once a week during the school year, a message is sent out with information about upcoming sessions of the advanced circle and any other upcoming contests or events in the Bay Area that might be of interest to math students (of any pre-college age) in the Bay Area.

The Stanford math circle expects to be a test site for several math competitions in 2013-2014, as we have done in previous years. In 2012-2013, the contests we offered were; The AMC 8 (for students in 8th grade and younger), The AMC10 and AMC12, BAMO (Bay Area Math Olympiad), AIME (for those who qualified on the AMC 10/12), USAMO/USAJMO (for those who qualified on the AIME) and the Math Talent Quest Screening and Team Selection Tests.

Students do not have to be participants in the Stanford Math Circle in order to take these tests with us; we post signup lists about a month in advance of the contests and will take as many students as we have space for -- however, many of these contests are also offered at some local schools (almost all local public high schools offer the AMC 10 and 12, for example), and students who attend a school where the contest is offered must take it at their school.

Congratulations to the SF Bay Area ARML teams, the national champions for 2013! Top students from different high schools throughout the region come together and work on 15-person teams to solve challenging problems. The contest took place May 31-June 1 at four different locations across the country simultaneously! West coast teams competed at UNLV in Las Vegas. Portions of the test involve individual work and others involve group work; Some portions are short-answer questions, others require written proofs. You can see a bit more about the contest at

SFBA teams are formed with the aid of and practices are run at Stanford under the supervision of the Stanford Undergraduate Math Organization (SUMO). The top few teams are selectively chosen, but we bring as many students as want to participate and can fit on the bus! The practice schedule is at and additional team information and instructions are at:

The AMS/MSRI Mathematical Circles Library is an excellent series of books published jointly by the American Mathematical Society (AMS) and the Mathematical Sciences Research Institute (MSRI). There are currently 12 volumes, and they cover different age ranges and levels of difficulty. Some are aimed at students and some are aimed at teachers. Most of the books cost \$18.75 (plus shipping) if ordered directly from the AMS web site..

still older announcements

Summer 2012: There are two summer puzzles available, based on problems from the spring quarter of the (primarily high school) math circle.

Please visit our Archives to see information about previous sessions (including sample lecture notes, handouts, and other SMC materials). including the Spring 2013 schedule.

Students in grades 9 or above who would like to see if the Advanced Math Circle is right for them are welcome to come to a session or two to see what it's like; if they decide to continue they should register. The Elementary Math Circle (for students in grades 1-4) is not able to accept unannounced visitors. Please email the director if you have any questions about the SMC!

Note: Stanford Math Circle is a solution of the following problem: Draw 12 circles in a plane so that every circle is tangent to exactly 5 others. Can you find other solutions?

Thanks to Paul Mennen, who wrote the code to generate this particular solution.