Berkeley Math Circle

The Mosse Foundation program for education at Mathematical Sciences Research Institute.


Project of the Mathematical Sciences Research Institute and co-sponsored by the UC Berkeley Mathematics Department and partially supported through the NSF Career Grant to R. Vakil of Stanford University.


Introduction: What are BMC and BAMO?


The Berkeley Math Circle (BMC) is a weekly program for over 30 San Francisco Bay Area high and middle school students. The program is administered by the Mathematical Sciences Research Institute (MSRI), and meets on Sundays on the UC Berkeley campus. The Bay Area Mathematical Olympiad (BAMO) is an annual competition among 250 Bay Area students, consisting of 5 proof-type math problems for 4 hours. The program was founded in 1998 by Zvezdelina Stankova (then at MSRI, now at Mills College), Paul Zeitz (University of San Francisco), and Hugo Rossi (MSRI). Emulating famous Eastern European models, the program aims at drawing kids to mathematics, preparing them for mathematical contests, introducing them to the wonders of beautiful mathematical theories, and encouraging them to undertake futures linked with mathematics, whether as mathematicians, mathematics educators, economists, or business tycoons.

BMC and BAMO have been extremely popular during every one of their five years of existence. One piece of evidence of this success is the Bay Area representation of three students on the six-member US team, to tie for second place with Russia (after China) among 80 countries at the International Mathematical Olympiad in 2001, Washington DC.

Under the aegis of Mathematical Sciences Research Institute and with the work of Professors Stankova and Zeitz, the BMC and BAMO program has come of age and established itself as the most prestigious and sought-after program by students, teachers and parents in mathematical olympiad and theory training in the Bay Area.


Berkeley Math Circle (BMC)

The heart of the Circle is the Weekly Math Circle lectures. Each Sunday during the academic year middle and high school students from the San Francisco Bay Area gather for two hours in the afternoon on the campus of the University of California at Berkeley for a lecture on a specific mathematical topic. University professors and teachers, well-known locally, nationally and even internationally for their expositional and problem-solving skills, present the lectures. Frequently, the lectures take the form of an interactive discussion between the instructor and students, and the students volunteer to explain solutions and problems to the rest of the group. The style, organization, level and topic of the lectures varies from meeting to meeting. Some lectures are aimed at problem-solving for mathematical competitions. Other lectures introduce the students to exciting advanced math topics whose level range from elementary high school to advanced undergraduate. Yet, a third type of lectures deal with connections between mathematics and other sciences such as physics, biology, computer science, and economics.

Here follow a few samples of lectures at BMC 2003:

1. “How to make a Möbius band out of paper?", by Dmitry Fuchs;
2. “Accidental Summations” by Joshua Zucker;
3. “The smallest prime factor (and other objects from number theory)” by Kiran Kedlaya;
4. “Classical Theorems in Geometry” by Maksim Maydanskiy;
5. “Inversion in the Plane” by Zvezdelina Stankova;
6. “Four Points on a Circle” by Tom Davis.

A full list of the lectures being given during the 2002-2003 academic year is appended (see Berkeley Math Circle 2002-2003 Academic Program), and can be found on the Berkeley Math Circle website.

The uniqueness and success of the Math Circle is based on the great variety of instructors: distinguished professors, world-famous problem solvers, high school teachers, local competition stars and former circle participants. More detailed personal information about each instructor can be found on the BMC website.

Another feature of the BMC are the Monthly Math Circle contests. Each month, the students are given an informal take-home 5-problem contest, which is graded by the Math Circle instructors. Because the problems tend to be very challenging and the students have a whole month to work on them, the contest comes closer to emulating actual scientific research than anything the students are likely to encounter in high school. The winners receive mathematics books and certificates of accomplishment. The books are especially chosen by the instructors to lead the students further into advanced mathematics and problem solving: students on their own often cannot afford or do not know how to choose suitable mathematical books.

There is a selection procedure or entrance exam to the Berkeley Math Circle. On average, there are about 30 middle and high school students, and occasionally, the attendance rises to 50-60 participants. Teachers and parents are also welcomed to every circle meeting. The circle was founded in 1998, thus accomplishing its 5th year of activities in 2002-2003.



Bay Area Mathematical Olympiad (BAMO)

The annual BAMO contest is an exam given once a year to students at participating high schools and middle schools, most of whom are in the San Francisco Bay Area. The exams are mailed out to the schools, proctored locally, then returned to be graded by a group of math circle instructors and educators.

The following weekend, there is an awards ceremony, with prizes for individuals and schools, lunch for everybody, and a math lecture by a distinguished mathematician. The event has been hosted each year by a different academic institution in the Bay Area: UC Berkeley in 1999, University of San Francisco in 2000, Mills College in 2001, San Jose State University in 2002, and Stanford University in 2003. The awards ceremony has become an annual focal point for the Bay Area middle and high school activities, where 180-200 students, teachers and parents gather for an exciting day of Mathematics. The event has been made even more worthwhile by the staggering sequence of famous lecturers and their fabulous talks:

1. Alan Weinstein (University of California at Berkeley), “The Geometry of Random Expectation”, 1999.

2. Persi Diaconis (Stanford University), “Card Tricks and the Mathematics of Magic”, 2000.

3. Ron Graham (University of California at San Diego), “Mathematics in the 21st Century: Problems and Prospects", 2001.

4. Joseph Gallian (University of Minessota at Duluth), “Breaking Driver's Licence Codes”, 2002.

5. Ravi Vakil (Stanford University), "Why is the Golden Mean Everywhere?" 2003.

The 18 individual BAMO prizes are awarded in 3 age groups: 11-12th grades, 9-10th grades, and 8th grade and below, thus, giving opportunity to younger participants with less mathematical experience to be acknowledged for their bold and creative participation in the Olympiad. There are 3 top team awards and 3 top school awards, as well as a grand prize award for highest overall BAMO score and a brilliancy award for an unanticipated original solution. It is the grand prize that we propose to name for Hilde L. Mosse.

The difficulty of the BAMO problems ranges from very easy and accessible to middle school students problem 1 to a die-hard problem 5, usually solved by only a handful of students, if any. In each of the 5 years of BAMO, there have
been one or two students with perfect or near perfect scores. For three years the BAMO grading committee was delighted to award the brilliancy award for particularly nice solutions to one of the harder problems.

BAMO differs from many other math competitions in that it is proof/essay-style - the problems demand creative thinking and clearly reasoned arguments, not just the ability to calculate quickly. BAMO provides a tangible goal for the students to focus on, and helps achieve an objective of the Berkeley Math Circle to reach out to an even larger group of students, since participation in BAMO is not limited to those who attend the weekly lectures. BAMO has been held each year in February, with the first one having taken place in 1999 (one year after the founding of Berkeley Math Circle). The average participation is 250 students from approximately 45 schools.


BMC Website

An extensive website has been developed for posting materials and resource links to the math circle students, as well as any BAMO participants and other interested students, parents and teachers: There one can find lecture notes from the weekly circle meetings since the circle was conceived in 1998, the monthly contest and BAMO problems and solutions, information on the USA National Math Olympiad and other competitions and circles.





Entire Web Berkeley Math Circle site

2003-2004 Property of Berkeley Math Circle, Berkeley,California

Special thanks to George Csicsery, producer and director, and MSRI, sponsor, for allowing the use of some images from the movie "Invitation to Discover". For more information about George Csicsery's films, please visit