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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.
6. Joe Buhler
(Center for Communications Research and Reed College), "Juggling Permutations," 2004.
7. Melanie Woods
(Princeton University) "Ramsey Theory: Amongst enough chaos, can we find order?" 2005. |
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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, Stanford University in 2003, University of San Francisco in 2005, and now the MSRI in 2006. 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.
Dr. Hugo Rossi (on the left),
the Deputy Director of MSRI, was on the 2004 BAMO Awards Ceremony.
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.
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
Prof. Zvezda & BAMO 2005 Awards
The BAMO 2005 lecturer, Malanie, was on the 2005 Award Ceremony
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The BAMO 2006 Exam will take place on Tuesday, February 28, 2006 at participating schools. The awards ceremony will take place on Sunday, March 12, 2006 at the Mathematical Sciences Research Institute. (more...)
Previous Exams:
Here are some examples of problems from past BAMO exams:
Let D be a dodecahedron which can be inscribed in a sphere with radius R. Let I be an icosahedron which can also be inscribed in a sphere of radius R. Which has the greater volume, and why?
Note: A regular polyhedron is a geometric solid, all of whose faces are congruent regular polygons, in which the same number of polygons meet at each vertex. A regular dodecahedron is a polyhedron
with 12 faces which are regular pentagons and a regular icosahedron is a polyhedron with 20 faces which are equilateral triangles. A polyhedron is inscribed in a sphere if all of its vertices lie on the surface of
the sphere.
(The illustration below shows a dodecahdron and an icosahedron, not necessarily to scale.)
(from BAMO 2005 Exam#5)
Solution Link
A lattice point is a point (x, y) with both x and y integers. Find, with proof, the smallest n such that every set of n lattice points contains three points that are the vertices of a triangle with integer area. (The
triangle may be degenerate, in other words, the three points may lie on a straight line and hence form a triangle with area zero.)
(from BAMO 2003 Exam#3)
Solution Link
A game is played with two players and an initial stack of n pennies (n ≥ 3). The players take turns choosing one of the stacks of pennies on the table and splitting it into two stacks. The winner is the player who makes a move that causes all stacks to be of height 1 or 2. For which starting values of n
does the player who goes first win, assuming best play by both players?
(from BAMO 2002 Exam#3)
Solution Link |
Let ABC be a triangle with D the midpoint of side AB, E the midpoint of side BC, and F the
midpoint of side AC. Let k1 be the circle passing through points A, D, and F; let k2 be the
circle passing through points B, E, and D; and let k3 be the circle passing through C, F, and
E. Prove that circles k1, k2, and k3 intersect in a point.
(from BAMO 2000 Exam#2)
Solution Link
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