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Integration is one of the core constructions in modern mathematics. It is attached to famous names such as Newton, Leibnitz, Riemann, Lebesgue, Stieltjes, Wiener, Itô, Stratonovich, Skorohod, and many others. By definition, the integral of a (nice) function is the area of the region bounded below the graph of that function. The Fundamental Theorem of Calculus (the cornerstone of calculus, as taught, for example, in 18.01) allows the calculation of integrals using another key calculus ingredient - differentiation - in reverse. While differentiation is completely routine, applying it backward to integrate requires skill and creativity.
For many years (though probably less than 128), MIT has held the world's most prestigious (and first) Integration Bee. The format has varied, ranging from a traditional round-robin to an NHL-style playoff tournament. Each year the bee draws a large crowd (in 2007, there were more than 150 spectators). Come cheer on MIT's best
speed-integration specialists, and watch them vie for the coveted title Grand Integrator!
This year's finalists, ranked in order of their performance on the qualifying test, are:
| The 2009 Integration Bee is a four round seeded
tournament, with pairing progression detailed on the diagram below. The
four highest ranked finalists have byes in the first round, which
is sudden death elimination: each pair will be given one integral,
and the first competitor to correctly solve it progresses to round 2,
while the other competitor is eliminated. In all rounds, the
integrals will be projected onto the screen along with the timer. In the second round, the first through fourth seeded finalists match the first round winners in first-to-two-integrals elimination. The four successful competitors proceed to round 3, which is also first-to-two-integrals elimination. The two remaining competitors then square off in the championship round, where the first to correctly solve 3 integrals will be declared the Grand Integrator! All integrals will be at approximately the same level of difficulty, none trivial. The finalists will have a maximum of 3 minutes to solve each integral; if neither gives a correct solution within 3 minutes, both start with a new integral. When a competitor circles a solution, the clock is stopped, and the judges consider it. If it is judged correct, the competitor has won an integral point; if incorrect, the clock is started again, and either competitor may present a solution within regulation time. (A competitor may not present more than 3 solutions for one integral.) |
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| All finalists will receive gift certificates to Toscanini's ice cream. The final two competitors will receive book prizes, and the winner of the championship round will be crowned Grand Integrator. |