Park City Mathematics Institute 2013
Bowen Kerins and Darryl Yong
Probability, Randomization, and Polynomials
Pick two positive integers at random. What is the probability that the two numbers don't have a common factor? What happens to the probability if the numbers are picked from 1 to 100. 1 to 1000? 1 to infinity? Roll 5 dice. What is the probability of rolling a sum of 13? What sum is most likely? What does the distribution of sums look like? These questions can be answered with the help of algebra. The course will also explore the meaning and definition of standard deviation and variance, the effects of repeating an experiment many times, and ways to generate or test random data. The contexts and methods developed in the course will be low-threshold, high-ceiling, with plenty of interesting mathematics for any grade level.
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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540.
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With generous support from Robert and Lynn Johnston