Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Randall Dougherty (born 1961) has made contributions in widely varying areas of mathematics, including set theory, logic, real analysis, discrete mathematics, computational geometry, information theory and coding theory. Dougherty is a three-time winner of the U.S.A. Mathematical Olympiad, 1976, 1977, 1978 and a three time medalist in the International Mathematical Olympiad. He is also a three-time Putnam Fellow 1978, 1979, 1980. Dougherty earned his Ph.D. in 1985 at University of California, Berkeley under the direction of Jack Silver. His notable accomplishments include the following. With Matthew Foreman he showed that the Banach-Tarski decomposition is possible with pieces with the Baire property, solving a problem of Marczewski that remained unsolved for more than 60 years.

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