Randall Dougherty (born 1961) is an American mathematician. Dougherty has made contributions in widely varying areas of mathematics, including set theory, logic, real analysis,

discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

computational geometry Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems ar ...

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

, 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 The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

. 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 Jack Howard Silver (23 April 1942 – 22 December 2016) was a set theorist and logician at the University of California, Berkeley. Born in Montana, he earned his Ph.D. in Mathematics at Berkeley in 1966 under Robert Vaught before taking a posi ...

. With

Matthew Foreman Matthew Dean Foreman is an American mathematician at University of California, Irvine. He has made notable contributions in set theory and in ergodic theory. Biography Born in Los Alamos, New Mexico, Foreman earned his Ph.D. from the Univer ...

he showed that the Banach-Tarski decomposition is possible with pieces with the

Baire property A subset A of a topological space X has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set U\subseteq X such t ...

, solving a problem of Marczewski that remained unsolved for more than 60 years. With Chris Freiling and Ken Zeger, he showed that linear codes are insufficient to gain the full advantages of

network coding In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, ...

.Dougherty, Freiling, and Zeger. Insufficiency of Linear Coding in Network Information Flo

an

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Selected publications

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References

1961 births Living people 20th-century American mathematicians 21st-century American mathematicians University of California, Berkeley alumni Ohio State University faculty International Mathematical Olympiad participants Putnam Fellows {{US-mathematician-stub