Bateman's academic assignments included lecturer in economics at the University of Ghana, 1963; assistant professor of economics at the United States Air Force Academy, 1964–1967; associate professor of economics at BYU, 1967–1969; professor of economics at BYU, 1969–1971; and former dean of the BYU business school, now the Marriott School of Management, 1975–1979.
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In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A Horn, of The University of Utah, who proposed it in 1962.
Rademacher had a number of well known students, including George Andrews, Paul T. Bateman, Theodor Estermann and Emil Grosswald.
Bateman attended Upper Moreland High School, which recognized his accomplishments by inducting him into its Hall of Fame in 1999.