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Function Series, Catalan Numbers, and Random Walks on Trees

by Ibetsam Bajunaid, Joel M. Cohen, Flavia Colonna, and David Singman

Year of Award: 2006

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 112, (2005), pp. 755-785

Summary: Discusses the Catalan numbers, a basic Calculus style function, functional equations, random walks on trees and on the nonnegative integers and properties of series convergence.

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About the Authors: from The American Mathematical Monthly, (2005)

Ibetsam Bajunaid is an assistant professor of mathematics at King Saud University in Saudi Arabia. She received her Ph.D. from King Saud University in 1999 under the direction of Victor Anandam. She was the first woman to be granted a Ph.D. in mathematics from King Saud University. Her primary mathematical interest is potential theory, and she is currently collaborating with Dr. Anandam on polypotentials on trees.

Joel M. Cohen has been professor of mathematics at the University of Maryland since 1978. He received his Ph.D. in mathematics from MIT in 1966 and also taught at the University of Chicago and the University of Pennsylvania. His early work in algebraic topology and low dimensional complexes led to an interest in combinatorial group theory. The study of free groups led naturally to trees. The trees then led him astray to functional analysis, harmonic analysis, integral geometry, and potential theory. In his spare time he is active in politics, and is national chair of the liberal political group Americans for Democratic Action.

Flavia Colonna is professor of mathematics at George Mason University. Before her tenure there, she was a junior faculty member at the University of Bari, Italy. She received a Ph.D. in mathematics from the University of Maryland in 1985. Her research interests include complex and harmonic analysis, potential theory, integral geometry, and image processing. She has been involved in various outreach programs for girls in sixth through eighth grades and serves as a judge in the Mathcounts National Competition.

David Singman is professor of mathematics at George Mason University. He received a Ph.D. degree in mathematics from McGill University in 1980. His research interests include potential theory in classical, axiomatic, and discrete settings.

Subject classification(s): Index
Publication Date: 
Wednesday, October 22, 2008