# Boyadzhiev to be honored for paper

Khristo Boyadzhiev, Ph.D., professor of mathematics, will receive the Mathematical Association of America’s Carl B. Allendoerfer Award for his paper “Close Encounters with the Stirling Numbers of the Second Kind.” The article was published in Mathematics Magazine, Vol 85, No. 4, October 2012.

The award will be presented Aug. 2, 2013, at MathFest in Hartford, Conn. The Carl B. Allendoerfer Awards were established in 1976 and are given for articles of expository excellence published in Mathematics Magazine. The awards are named for Carl B. Allendoerfer, a distinguished mathematician at the University of Washington and president of the Mathematical Association of America, 1959-60.

The citation for Boyadzhiev says, “The Scottish mathematician James Stirling, in his 1730 book “Methodus Differentialis,” explored Newton series, which are expansions of functions in terms of difference polynomials. The coefficients of these polynomials, computed using finite differences, are the Stirling numbers of the second kind. Curiously they arise in many other ways ranging from scalar products of vectors of integer powers with vectors of binomial coefficients to polynomials that can be used to compute the derivatives of tan x and sec x. This well-written exploration of Stirling numbers visits the work of Stirling, Newton, Gr ¨unert, Euler and Jacob Bernoulli.

“Boyadzhiev’s fascinating historical survey centers on the representation of Stirling numbers of the second kind by a binomial transform formula. This might suggest a combinatorial approach to the study, but the article is novel in its analytical approach that mixes combinatorics and analysis. Grounded in Stirling’s early work on Newton series, this analytical approach illustrates the value of considering alternatives to Taylor’s series when expressing a function as a polynomial series. The story of Stirling numbers continues with the exponential polynomials of Johann Gr ¨unert and geometric polynomials in the works of Euler. Boyadzhiev shows the relation of Stirling numbers of the second kind to the Bernoulli numbers and Euler polynomials. The article closes with a brief look at Stirling numbers of the first kind, a nice touch that deftly brings the proceedings to a close. Boyadzhiev’s lively exposition engages the reader and leaves one eager to learn more.”