The 2019 Bernd Aulbach Prize, the top honor given by the International Society of Difference Equations (ISDE), was awarded to Professor Emeritus Allan Peterson of the Department of Mathematics at the University of Nebraska–Lincoln. The winner delivers a lecture at the annual meeting of ISDE, which Peterson gave at the London meeting in July.
Professor Bernd Aulbach, from the University of Augsburg, Germany, was involved in the early establishment and founding of the ISDE. In his memory, the Aulbach Prize was established and is awarded to someone who has contributed fundamental results to the general area of difference equations.
Peterson has been continuously elected to the Board of Directors of ISDE since its inception in 2001. An ambassador for difference equations and for mathematics, evidenced by his wide outreach appeal to undergraduates and record number of doctoral students, Peterson and his research and teaching contributions span ordinary differential equations, finite difference equations, and, more recently, dynamic equations on time scales.
Peterson received his B.S. and M.S. degrees in mathematics at the South Dakota School of Mines & Tech in 1963 and 1965, respectively, and his Ph.D. in mathematics at the University of Tennessee in 1968 under the guidance of the well-known Professor John Barrett. Since 1968, he has been a faculty member at Nebraska. He has supervised more than 50 undergraduate REU students and has advised 34 doctoral students. Peterson retired in 2019.
Peterson is the author of eight textbooks and monographs and 205 research articles, accumulating more than 5,000 citations; editor of 17 mathematical journals; and reviewer for numerous scientific journals. He also holds Distinguished Teaching Awards, is the Centennial Alumni Award Winner of the South Dakota School of Mines, received a Certificate of Appreciation from the United States Department of Education, a Professor Pizzaz Teaching Award, and has been the Charles Bessey Distinguished Professor at Nebraska since 2006.
His textbook “Difference Equations: An Introduction with Applications” with Professor Walter Kelley, which arguably set the standard for books in that area, is now in its second edition, as is another more recent textbook with Kelley, “The Theory of Differential Equations.” His 1996 monograph “Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations,” co-authored with Professor Calvin Ahlbrandt, was presented as the keynote address at the 1997 Rocky Mountain Mathematics Consortium Summer Conference at the University of Wyoming.
Influenced greatly by Stefan Hilger and Aulbach and the presence of Professor Lynn Erbe at Nebraska, Peterson directed his research and teaching efforts toward dynamic equations on time scales in 1998. In 2001, he published “Dynamic Equations on Time Scales: An Introduction with Applications,” with Martin Bohner. In the MathSciNet database, out of all items originally published in 2001, this book currently has the second-highest number of citations.
Peterson’s latest book, “Discrete Functional Calculus,” serves as an introduction to the subject, and was co-authored with his Ph.D. student Christopher Goodrich in 2015.
– Lindsay Augustyn and Lynn Erbe