Alan Horwitz received his B.A. and Ph.D. in Mathematics from Temple University. Dr. Horwitz has published six papers involving means, several of which were cited in A Handbook of Means and Their Inequalities, by P. S. Bullen. Dr. Horwitz has also published four papers involving ratio vectors of polynomials and a paper on Engineering Applications in Differential and Integral Calculus with Arya Ebrahimpour. Some of his research has a strong geometric flavor, including work on ellipses inscribed in, and circumscribed about, convex quadrilaterals. His research involves many diverse areas of analysis, including polynomial interpolation, numerical integration, and algebraic differential equations.
Dr. Horwitz served as a member of the University Faculty Senate of Penn State University from 2002 through 2006. He has used graphing calculators in the classroom for many years as a useful tool in exploring some of the concepts in calculus, linear algebra, and differential equations. He feels strongly that symbolic calculators can help with some of the more tedious computations and also show students that even when using technology with advanced symbolic capabilities; it is still useful and necessary to understand the mathematics behind the technology.
Dr. Horwitz has a strong interest in computers and in reading computer magazines and forums online. He also has built several of his own desktop PCs and helps family and friends with computer problems.
Recent Publications and Presentations
“Ratio vectors of polynomial--like functions”, “Journal of Inequalities in Pure and Applied Mathematics”, Volume 9, Issue 3, Article 76(2008).
“Means and Hermite Interpolation”, Journal of Mathematical Inequalities, Volume 2, Number 1 (2008), 75–95.
“Complex Ratios of Cubic Polynomials”, International Journal of Pure and Applied Mathematics, vol. 33, No. 1 (2006), 49-62.
“Ratio vectors of fourth degree polynomials”, Journal of Mathematical Analysis and Applications, 313(2006), 132-141.
“Ellipses of maximal area and of minimal eccentricity inscribed in a convex quadrilateral”, Australian Journal of Mathematical Analysis and Applications, 2(2005), 1-12.