Charles L. Samuels Oklahoma City University Department of Mathematics 2501 N. Blackwelder Oklahoma City, OK 73106-1493 Email: clsamuels (at) okcu (dot) edu

Personal Information

I am currently an Assistant Professor of Mathematics at Oklahoma City University. I finished my Ph.D. in August 2007 under the supervision of Dr. Jeffrey D. Vaaler at the University of Texas at Austin and worked as a lecturer in the same department for the following academic year. I spent one year as a postdoctoral fellow at the Max-Planck-Institut für Mathematik in Bonn, Germany followed by two years simultaneously at the University of British Columbia and Simon Fraser University in Vancouver, British Columbia. More detailed information is available in my vita.

Teaching

My teaching experience extends back to 2004 as a graduate student at the University of Texas at Austin. I began my time there as a Teaching Assistant, and was later promoted to Assistant Instructor, at which point I became the instructor of record for two Precalculus courses. After obtaining my Ph.D., I continued working as a Lecturer in the same department for the Fall 2007 and Spring 2008 semesters, teaching three different levels of Calculus as well as an introductory Real Analysis course. More recently, I taught one section of Multivariable Calculus and Introduction to Complex Variables at the University of British Columbia as well as Calculus I for the Biological Sciences at Simon Fraser University. In my two semester at OCU, I have taught College Algebra, Calculus I and II, Abstract Algebra and Real Analysis. During the summer term, I will be teaching one section of Business Calculus.

Research

My research interests lie in number theory. A significant part of my work is concerned with the study of Lehmer's problem and other questions that involve giving lower bounds on the Mahler measure of polynomials with integer coefficients. Among other things, I am interested in using projective heights, heights on subspaces, heights on polynomials as well as the Weil height to solve these sorts of problems. I have worked substantially with certain metric versions of the Mahler measure and have studied problems related to the Goldbach conjecture.

• Metric heights on an Abelian group, preprint.


• Two inequalities on the areal Mahler measure (with K.K. Choi), Illinois J. Math., to appear.


• The t-metric Mahler measures of surds and rational numbers (with J. Jankauskas), Acta Math. Hungar. 134 (2012), no. 4, 481--498.


• Polynomials whose reducibility is related to the Goldbach conjecture (with P. Borwein, K.K. Choi and G. Martin), JP J. Algebra Number Theory Appl., to appear.


• The parametrized family of metric Mahler measures, J. Number Theory 131 (2011), no. 6, 1070--1088.


• A collection of metric Mahler measures, J. Ramanujan Math. Soc. 25 (2010), no. 4, 433--456.


• The finiteness of computing the ultrametric Mahler measure, Int. J. Number Theory 6 (2010), no. 8, 1731--1753.


• The infimum in the metric Mahler measure, Canad. Math. Bull. 54 (2011), 739--747.


• On the non-Archimedean metric Mahler measure (with P. Fili), J. Number Theory 129 (2009), 1698--1708.


• Estimating heights using auxiliary functions, Acta Arith. 137 (2009), no. 3, 241--251.


• Auxiliary polynomials and height functions, Ph.D. Dissertation, The University of Texas at Austin (2007).


• The Weil height in terms of an auxiliary polynomial, Acta Arith. 128 (2007), no. 3, 209--221.


• Lower bounds on the projective heights of algebraic points, Acta Arith. 125 (2006), no. 1, 41--50.