Benjamin Purkis
Assistant Professor of Mathematics
Benjamin Purkis is an assistant professor of mathematics, with a research focus in operator algebras and projective multiresolution analyses.
Dr. Purkis’s courses include a transition to calculus, calculus I and II, multivariable calculus, and differential equations, as well as an introduction to Java programming. He has also been a participant in the Oxford College Discovery Seminar program since its inception. His seminar, “The Origins of Mathematics,” focuses on problem solving in the history of mathematics.
He has presented at conferences such as the Great Plains Operator Theory Symposium and sectional meetings of the American Mathematical Society. He also delivered a presentation at the Erwin Schrödinger International Institute for Mathematical Physics in Vienna, Austria, as part of the Modern Methods of Time-Frequency Analysis workshop.
He received BA degrees in mathematics with honors and in computer science from Amherst College and an MA degree in mathematics from University of Colorado, Boulder. After receiving his PhD in mathematics from University of Colorado, Boulder, he taught at Rhodes College. He joined the faculty of Oxford College in 2015.
Education
BA| Amherst College| 2007
MA| University of Colorado, Boulder| 2010
Ph.D.| University of Colorado, Boulder| 2014
Courses Taught
Transition to Calculus
Calculus I
Calculus II
Multivariable Calculus
Differential Equations
The Origins of Mathematics
Introduction to Programming
Publications
“Projective Multiresolution Analyses over Irrational Rotation Algebras,” Contemporary Mathematics 603, 73-85, 2013
Presentations
“Projective Multiresolution Analyses over Irrational Rotation Algebras,” Great Plains Operator Theory Symposium, 2014
“Constructing a Projective Multiresolution Analysis for an Aα-module,” Modern Methods of Time-Frequency Analysis workshop, 2012
Research Interests
My main research interest lies in the construction of projective multiresolution analyses, particularly involving noncommutative C*-algebras. My doctoral work focused on the construction of such structures for Hilbert C*-modules over irrational rotation algebras, with both free and non-free initial modules. My current research is generalizing these constructions to more general noncommutative C*-algebras. I have also developed an interest in the scholarship of teaching and learning, specifically studying whether a problem-solving course in the history of mathematics changes student attitudes towards mathematics.