Dr. Burton currently serves as the Director of Academic Effectiveness and as Associate Professor of Mathematics. He has served on the faculty at Franciscan University of Steubenville since 1997 and currently teaches mathematics courses at all levels. He has also occasionally taught courses in positional astronomy and celestial mechanics. His favorite courses to teach are the ones he’s teaching right now. He received his M.A. and his Ph.D. in Mathematics from Vanderbilt University. His doctoral dissertation was done under the direction of Daoxing Xia in the area of Operator Theory. He does mathematical research that starts in the classroom through his interaction with students. His 2009 paper “Quasi-Cauchy Sequences” (co-authored with Dr. John Coleman) was published in the American Mathematical Monthly and explored a common student “error” that results in interesting mathematics. His 2019 paper “Quasi-exponential Functions” (also co-authored with Coleman) is to appear in Mathematics Magazine and explores an aspect of exponential decay that is often mischaracterized by students and teachers alike. He also received a Bachelor of Science degree in Mathematics from the United States Naval Academy in 1981. He served as a nuclear submarine officer in the U.S. Navy from 1981 until 1989, where he qualified as Engineer for the S8G reactor plant on an Ohio-class SSBN. He also worked in the defense industry as an anti-submarine warfare analyst for two years.
Franciscan University of Steubenville: 1997-present. Associate Professor of Mathematics. Teach all levels of Mathematics. Developed the first course in Real Analysis, History of Mathematics, Euclidean and non-Euclidean Geometry, and Celestial Mechanics. Developed the first Hybrid (online and on-ground) course in the math department. Developed first team-taught course in math department (in Baseball Statistics) along with department chair. Department Chairman from 2001-2011. Promoted to Associate Professor in 2003. Director Student Learning Assessment from 2015-2018. Director of Academic Effectiveness 2018-present.
Vanderbilt University: 1992-1997. Graduate Teaching Scholar. Taught Calculus at all levels in the Engineering and non-Engineering sequence. Twice taught senior level partial differential equations course.
The Learning Lab: Brentwood, Tennessee, 1992-1996. Tutored over 100 hours in Junior High through College level mathematics.
The Learning Center: Vanderbilt University, 1995-1996. Weekly group tutoring sessions in Calculus.
Information Spectrum, Inc., Naples, Italy. 1989-1992. Worked under contract to U.S. Navy providing anti-submarine warfare analysis products. Made extensive use of mathematical models and probability theory.
Staff Naval Officer, Submarine Group 8, Naples, Italy. 1986-1989. Worked on the staff of a two-star Admiral planning submarine operations and arranging diplomatic clearance for politically sensitive nuclear submarine port visits. Awarded a second Navy Achievement Medal by the Secretary of the Navy.
Main Propulsion Assistant, USS Nevada, Groton, Connecticut. 1984-1986. Supervised the testing and maintenance of all propulsion plant mechanical systems of the advanced design Trident nuclear submarine reactor plant. Awarded a Navy Achievement Medal by the Secretary of the Navy. Qualified as Engineer while on board.
Junior Officer, USS Greenling, Groton, Connecticut. 1982-1984. Served as Communications Officer working with top secret cryptography gear and as Reactor Controls Assistant working with electronic instrumentation systems.
General: Operator Theory, Celestial Mechanics
Joint-hyponormality of linear operators.
Analytic models of hyponormal operators on Hilbert space.
On Hyponormal Tuples of Commuting Operators with Finite Rank Self-Commutators. Doctoral Dissertation. UMI 1997.
David Burton and John Coleman, “Quasi-Cauchy Sequences,” American Mathematical Monthly, Vol. 117, No. 4, April 2010, pp. 328-333.
David Burton and John Coleman, “Quasi-Exponential Growth and Decay” accepted by referees for publication (pending revisions) by Mathematics Magazine.