D. P. Dwiggins, PhD


Department of Mathematical Sciences

The University of Memphis

Memphis TN 38152




Curriculum Vitae

Bachelor of Science, Physics, Southwestern at Memphis, 1980

Master of Science, Mathematics, Memphis State University, 1984

Doctor of Philosophy, Mathematics, Southern Illinois University, 1993

Dissertation: Fixed Point Theory and Periodic Solutions for Differential Equations

Major Professor: T. A. Burton



Ø             "Uniqueness without Continuous Dependence," Equadiff 6 (Brno, 1985)

Lecture Notes in Mathematics 1192, pages 115-121 (with T. A. Burton)

Ø             "An Asymptotic Fixed Point Theorem for a Locally Convex Space" (1988)

Proceedings of the American Mathematical Society 103 (1), pages 247-251

(with T. A. Burton)

Ø             "Periodic Solutions of Functional Differential Equations with Infinite Delay"

(1989) Journal of the London Mathematical Society 40 (2), pages 81-88

(with T. A. Burton and Y. Feng)

Ø             “A new, reliable, and simple-to-use method for the anlaysis of a population of values of a random variable using the Weibull probability distribution: Application to acrylic bone cement fatigue results” (2005), Bio-Medical Materials and Engineering 15 (5), pages 349-355 (with S. Janna and G. Lewis)


Employment History

  • Instructor, Department of Mathematical Sciences
    • Memphis State University, 1989-94
  • Research Associate, Center for Earthquake Research and Information
    • The University of Memphis, 1994-97
  • Odd Jobs, Honing Computer Skills, 1997-99
  • Systems Support, Office of Admissions
    • The University of Memphis, 1999-2006
  • Instructor, Department of Mathematical Sciences
    • The University of Memphis, 2006-Present


  Teaching Qualifications


  • Five years experience teaching high school math, chemistry, and physics (Memphis University School and Immaculate Conception High School for Girls).
  • Fifteen years experience teaching at the collegiate level, both as a graduate assistant and as a faculty member.  While working as an instructor in the Department of Mathematical Sciences at Memphis State University, I served as course coordinator for both the Concepts courses and first-year Calculus.  One of my duties then was serving on a faculty committee charged with creating a concentration for math majors intending on a career in math education.  One contribution to this cause was the creation of a new course in College Geometry, still being taught by the department.
  • One year experience as an adjunct graduate faculty member (current appointment is through 2010).


Other Contributions to the University


  • Installed and maintained EDI (electronic transcript data interchange) system for Admissions office, 2002-2005
  • Created and maintained new website for Admissions office, including electronic magazine for new freshmen
  • Helped inaugurate the Summer Math Academy for the Recruitment office, 2007-2008
  • Helped organize Teachers Excellence Workshop, June 2008
  • Pre-semester (August) Math Bootcamp, 2006, 2008
  • MemphiSTEM Committee, including website creation, 2008-2009
  • Fresh Connections instructor, 2006-2008
  • Undergraduate Curriculum Committee, 2008-2009


 Summary of Research Interests


         During my time spent working with T. A. Burton, we were trying to find ways to extend results from Fixed Point Theory which were known to work in a Banach space to a space without the structure of the norm.  As I neared completion of my dissertation, I discovered that many of the results which had been used for years (such as Schauder’s Theorem, published in 1935) did not actually require a normed space, and that a weaker structure, namely a Frechet space, would suffice.  I have since then worked off and on trying to find other theorems which could be extended from a Banach space to a Frechet space, such as Nussbaum’s Asymptotic Fixed Point Theory from the 1970’s.

         In trying to sort out the technicalities, I have needed to use techniques from not only functional analysis but also topology and a bit of degree theory.  When trying to collate ideas from different areas of mathematics, it became apparent there was not always an agreed-upon consensus of certain ideas.  For example, I found six totally different definitions of what a Frechet space should be, and I attempted to unify most of these in a talk I gave at a conference in Chicago, called “What is a Frechet space?”  This talk (at which I was very nervous, since I followed Constantine Corduneanu) may be considered as the pinnacle of my career in pure mathematical research, because by that time I had started a new career in scientific research.

         During the past twelve years the most call I have had for my mathematical expertise has been in the area of statistics, and in particular regression analysis.  While at the Center for Earthquake Research and Information, I developed a new method of linear regression (Orthogonal L1 Regression) in order to better define the equations used to calculate earthquake magnitudes based on the lengths of seismic signatures.  To my knowledge this is still original research needing to be published.  My most recent publication was another application of regression analysis, this time to a bio-medical engineering problem, part of the doctoral dissertation for one of my former calculus students.

         Other than this statistical aside, my main interests lie in applied analysis, and I recently returned as a contributing member of the Analysis Seminar in the Department of Mathematical Sciences at The University of Memphis. In Spring 2009 Dr. Burton will be on campus as a visiting professor, and I will be studying the topic of Integral Equations with him, in particular the application of Fixed Point Theory to the existence and stability of solutions of integral equations, as well as the existence of periodic or asymptotically periodic solutions.