Over the years I have greatly enjoyed the challenges and rewards of
teaching from the beginning undergraduate to
advanced graduate levels, and also of conveying the excitement and
relevance of mathematics beyond the confines
of academia to the interested public. A major project of mine during the years 1992
to 1994 was the introduction of high level computer
graphics into the first year calculus
classroom. When the Web came into being I transferred some of these to
a Graphics for the Calculus Classroom web
page, which is now listed in the list of
the 60 most frequently linked pages in the mathematical sciences. In
spring 1997, I developed some Graphics for
Complex Analysis as well. In 1996 I was also honored to receive the George W.
Atherton Award for Excellence in Teaching, Penn State's
highest level of recognition for undergraduate education.
Public outreach
I have given public lectures in various venues on various mathematical
topics. A lecture I gave on the mathematics of golf can be
seen here. My family
has also endowed an annual public lecture held at the IMA.
Course materials
Some of my course materials are available on the web. As a motivator for numerical
analysis students I have collected some examples of
real life disasters resulting from bad
numerics. I have extensive lecture notes on complex analysis and functional analysis at the level
of a first year graduate course.
Other materials is linked from various course home pages:
 Penn State MATH/CSE 455, senior level numerical analysis
 Penn State MATH 502, graduate level analysis
 Penn State MATH 597I, graduate level numerical analysis
 UMN MATH 8445, graduate level numerical PDE, 1st semester
 UMN MATH 8446, graduate level numerical PDE, 2nd semester
Ph.D. students
University of Maryland
My first Ph.D. student, Raymond Cheng received his
degree in 1987 with a
thesis entitled
DeltaTrigonometric and SplineTrigonometric Methods using the
SingleLayer Potential Representation. Ray went on to become a research team
leader in the Computational Mechanics Division of the Navy's David
Taylor Model Basin.
Patrick Noon received his Ph.D. in 1988. His thesis was entitled
The Single Layer Heat Potential and Galerkin Boundary Element
Methods for the Heat Equation. Pat
is currently Senior Software Support Engineer at AudioCodes USA.
Penn State University
Xiaobo
Liu received his degree in 1993. Xiaobo wrote his thesis
on
Interior Estimates for Some Nonconforming and Mixed Finite
Element Methods.
He is now a managing director
at Citibank.
Jinshui (Jason) Qin completed his degree in 1994
with a thesis
On the Convergence of Some Low Order Mixed Finite Elements
for Incompressible Fluids.
He currently works in software engineering and R&D for
telecommunications and financial services.
Changyi Chen graduated in 1995 with a thesis
entitled
Asymptotic convergence rates for the Kirchhoff
plate model. He
is currently on the faculty at College of Lake County.
Arup
Mukherjee completed Ph.D. in 1996 with a thesis
entitled An Adaptive Finite
Element Code for Elliptic Boundary Value Problems in three dimensions
with applications in Numerical Relativity.
Arup is now an associate professor at Montclair State University.
Alexandre
Madureira completed his Ph.D. in 1999 with a thesis entitled
Asymptotics
and Hierarchical Modeling of Thin Domains.
He is a researcher at the Laboratório Nacional de Computaçio Científica
(LNCC) in Brazil, where he has also served as
chair of the Department of Applied and Computational Mathematics.
Sheng Zhang completed his Ph.D. in 2001.
In his thesis, which is entitled A Linear Shell Theory Based on
Variational Principles, he studied a variational approach to
the derivation of dimensionally reduced models for elastic shells and
obtains rigorous convergence estimates and rates for them.
Sheng is associate professor at Wayne State University.
University of Minnesota
Nicolae Tarfulea completed his Ph.D. in 2004.
In his thesis entitled Constraint Preserving Boundary
Conditions for Hyperbolic Formulations of Einstein's Equations,
he studied wellposed boundary conditions which preserve given
differential constraints for first order symmetric hyperbolic evolutions
relevant to Einstein's equations in a 3+1 formulation.
Tarfulea is associate professor at Purdue
University Calumet.
Marie E. Rognes obtained her Ph.D. in 2008 from the University
of Oslo where her primary advisor was Ragnar Winther. A portion of her thesis
Mixed finite element methods with applications
to viscoelasticity and gels, was written with me at the University of Minnesota during 20072008.
Rognes is now a researcher at the Norwegian research laboratory Simula.
Hongtao Chen obtained his Ph.D. in 2011 from the Chinese Academy of Sciences
where his primary advisor was Lin Qun. His thesis was based on work carried out during 20102011
under my direction at University of Minnesota. Chen is now an assistant professor
at Xiamen University.
Jeonghun (John) Lee completed his Ph.D. in 2012 at the University
of Minnesota with a thesis entitled
Mixed methods with weak symmetry for time dependent problems of elasticity and viscoelasticity. Jeonghun took a postdoctoral
position at Aalto University in Helsinki.
