Applied Mathematics
Education
2000 Ph.D. Applied Mathematics, University of Washington
1992 M.S. Applied Mathematics, University of Washington
1988 M.S. Mathematics, University of Arizona
1986 B.A. Mathematics, University of Colorado in Boulder
Title of Dissertation
The Influence of Seasonal and Climatic Environmental Changes on Plankton
in the Marine Mixed Layer
Dissertation Topics
- Mixed-layer models of the upper ocean
- Plankton ecology
- Climate change
Summary
There have been five phases to my mathematical education and
experience. Most recently, I was a lead designer of software for
mathematically modeling prokaryotic organisms as networks of metabolic
reactions at a bioinformatics firm. While working on my dissertation,
I studied the effects of seasonal and climatic variations in
environmental factors on plankton populations in the marine mixed
layer using a periodically-forced nonlinear ordinary differential
equation model. Prior to my dissertation work, I studied boundary
layer meteorology and mixed-layer models of the troposphere and
contributed to the development of a large eddy simulation cloud model.
During a year at the University of Colorado in Denver and during my
first couple of years at the University of Washington, I studied
numerical analysis and performed research on preconditioned conjugate
gradient methods for solving the linear systems that arise from
discretizing elliptical partial differential equations. I began my
graduate career as a pure mathematics student at the University of
Arizona, studying abstract algebra, various types of analysis,
topology, and differential geometry.
Integrated Genomics, Inc. (2001)
One of two lead designers in a team of five people creating
software for mathematically modeling prokaryotic organisms as
networks of metabolic reactions and for developing and
maintaining the company's biochemical pathway collection. The
purposes of the modeling effort were to estimate the optimal
production rates of desired compounds in organisms, suggest
optimal growth media for organisms, and allow microbiologists to
explore the possible consequences of gene additions and
deletions within organisms.
Dissertation Work (1993 - 2000)
- Studied effects of seasonal and climatic changes in irradiance
and mixed-layer depth on plankton in the marine mixed layer using a
periodically-driven nonlinear ordinary differential equation model
of plankton and limiting nutrient in the mixed layer.
- Analyzed the model using dynamical systems theory and numerical
techniques.
- Created a tool that performs global analysis of arbitrary-dimension,
periodically-driven systems of ordinary differential equations using
simple cell mapping. Tool is operated through a GUI and provides
facilities for viewing slices of data sets along coordinate directions
and making movies of how the dynamics vary as parameters change or
along coordinate directions.
- Wrote software for constructing bifurcation diagrams for the system.
- Used continuation software to further investigate bifurcations and to
verify results from software I wrote.
- Utilized JGOFS data and climatologies to estimate parameters
and construct seasonal cycles.
Atmospheric Sciences (1990 - 1993)
- Wrote conjugate gradient and multigrid poisson solvers and code for
adaptively regridding solution domains for use in a large eddy simulation
numerical cloud model.
- Studied boundary layer thermodynamics and meteorology and mixed layer
models of the troposphere for use in assessing the impact of climatologically
important sulfur gasses that plankton produce.
Numerical Analysis (1988 - 1992)
- Studied the numerical solution of partial and ordinary differential
equations via finite difference, finite element, and multigrid methods,
numerical linear algebra, and approximation theory.
- Performed research on preconditioned conjugate gradient methods.
- Wrote code that solves the linear equations that arise from
discretization of elliptic partial differential equations using
the conjugate gradient method with a multigrid solver as a preconditioner.
Other Applied Mathematics Courses
Calculus of variations, perturbation theory, mathematical biology,
dynamical systems and chaos, complex analysis, ordinary differential
equations, partial differential equations, mathematical modelling,
probability.
Pure Mathematics (1986 - 1988)
- M.S. in Mathematics from the University of Arizona.
- Studied abstract algebra, complex analysis, real analysis, functional
analysis, differential geometry, and point-set and algebraic topology.
Related Skills
Scientific Software
MATLAB, Maple, gnuplot, xmgrace, plotmtv, Content, xfig, LaTeX, DISLIN,
GNU Plotutils, pic, eqn, PV-Wave, SPSS, Sigma Plot, xgobi, Framemaker
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Last modified: Wed Jul 3 09:41:53 CDT 2002