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

Strong software development, systems administration, web development, and instruction skills. See other sections for details.

Scientific Software

MATLAB, Maple, gnuplot, xmgrace, plotmtv, Content, xfig, LaTeX, DISLIN, GNU Plotutils, pic, eqn, PV-Wave, SPSS, Sigma Plot, xgobi, Framemaker

Last modified: Wed Jul 3 09:41:53 CDT 2002