Warren College Faculty

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Michael Holst

Professor of Mathematics

I came to the UCSD Mathematics Department in summer 1998. Prior to arriving here, I was an Assistant Professor at UC Irvine during the 1997-1998 year, and from 1993-1997 I was a Prize Research Fellow and a von Karman Instructor of Applied Mathematics at the California Institute of Technology. To support my research work in applied mathematics at UCSD, I started writing grant proposals immediately after arriving (this challenging task is something I had managed to avoid until coming to UCSD). My first successful proposal was for a local UCSD Hellman Fellowship in 1998, followed by an NSF CAREER Award in 1999. I was promoted to tenured Associate Professor of Mathematics in 2000, and to Full Professor of Mathematics in 2003. I am currently involved in several interdisciplinary research projects and centers at UCSD, including the La Jolla Interfaces in Science Training Program (http://ljis.ucsd.edu), the Center for Theoretical Biological Physics (http://ctbp.ucsd.edu), the National Biomedical Computation Resource (http://nbcr.ucsd.edu), the Bioinformatics Ph.D. Program (http://bioinformatics.ucsd.edu), and the Computational and Applied Mathematics Research Group within the UCSD Mathematics Department (http://cam.ucsd.edu).

My general research background and interests are in a broad area called computational and applied mathematics; my specific research areas are partial differential equations (PDE), numerical analysis, approximation theory, applied analysis, and mathematical physics. My research projects center around developing mathematical techniques (theoretical techniques in PDE and approximation theory) and mathematical algorithms (numerical methods) for solving certain types of mathematical problems called nonlinear PDE. These types of problems arise in nearly every area of science and engineering; this is just a reflection of the fact that physical systems that we try to manipulate (e.g., the flow of air over an airplane wing, or the chemical behavior of a drug molecule), or build (e.g., the wing itself, or a semiconductor), or simply study (such as the global climate, or the gravitational field around a black hole) are described mathematically by nonlinear PDE. In simple cases, these problems can be simplified so that purely mathematical techniques can be used to solve them (in fact, the very techniques I teach in Math 20D), but in most cases we can only solve them using sophisticated mathematical algorithms designed for use with computers. Computational simulation of PDE is now critical to almost all of science and engineering; the mathematicians provide the mathematical tools and understanding so that scientists in physics, chemistry, biology, engineering, and other areas can confidently use the modern techniques of computational science in the pursuit of new understanding in their fields of study. To learn more about my particular research program, please see my webpage: http://cam.ucsd.edu/~mholst

Degrees/institutions:
    Ph.D., University of Illinois at Urbana-Champaign, 1993.
    M.S., University of Illinois at Urbana-Champaign, 1990.
    B.S., Colorado State University, 1987.

Courses:
    Math 273ABC   Scientific Computation
    Math 174   Numerical Methods in Science & Engineering
    Math 170C   Numerical Ordinary Differential Equations
    Math 20C   Introduction to Differential Equations