University of Washington
Mathematical biology is a large and well-established branch of applied mathematics. The size of the field reflects both the importance of the biological and biomedical sciences and an appreciation for the mathematical subtleties and challenges that arise in modelling complex biological systems. Our interest, as a group, lies in understanding the spatial and temporal patterns that arise in dynamic biological systems and in understanding how these patterns affect biological function. Our mathematical activities range from nonlinear and chaotic dynamics, to reaction-diffusion equations, to optimization. We employ a variety of tools and models to study problems that arise in biomechanics, cell biology, development, ecology, epidemiology, neuroscience, and resource management. We maintain collaborations with a large number and variety of biologists and with biological and biomedical departments both here and elsewhere.
We teach a number of courses in mathematical biology including:
Computational Modeling of Biological Systems
Fundamental models that arise in biology and their analysis through modern scientific computing. Discrete and continuous-time dynamics, in deterministic and stochastic settings, with applications from molecular biology to neuroscience to population dynamics. Statistical analysis of experimental data. MATLAB or R programming taught from scratch.
Prerequisite: working knowledge of calculus.
Mathematical Analysis in Biology and Medicine
This course focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications are drawn from many branches of biology and medicine. Students will gain experience in applying differential equations, difference equations, and dynamical systems theory to biological problems.
Prerequisite: Background equivalent to AMATH 351, AMATH 422, or Math 307
Focuses on the construction and analysis of mathematical models for infectious disease transmission and control. Emphasizes evaluation and comparison of vaccination programs. Applications are presented for a variety of diseases such as measles, rubella, smallpox, rabies, etc.
Prerequisite: AMATH 351 or equivalent.
Mathematical Theory of Cellular Dynamics
Biological cells are biochemical systems that obey the laws of physics. This course develops a coherent mathematical theory for processes inside living cells. It focuses on analyzing dynamics leading to functions of cellular components (gene regulation, signaling biochemistry, metabolic networks, cytoskeletal biomechanics, epigenetic inheritance) using deterministic and stochastic models.
Prerequisites: 402 and 403 and working knowledge of probabilityAutumn 2010 Course Web Page
Mathematics of Genome Analysis and Molecular Modeling
Genome analysis, i.e., bioinformatics, and molecular modeling in terms of molecular dynamics (MD) and Brownian dynamics are now fast growing areas of applied mathematics in molecular biology. This course introduces the fundamentals of these approaches in terms of discrete probability, classical mechanics, theory of diffusion, and Monte Carlo simulations.
Prerequisites: 506 or 572, or with permission from the instructor
Neural Control of Movement
This class provides a comprehensive view of how the brain controls movement. It brings together elements of biomechanics and muscle physiology, neuroanatomy and neurophysiology of the motor system, sensorimotor psychophysics and kinesiology, and movement disorders. Empirical data are interpreted in the context of control-theoretic models whenever possible.
Dynamics of Neurons and Networks
Mathematical analysis and computational modeling on three interconnected scales \(em neurons, networks, and populations \(em including (1) oscillations and synchrony, (2) role of network structure and symmetry, (3) statistical mechanics tools for large-scale models, (4) bifurcation and reduction methods for biophysical models. Emphasizes links between system dynamics and signal processing.
Prerequisite: CSE/NBB 528, or knowledge of differential equations and probability at similar level.
This course considers models, methods, and issues in population ecology. Topics include the effects of density dependence, delays, demographic stochasticity, and age structure on population growth; population interactions (predation, competition, and mutualism); and applications of optimal control theory to the management of renewable resources.
Prerequisite: AMATH 402 or AMATH 423 or permission of the instructorSpring 2011 Course Web Page
Spatial Models in Ecology and Epidemiology
This course considers models for the growth and dispersal of biological populations. Topics include population persistence, climate-induced range shifts, and rates of spread of invading organisms. We will consider reaction-diffusion equations, integrodifference equations, branching random walks, and other relevant classes of models.
Prerequisite: AMATH 403 or permission of the instructorSpring 2012 Course Web Page
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Schedule of Mathematical Biology Courses:
The Mathematical Biology Journal Club (MBJC) consists a group of students and faculty members in mathematics, biological and physical sciences, medicine, as well as engineering who are interested in the interface of biology and medical science and mathematics. MBJC meets once a week in an informal atmosphere and encourages participants to explore and develop various topics of common interest.
Andrea Barreiro Mark Kot Hong Qian Eric Shea-Brown Emanuel Todorov
E. David Ford Elizaebeth Halloran Ira Longini Suresh Moolgavkar Kristin Swanson