About this Title
Mark A. Lewis, University of Alberta, Edmonton, AB, Canada, Mark A. J. Chaplain, University of Dundee, Dundee, Scotland, James P. Keener, University of Utah, Salt Lake City, UT and Philip K. Maini, University of Oxford, Oxford, England, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2009; Volume 14
ISBN: 978-0-8218-4765-7 (print)
MathSciNet review: MR2490559
MSC: Primary 92-06; Secondary 34C60, 35Q92, 37N25, 92-01, 92-02
This volume is not part of this online collection.
Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present lectures on a major area of mathematics. A unifying theme of the mathematical biology courses presented here is that the study of biology involves dynamical systems. Introductory chapters by Jim Keener and Mark Lewis describe the biological dynamics of reactions and of spatial processes.
Each remaining chapter stands alone, as a snapshot of in-depth research within a sub-area of mathematical biology. Jim Cushing writes about the role of nonlinear dynamical systems in understanding complex dynamics of insect populations. Epidemiology, and the interplay of data and differential equations, is the subject of David Earn's chapter on dynamic diseases. Topological methods for understanding dynamical systems are the focus of the chapter by Leon Glass on perturbed biological oscillators. Helen Byrne introduces the reader to cancer modeling and shows how mathematics can describe and predict complex movement patterns of tumors and cells. In the final chapter, Paul Bressloff couples nonlinear dynamics to nonlocal oscillations, to provide insight to the form and function of the brain.
The book provides a state-of-the-art picture of some current research in mathematical biology. Our hope is that the excitement and richness of the topics covered here will encourage readers to explore further in mathematical biology, pursuing these topics and others on their own.
The level is appropriate for graduate students and research scientists. Each chapter is based on a series of lectures given by a leading researcher and develops methods and theory of mathematical biology from first principles. Exercises are included for those who wish to delve further into the material.
Graduate students and research mathematicians interested in mathematical biology.
Table of Contents
- Introduction to dynamics of biological systems
- Spatial dynamics in ecology
- Matrix models and population dynamics
- Mathematical epidemiology of infectious diseases
- Topological approaches to biological dynamics
- Mathematical modelling of solid tumour growth: from avascular to vascular, via angiogenesis
- Lectures in mathematical neuroscience