MATHEMATICAL BIOLOGY  |  Overview  |  Courses  |  Flier  |  Schedule  |  Journals  |  Journal Clubs  |  Faculty  |  Postdocs  
 
     

MATHEMATICAL BIOLOGY


Department of Applied Mathematics



University of Washington

Overview


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.

Courses


We teach a number of courses in mathematical biology including:



Undergraduate/Graduate:

Graduate:

AMATH 422/522

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.

Prerequisites:



Either a course in differential equations or permission of the instructor


Course Web Page (Winter 2013)

AMATH 423/523

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.

Prerequisites:



Either courses in differential equations and probability and statistics, or permission of the instructor


Course Web Page (Spring 2013)

AMATH 504

Mathematical Epidemiology

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.

Prerequisites:



AMATH 351 or equivalent

AMATH 531

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:



Either courses in dynamical systems, partial differential equations, and probability, or permission of the instructor


Course Web Page (Autumn 2012)

AMATH 532

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:



Either Amath 506 or permission of the instructor

AMATH 533

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.

Prerequisites:



Vector calculus, linear algebra, MATLAB, or permission of the instructor

AMATH 534

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.

Prerequisites:



Eithr CSE/NBB 528 or permission of the instructor

AMATH 535

Mathematical Ecology

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.

Prerequisites:



Either a course in differential equations or permission of the instructor


Course Web Page (Spring 2011)

AMATH 536

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.

Prerequisites:



Either a course in partial differential equations or permission of the instructor


Course Web Page (Spring 2014)

Flier


Here is a



course flier


to help you remember our courses.

Schedule


Schedule of Mathematical Biology Courses:



Academic Year:

2010-2011


Fall Winter Spring
Amath 422/522 Amath 423/523
Amath 531 Amath 533 Amath 535

2011-2012


Fall Winter Spring
Amath 422/522 Amath 423/523
Amath 532 Amath 534 Amath 536

2012-2013


Fall Winter Spring
Amath 422/522 Amath 423/523
Amath 531 Amath 533  

2013-2014


Fall Winter Spring
Amath 422/522 Amath 423/523
Amath 532 Amath 534 Amath 536

Journals




Some of the better known journals of mathematical biology include:



All journals are not created equal.
Please check the age, impact factor, editorial board, and
contents of each journal to get some sense of its worth.

Journal Clubs




Mathematical Biology



Mathematical Ecology


Theoretical Neuroscience

Biology



The Mathematical Biology Journal Club (MBJC) is a group of students and faculty in mathematics, biological and physical sciences, medicine, as well as engineering who are interested in the interface of biology, medical science, and mathematics. MBJC meets once a week and encourages participants to explore topics of common interest.

During autumn, 2013, MBJC will meet



Friday, from 11:00-12:00, in Lewis 208

Ecology



The Mathematical Ecology Journal Club (MEJC) is a group of students and faculty in applied mathematics, biology, and quantitative ecology and resource management who are interested in the mathematical aspects of ecology and resource management. MEJC meets once a week and encourages participants to explore topics of common interest.

During autumn, 2013, MEJC will meet



Tuesday, from 3:30-4:20 pm, in Lewis 208


(Please follow the link for registration information.)

This fall, the journal club will read through the new book

Post, E. 2013. Ecology of Climate Change: The Importance of Biotic Interactions. Princeton University Press.

The schedule for the quarter is:







Date Chapter Topic Moderators
10/1 P, 1 Recent Climate Change Cole Monnahan
10/8 2 Pleistocene Warming and Extinctions James Faulkner
10/15 3 Life History Variation and Phenology Alex Hornof
10/22 4 Population Dynamics and Stability Rosie Leung & Scott Rinnan
10/29 5 The Niche Concept Melissa Muradian & Chloe Bracis
11/5 6 Community Dynamics and Stability Brooke Davis & Brendan Zehnder
11/12 6 Community Dynamics and Stability Kiva Oken & Lowell Thomson
11/19 7 Biodiversity, Distributions, and Extinction Pamela Moriarty & Austin Phillips
11/26 8 Ecosystem Function and Dynamics Christine Stawitz & Laurel Ohm
12/2 8, 9, P Leftovers, Overflow, and Conclusions  



Neuroscience



The Theoretical Neuroscience Journal Club (TNJC) is a group of students and faculty in applied mathemaics, biology, and neurobiology who are interested in theoretical neurobiology. TNJC meets once a week, on



  • Tuesdays, from 9:30-10:20 am, in Lewis 208

and encourages participants to explore topics of common interest.

Faculty




Core Faculty



Adjunct Faculty


Temporary Faculty


Visiting Faculty

Core Faculty



Mark Kot



Hong Qian


Eric Shea-Brown


Emanuel Todorov

Adjunct Faculty



E. David Ford



Elizabeth Halloran

Temporary Faculty



Braden Brinkman



Joel Zylberberg


Visiting Faculty



Postdocs




Melanie Harsch