Course Materials for MATH35032, Mathematical Biology
New lecturer in 201819
The examples of lecture notes, problem sets and exams that appear
below come from the period 20162018, but a new lecturer,
Prof. Oliver Jensen,
will be teaching Mathematical Biology starting in 201819 and he is likely to revise
the course.
Lecture Notes and Articles
The first 56 weeks of the term will be devoted to what one might describe
as mathematical biology in the classical style and the lectures will
follow sections of Jim Murray's famous text, Mathematical Biology I: An Introduction. This book is available
online, though only from within
the University's network (e.g. in the
campus clusters or in the halls), but
if you want to access it from off campus, you can install software that will
allow you to use all the Library's services via the
University's excellent Virtual Private Network (VPN).
The notes below are examples of the kind of material the course has covered in recent years, but
Prof. Jensen is likely to make changes of both content and emphasis.
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Opportunities for feedback
The main channel for formal, written feedback in this module is the coursework. It will be a problem set similar
to the ones provided below, but devoted to a novel application that uses the ideas from the course. You'll prepare written solutions
and I'll mark them over the Easter Break, providing both written comments and a mark. In addition, the weekly examples classes
provide further opportunities for verbal feedback and—for students who bring written solutions to the
exercises—onthespot marking and written feedback as well.
Problem Sets & Solutions
The problems below are intended as a guide for students considering taking the course in 201819 though, once again,
Prof. Jensen may change the course.

Problems


Solutions

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Coursework & Exams
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Intended Learning Outcomes
Once you've successfully completed this module you should be able to:

Interpret differential equation models for populations,
relating the expressions appearing in the model to processes
that affect the population.

Formulate and analyse ordinary differential equation (ODE)
models for the population of a single species, finding
equilibrium populations and determining how their stability
depends on parameters.

Analyse delaydifferential equation (DDE) models for the
population of a single species and use linear stability
analysis to determine which values of the parameters induce
oscillatory instabilities.

Analyse ODE models for the populations of two interacting
species, finding equilibria and using information about their
linear stability to characterise the longterm behaviour of
the system.

Define a conserved quantity for a system of ODEs
and, where possible, use such quantities to determine the
longterm behaviour of both twospecies ODE models and
singlespecies models population models include diffusion.

Construct the ODEs associated with a system of chemical
reactions subject to massaction kinetics and analyse them to
discover conserved quantities.

Construct the Markov process associated with a system of
chemical reactions and, for small numbers of reactions,
analyse it to determine the longterm behaviour of the system.

Analyse two key models, Wolpert's Frech flag model
and Turing's reactiondiffusion model, relating the
solutions of the associated PDEs to the processes of
patternformation in developing organisms.

Explain the notion of a motif in a genetic
regulatory network and, for small examples, compute the
probability of seeing k instances of a given motif
in a randomlyassembled network.

Reading Matter
A hyperlinked version of the lists below is available from Manchester University
Library's Link2Lists system.
I studied the following—more or less mathematicallyminded—books while preparing this course.

James D. Murray,
Mathematical Biology I: An Introduction 3rd edition, (Springer, 2002). ISBN 0387952233

James D. Murray,
Mathematical Biology II: Spatial Models and Biomedical Applications 3rd edition, (Springer, 2002). ISBN 0387952284

Lee A. Segel,
Modeling dynamic phenomena in molecular and cellular biology (Cambridge University Press, 1984). ISBN 052127477X

Edda Klipp, Wolfram Liebermeister, Christoph Wierling, Axel Kowald, Hans Lehrach, Ralf Herwig (2009),
Systems Biology: A Textbook, WileyBlackwell. ISBN 9783527318742

Uri Alon,
An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall/CRC, 2007). ISBN 1584886420

Darren J. Wilkinson,
Stochastic Modelling for Systems Biology (Chapman & Hall/CRC, 2006). ISBN 1584885408

I also looked at the books below for biological background.

Bernhard Ø. Palsson,
Systems Biology: Properties of Reconstructed Networks (Cambridge University Press, 2006). ISBN 0521859034

Eric H. Davidson,
The Regulatory Genome (Academic Press, 2006). ISBN 0120885638

Terry A. Brown,
Genomes 3 (Garland Science, 2007). ISBN 0815341385
The previous edition, Genomes 2, is available online from the National Center for Biotechnology Information (NCBI)
Bookshelf, a service of the U.S.A's National Institutes of Health (NIH).

Bruce Alberts, Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts and Peter Walter,
Molecular Biology of the Cell 4th edition, (Garland Science, 2002). ISBN 0815340729

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