DURHAM UNIVERSITYBiophysical Sciences Institute

Department of Mathematical Sciences

MSc in BIOMATHEMATICS

2011-2012

Science LaboratoriesSouth RoadDurham Email: maths.office@durham.ac.ukDH1 3LE Web: www.maths.dur.ac.uk

Contents

1 Introduction 6

2 The MSc in Biomathematics Degree 7

2.1 The general structure of the degree . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Detailed content of the taught modules . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Biological Physics I - MAGIC/DURHAM (15 lectures) . . . . . . . . . . . 9

2.2.2 Computational Mechanics (18 lectures) . . . . . . . . . . . . . . . . . . . 9

2.2.3 Representation theory of finite groups (20 lectures) . . . . . . . . . . . . . 10

2.2.4 Modeling of Macrobiomolecule Dynamics (15 lectures) . . . . . . . . . . 10

2.2.5 Quantum Mechanics for Biomaterials (15 lectures) . . . . . . . . . . . . . 10

2.2.6 Systems Biology and Bayesian Inference (15 lectures) . . . . . . . . . . . 10

2.2.7 Biological Physics II -MAGIC/DURHAM (15 lectures) . . . . . . . . . . 11

2.2.8 Communicating Science (10 contact hours) . . . . . . . . . . . . . . . . . 11

2.2.9 Introduction to Protein Crystallography (15 lectures) . . . . . . . . . . . . 11

2.2.10 Mathematical Virology (18 lectures) . . . . . . . . . . . . . . . . . . . . 12

2.2.11 Soft-condensed Matter inspired Biology (16 lectures) . . . . . . . . . . . 12

2.2.12 Regulatory Networks in Biology (15 lectures) . . . . . . . . . . . . . . . 13

2.2.13 *Bayesian Statistics (38 lectures) Lectures as for MATH3341 . . . . . . . . 14

2.2.14 **Topics in Statistics (38 lectures) Lectures as for MATH3361 . . . . . . . 14

2.2.15 *Continuum Mechanics (38 lectures) Lectures as for MATH4081 . . . . . 15

2.2.16 **Solitons (38 lectures) Lectures as for MATH4121 . . . . . . . . . . . . . 16

2.2.17 Dynamical Systems (38 lectures) Lectures as for MATH3091 . . . . . . . 17

2.2.18 Mathematical Biology (38 lectures) Lectures as for MATH3171 . . . . . . 17

2.2.19 Partial Differential Equations (38 lectures) Lectures as for MATH3291 . . 18

2.2.20 Statistical Methods (38 lectures) Lectures as for MATH3051 . . . . . . . . 19

2.2.21 *Stochastic Processes (38 lectures) Lectures as for MATH4091 . . . . . . 19

2.2.22 **Probability (38 lectures) Lectures as for MATH4131 . . . . . . . . . . . 20

2.3 The Dissertation module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Aims of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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2.3.2 Choosing a topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.3 Details of how dissertation period is to be supervised . . . . . . . . . . . . 27

2.3.4 Work back-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.5 Length of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.6 Style and format for the dissertation . . . . . . . . . . . . . . . . . . . . . 27

2.3.7 Assertion of authorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.8 Plagiarism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.9 Handing in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Research Environment 28

4 Examinations and Assessment 31

4.1 Regulations for the taught MSc . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 University assessment process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Board of Examiners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Generalities on summative assessment of the MSc in Biomathematics modules . . 32

4.5 Passing the course, distinction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.6 Assessment criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.6.1 Assessment of double modules (Core Biomathematics I, Core Biomathe-matics II and Biomathematics III) . . . . . . . . . . . . . . . . . . . . . . 33

4.6.2 Assessment of the dissertation module (Dissertation) . . . . . . . . . . . . 35

4.7 Formative continuous assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.8 Calculators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.9 Plagiarism, cheating and collusion . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.10 Illness and Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.11 Award of degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Further Learning and Teaching details 39

5.1 Sources of advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Private study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.3 Set work, handing in and help . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.4 Computers, ICT and DUO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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5.5 Timetabling and other information . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.6 Staff-Student consultation and feedback . . . . . . . . . . . . . . . . . . . . . . . 41

5.7 Absence and illness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.8 Students with special needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6 Practicalities 42

6.1 Getting started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.2 Useful contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.3 The University Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.4 Computing facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.5 Smoking and Mobile Phones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

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1 Introduction

Welcome to the taught MSc in Biomathematics! The aim of the course is to bring you in twelvemonths to a position where you can start with confidence on a wide range of careers at the inter-face between Mathematics and Biology, including a PhD in an interdisciplinary area within theBiophysical Sciences Institute1. You can look forward to an enjoyable year.

The Biophysical Sciences Institute (BSI) was established in June 2007, with the assistance of aleadership gift from the Wolfson Foundation. It is an exciting new initiative that brings togetherresearch excellence and expertise from across all of the Departments in Durham University’s Sci-ence Faculty.

A characteristic of the BSI, that distinguishes it from similar activities elsewhere, is to use exper-iment, theory and simulation in a completely integrated, multi-scale approach to the solution ofbiological problems. Through collaborative research the BSI seeks to increase understanding ofbiological processes such as stress, ageing and signalling mechanisms, and dynamics within thecell. Such research will in turn lead to the development of new enabling technologies.

The BSI is a vibrant interdisciplinary community that sits at the heart of research excellence inbiophysical sciences. It is dedicated to providing scientific discoveries and technological break-throughs for application in further research, medicine and biotechnology and will drive futurewealth creation, as well as industrial and social development.

The creation of the BSI in Durham underpins a new approach to research in the life sciences,where the traditional academic distinctions between physicists, chemists, biologists, engineers andmathematicians are becoming increasingly irrelevant, and where significant progress is expectedfrom learning from one another.

Mathematics plays a privileged and essential role in this new venture. It provides a frameworkwithin which one attempts to organise the plethora of data biologists are now able to collect, thanksto the nanotechnology revolution. It underlies the construction of a new generation of models,where ideas from physics and chemistry are incorporated in order to describe many biologicalprocesses in a way that predictions can be made. By embarking on this MSc in Biomathematics,you join a new generation of mathematicians, physicists, chemists and engineers who are willingto broaden their scientific horizons in order to provide an expertise sought after by biologists anda wide range of biomedical industries.

This booklet contains information specific to the MSc in Biomathematics. For information con-cerning general University regulations, examination procedures etc. you should consult the FacultyHandbooks and the University Calendar, which provide the definitive versions of University policy.

If at any time you would like to discuss aspects of your course, or if there are any questions aboutthe Department which this booklet leaves unanswered, please contact the MSc Course Director(Prof. Anne Taormina, Room CM 302) or your Supervisor. Much information about the Depart-ment may be found on the web starting from the Mathematical Sciences Department Homepage athttp://www.dur.ac.uk/mathematical.sciences.

1http://www.dur.ac.uk/biophysical.sciences

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2 The MSc in Biomathematics Degree

This is a full-year degree course, starting early October and finishing in the middle of the subse-quent September.

Its aim is to ensure students from physical sciences, mathematics and engineering acquire the coreof knowledge essential to work at the life sciences interface.

2.1 The general structure of the degree

The degree consists of three 40 credit-MSc modules, and one 60-credit module consisting of adissertation to be written over the Easter term and Summer. Two of the double modules (CoreBiomathematics I and II) consist of tailor-made courses. One module is taught in Michaelmas andthe other in Epiphany. The third double module consists of two undergraduate courses taught byextraction, at level 3 or 4, chosen from a list of 7 as detailed later. The structure is illustrated in thefigure below, with the prerequisites represented by arrows.

Biomathematics III

Biomathematics I

Core Core

Biomathematics I Biomathematics II

40 credits 40 credits

40 credits

60 credits

Dissertation

Figure 1: Structure of the MSc in Biomathematics, with arrows indicating the prerequisites.

2.2 Detailed content of the taught modules

The next page summarizes the content of the three 40-credit taught modules, and how the teachingis spread over Michaelmas (Term 1) and Epiphany (Term 2). This description is followed, in thesubsequent pages, by a detailed syllabus for all tailor-made and extraction units within the threemodules.

All units in Core Biomathematics I and Core Biomathematics II are compulsory, while Biomathe-matics III consists of two optional units of 20 credits each, chosen from a list of seven undergrad-uate modules in each academic year. It will not be possible to choose a unit which covers materialidentical or similar to an undergraduate module you have taken as part of your undergraduatestudies. Your choices are subject to approval by the MSc Course Director.

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8

The syllabuses below are intended as guides to the modules. No guarantee is given that additionalmaterial will not be included and examined nor that all topics mentioned will be treated.

Core Biomathematics IAll units in Core Biomathematics I are tailor-made, except for the first ten lectures of Computa-tional Mechanics, which are taught by extraction from the undergraduate School of Engineeringprogramme. The lectures will be generally two a week during Michaelmas, but some units mightbe taught according to a more flexible timetable.

Some units are given by members of the Mathematical Sciences department as part of Durham’scontribution to MAGIC, an interactive distance mathematics learning consortium of 18 universi-ties. Details of all the MAGIC courses may be found athttp://www.maths.dept.shef.ac.uk/magic/courses.php.

2.2.1 Biological Physics I - MAGIC/DURHAM (15 lectures)

Aim: to introduce students with a background in mathematics and elementary physics to the worldof cells.

Content: Biological order. Key ideas from physics and chemistry. A lightning tour of the cell.Boltzmann distribution, Arrhenius rate law and origin of friction. Brownian motion. Biologicalapplications of diffusion and dissipation. Why bacteria do not swim like fish.

Recommended bookP. Nelson, Biological Physics, W.H. Freeman & Co, New York (2008), ISBN 9780716798972

2.2.2 Computational Mechanics (18 lectures)

Aim: To introduce students to the theoretical framework underpinning the Finite Element Methodand algorithmic strategies associated with its use. The lectures will focus on the 3D nonlineardeformation of solids (from soft tissue to ceramics and metals).

Content: Balance laws, development of the Galerkin Weighted Residual approach, hexahedralFinite Elements, Gaussian integration schemes, direct and iterative linear solvers, inelasticity, ap-plication of the Newton-Raphson method, instability issues, large-scale Finite Element programs.

Recommended booksBeletschko, Liu and Moran, Nonlinear Finite Elements for Continua and Structures, JohnWiley (2000); ISBN 0471987735.Bonet and Wood, Nonlinear Continuum Mechnaics for Finite Element Analysis, CUP (1997),ISBN 052157272 X.Ottosen and Petersson,Introduction to the Finite Element Method, Prentice Hall (1992), ISBN0134738772.

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2.2.3 Representation theory of finite groups (20 lectures)

Aim: To develop and illustrate the representation theory and that of complex characters of finitegroups.

Content: Representation theory is one of the central areas in mathematics with, in particular, ap-plications in biochemistry (e.g. crystallography). The representation theory of finite groups willinvolve the computation of group characters, an excellent prelude to the Mathematical Virologycourse taught in the second term.

Recommended booksJ-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, ISBN 0387901906W. Fulton and J. Harris, Representation Theory. A First Course, Springer-Verlag, ISBN 0387974954.

2.2.4 Modeling of Macrobiomolecule Dynamics (15 lectures)

Aim: To provide students with an overview of the cellular scaffolding from a biologist’s perspec-tive, and a mathematical modeling of its dynamics.

Content: Introduction to the cytoskeleton dynamics. Derivation of a thermodynamical model ofthe microtubule dynamics and analytical study of some solutions of a simplified version of themodel. Mechanical properties of the microtubules, and actin filaments.

Recommended booksNone, but several research papers to be determined in due course.

2.2.5 Quantum Mechanics for Biomaterials (15 lectures)

Aim: To provide the students with a working knowledge of modeling biomaterials at the atomiclevel using first principles electronic structure techniques. The course will be a mixture of lectureson the theory and methods of modeling materials from an electronic structure point of view andpractical sessions where the techniques will be put into practice.

Content: The many electron problem, density functional theory, Bloch’s theorem, basis sets, pseu-dopotentials, exchange-correlation interactions, computer modeling.

Recommended bookR.M. Martin, Electronic Structure Basic Theory and Practical Methods: Basic Theory andPractical Density Functional Approaches, CUP (April 2004); ISBN-10: 0521782856, ISBN-13:9780521782852.

2.2.6 Systems Biology and Bayesian Inference (15 lectures)

Aim: To provide students with an introduction to Bayesian Statistical Methodology and its appli-cation to stochastic models in Systems Biology.

Content: Bayesian Paradigm, conditional independence and conjugacy, Bayesian inference andMarkov Chain Monte Carlo. Systems Biology reaction networks, biochemical kinetics, stochastic

10

simulation of networks. The diffusion approximation and Bayesian Inference for rate parametersin stochastic kinetic models.

Recommended book:D. J. Wilkinson, Stochastic Modeling for Systems Biology, Chapman & Hall/CRC (2006); ISBN-10 1584885408 and ISBN-13 9781584885405.

Core Biomathematics IIAll units in Core Biomathematics II are tailor-made. The lectures will be generally two a weekduring Epiphany, but some units might be taught according to a more flexible timetable.

Some units are given by members of the Mathematical Sciences department and a member of theMathematics and Biology Departments at York University as part of Durham and York’s contri-butions to MAGIC, an interactive distance mathematics learning consortium of 18 universities.Details of all the MAGIC courses may be found athttp://www.maths.dept.shef.ac.uk/magic/courses.php.

2.2.7 Biological Physics II -MAGIC/DURHAM (15 lectures)

Aim: to introduce students with a background in mathematics and elementary physics to the con-ceptual ideas underlying nanotechnology and the field of soft materials.

Content: Cooperative transitions in macromolecules. Allosteric transitions in single macromolecules.Enzyme and molecular machines. Ion pumps and ATP synthase. Nerve impulses.

Recommended bookP. Nelson, Biological Physics, W.H. Freeman & Co, New York (2008), ISBN 9780716798972

2.2.8 Communicating Science (10 contact hours)

Aim: acquisition of skills relevant for the presentation of a poster, a seminar and a written scientificdissertation (Latex, powerpoint, computer graphics).

Content: Each student will be given six weeks to prepare a poster and a 15-minute presentation ona topic relevant to one aspect of mathematical biology. They will deliver the talk in front of theirpeers and at least two members of staff, and a poster session will be organized as a BSI event inthe Easter term.

2.2.9 Introduction to Protein Crystallography (15 lectures)

Aim: to provide a thorough understanding of the fundamental concepts and experimental methodsof protein crystallography. The course aims at students who are interested in structural biology andmacromolecular crystallography, and will be useful if they wish to continue their (research) careerin a wide variety of disciplines, not only in macromolecular crystallography but also in relatedareas including NMR, electron microscopy and biomolecular modeling.

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Content: Theory and practice of X-ray crystallography with an emphasis on structure determi-nation of biological macromolecules. Crystals and symmetry. Diffraction. X-ray physics. Phaseproblems. Molecular replacement. Multiple isomorphous replacement. Multiple anomalous diffrac-tion. Refinement and interpretation. Introduction to protein structure. Websources.

Recommended booksC. Branden and J. Tooze, Introduction to protein structure, Garland (1999); ISBN 10: 0815323050J. Drenth, Principles of protein X-ray crystallography, Springer (2006); ISBN 038794091XG. Giaccovazzo, H.L.Monaco, G. Artioli, D. Viterbo, G. Ferraris, G. Gilli, G. Zanotti & M. Catti,Fundamentals of crystallography, OUP (2002); ISBN13: 9780198509585

The first book (Branden & Tooze) is an excellent introduction to protein structure and function.Great examples of structure-function relationships, beautiful hand-coloured protein structure im-ages. The second book (Drenth) is for you if you have practiced crystallography but are unsureof the mathematical background. The third (Giacovazzo et al) is probably the best comprehensiveand consistent treatise of general and macromolecular crystallography available today. If you likemaths, this text is for you.

2.2.10 Mathematical Virology (18 lectures)

Aim: To introduce students to the power of group theory in modeling viral protein shells and moregeneral protein architectures with a degree of symmetry.

Content: Caspar-Klug classification of viral capsids and its limitations. Penrose tilings and viraltiling theory. Normal modes of vibrations of symmetrical protein structures. Spherical crystallog-raphy and viruses.

Recommended booksJ.E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Math-ematics, 29, CUP (1990); ISBN 0521436133J. Cornwell, Group Theory in Physics, Elsevier Science & Technology Book (1986); ISBN-13:9780121898038.S. Sternberg, Group Theory and Physics, CUP (1994); ISBN 0521558859.F.A. Cotton, Chemical Applications of Group Theory, Wiley (1963); ISBN-13: 9780471510949.Various selected research papers.

2.2.11 Soft-condensed Matter inspired Biology (16 lectures)

Aim: To introduce students to the theoretical methods used to understand equilibrium and outof equilibrium physics of soft and fragile matter in the context of Biology. The course dealswith statics and dynamics of polymers (one-dimensional elastic strings) and their flow-inducedinstabilities during the first half and membranes (two dimensional sheets) in the second.

Content:

1. Polymer Physics: properties of an isolated chain (statistical mechanics of flexible, semiflex-ible polymers, concept of persistence length), concentrated solutions and melts, (thermody-namic properties, concentration fluctuations), physics of gels, rubber elasticity (4 lectures).

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2. Polymer dynamics: motion of polymers in dilute solutions (Rouse and Zimm dynamics),motion of polymers in entangles solutions and melts (reptation of polymers), phenomeno-logical theory of viscoelasticity (4 lectures)

3. Thermodynamically induced fluid-fluid de-mixing studied using the Cahn-Hilliard equation,without hydrodynamics. Flow induced instabilities, including shear banding, analogy withequilibrium phase, coexistence in the Cahn-Hilliard systems, calculation of shear bandedstates within the context of a simple scalar model (4 lectures)

4. Physics of membranes, Review of differential geometry, interfacial tension, and fluctua-tions at interfaces, thermal fluctuations, roughening transition. Flexible interfaces, fluidmembranes, curvature modulii and derivation of the Helfrich-Canham Hamiltonian. Self-assembling interfaces lipid bilayers and structure of biological membranes (4 lectures)

Recommended Books:1. Polymer Physics (M. Rubinstein & R. Colby)2. Scaling Concepts in Polymer Physics (P. G. deGennes)3. Statistical mechanics of Membranes and Interfaces (Eds. D. R. Nelson, T. Piran and S. Wein-berg)4. Structure and dynamics of membranes: from cells to vesicles: Vols. 1 & 2 (R. Lipowsky).

Recommended papers:1. Soft Condensed Matter Physics: T. C. Lubensky http://arxiv.org/PS_cache/cond-mat/pdf/9609/9609215v1.pdf2. Soft Condensed Matter Physics: M. E. Cates http://arxiv.org/PS_cache/cond-mat/pdf/0411/0411650v1.pdf

2.2.12 Regulatory Networks in Biology (15 lectures)

Aim: To provide an overview of regulatory networks in biology and to introduce students to thetechniques in modeling regulatory networks in biology.

Content: regulation, regulatory networks and biological functions, enzymatic reactions, enzymatickinetics, kinetic modeling, modeling metabolic networks, modeling signalling networks, computersoftware.

Recommended bookE. Klipp, R. Herwig, A. Kowald, C. Wierling & H. Lehrach, Systems biology in practice, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim (2008); ISBN 3527310789.

Biomathematics IIIAll units in Biomathematics III coincide with courses from our large MMath programme. Theyhave two lectures per week in the first two terms with 2-4 revision lectures at the beginning of thethird Term.

You should make an initial choice of two units, in consultation with the Course Director, beforelectures start. You may, if you wish, attend the lectures for other units and make a final choice at

13

the end of the third week of the first Term. You must inform the Course Director of your choicesand gain their approval for them.

2.2.13 *Bayesian Statistics (38 lectures) Lectures as for MATH3341

Aim: To provide an overview of the theoretical basis for Bayesian statistics and of practicalBayesian statistical methodology together with important applications.

Content Term 1: Review: Bayesian paradigm; Conditional independence and conjugacy; Manipu-lation of multi- variate probability distributions.Foundations: Rational basis for subjective probability and Bayesian statistics; Exchangeability andde Finettis representation theorem; Parametric modelling.Exponential families: Regular exponential families; Canonical representation; Sufficiency; Conju-gacy. expectation.Hierarchical modelling: Motivation; Latent variables; Random effects; Conjugacy and semi-conjugacy.

Content Term 2: Bayesian graphical modelling: Directed acyclic graphs; Bayesian networks; Con-ditional indepen- dence; Moral graph; Separation theorem; Doodles in WinBUGS.Computation: Monte Carlo; Markov Chain Monte Carlo: Markov chains, equilibrium distribution,Gibbs sampling; Metropolis-Hastings: Metropolis random walk, independence sampler, Gibbssampling.Practicalities: Specification of prior beliefs; Analysis and interpretation of MCMC output; Win-BUGS.Model comparison: Bayes factors; Criteria for model choice. Case studies.

Recommended BooksP.M. Lee, Bayesian statistics: an introduction (2nd ed.), Arnold, 1997, ISBN 0340677856J.M. Bernardo and A.F.M. Smith, Bayesian theory, Wiley, 1994, ISBN 0471924164D. Gamerman and H.F. Lopes, Markov chain Monte Carlo : stochastic simulation for Bayesianinference (2nd ed.), Chapman & Hall/CRC, 2006, ISBN 1584885874P. Congdon, Bayesian Statistical Modeling, Wiley, 2001, ISBN 0471496006

The first two books try to cover large parts of the course whereas the remainder are more specialisedand authoritative. The first book is a general introduction to the theory of Bayesian statistics. Thesecond covers the more foundational theoretical material in the first term. The third discussesMarkov chain Monte Carlo in detail and some aspects of Bayesian modelling and the fourth isa more applied book which deals with graphical representation of statistical models and whichcontains many examples of the use of WinBUGS. None is completely suitable by itself as a textfor this module. Selected material will be made available via DUO in due course.

2.2.14 **Topics in Statistics (38 lectures) Lectures as for MATH3361

Aim: To provide a working knowledge of the theory, computation and practice of a variety ofwidely used statistical methods.

Content Term 1: Likelihood estimation: Likelihood- and scorefunction for multiparameter models,Fisher information, confidence regions, method of support, likelihood ratio tests, profile likelihood.Contingency tables: Log-linear models. Iterative Proportional Fitting. Model selection. Goodness

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of fit.

Content Term 2: Generalised linear models: Framework, exponential families, likelihood and de-viance, standard errors and confidence intervals, prediction, analysis of deviance, residuals, over-dispersion.Advanced topic: One of: multivariate analysis, time series analysis, medical statistics.

Recommended BooksSince the course is a selection of topics in statistics, no one book covers the material. The followingare recommended for reference and selected material from them will be made available via DUOin due course.

Y. Pawitan, In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford,2001, ISBN 0198507658A. Agresti, An Introduction to Categorical Data Analysis (2nd ed), Wiley, 2007, ISBN 0471226181A.J. Dobson, A. Barnett and K. Grove, An Introduction to Generalized Linear Models (3rd ed),CRC Press, 2008, ISBN 1584889500L. Fahrmeir & G. Tutz, Multivariate Statistical Modelling Based on Generalized Linear Mod-els (2nd ed), Springer, 2001, ISBN 0387951873G. Fitzmaurice, N. M. Laird & J. H. Ware, Applied Longitudinal Analysis, Wiley, 2004, ISBN0471214876

2.2.15 *Continuum Mechanics (38 lectures) Lectures as for MATH4081

Aim: To introduce a mathematical description of fluid flow and other continuous media to famil-iarise students with the successful applications of mathematics in this area of modeling. To preparestudents for future study of advanced topics.

Content Term 1: Description of fluid flows: continuum hypothesis, velocity field, particle pathsand streamlines, vorticity and compressibility. Euler equations: ideal (perfect) fluid. Bernoulli’sequation: irrotational flows, water waves. Navier-Stokes equations: viscous fluids and boundaryconditions; boundary layers.

Content Term 2: Examples: flows in a channel and a pipe, vortices, aerodynamic lift [this willlikely be spread throughout the course as appropriate]. Compressible flows: sound waves. Elasticmedia: time permitting.

Recommended BooksA.R. Paterson, A First Course in Fluid Dynamics, CUP, ISBN 0521274249A.J.M. Spencer, Continuum Mechanics, Longman, ISBN 0582442826G.A. Holzapfel, Nonlinear Solid Mechanics, Wiley, ISBN 0471823198G.K. Batchelor, An Introduction to Fluid Mechanics, CUP, ISBN 0521098173D.J. Acheson, Elementary Fluid Dynamics, OUP, ISBN 0198596790.

None of these covers everything but the book by Paterson gives reasonable coverage of the fluidspart of the course.

Preliminary Reading: This course is based on vector calculus (Analysis in Many Variables II). Inparticular, please review: gradient, divergence and curl (including Gauss’ and Stokes’ theorems);partial differential equations and Fourier series.

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M.J. Lighthill, An informal introduction to theoretical fluid mechanics, OUP, ISBN 0198536305.

Reading material relevant to biological applications: As most biological tissues are 90% water,fluid mechanics is highly relevant to the study of their dynamics. The concepts studied in thismodule could be readily applied to many situations of biological interests, for example, the motionof microorganisms treated in:

Geoffrey I. Taylor, Analysis of the swimming of microscopic organisms, Proc. R. Soc. Lond.,A209 (1951) 447-461Geoffrey I. Taylor, The action of waving cylindrical tails in propelling microscopic organisms,Proc. R. Soc. Lond., A211 (1952) 225-239

2.2.16 **Solitons (38 lectures) Lectures as for MATH4121

Aim: To provide an introduction to solvable problems in nonlinear partial differential equationswhich have a physical application, and to show how Davydov’s solitons arise in the description ofenergy and charge transfer in biological systems.

Content Term 1: Nonlinear wave equations: historical introduction; properties; dispersion anddissipation. Progressive wave solutions: D’Alembert, KdV and sine-Gordon. Topological lumpsand the Bogomolnyi bound. Backlund Transformations for Sine-Gordon Equation. The Liou-ville equation. Generation of multisoliton solutions of sine-Gordon by Backlund transformations.Breathers. Discussion of scattering. Conservation Laws in Integrable Systems. Hirota’s methodfor multisoliton solutions of the wave and KdV equations.

Content Term 2: The Nonlinear Schrodinger Equation and its connection with the Heisenberg fer-romagnet. The Inverse Scattering Method. Lax pairs. Spectrum of Schrodinger’s operator forpotential; Bargmann potentials. Scattering theory; asymptotic states, reflection and transmissioncoefficients, bound states. Two-Component Equations: MKdV equation and Miura transformation.Two-component Lax pair formulation of inverse scattering theory. Toda equations: Conservationlaws in integrable finite-dimensional models. The Toda molecule and the Toda chain. Conser-vation laws for the Toda molecule. Integrability: Hamiltonian structures for the KdV equation.Integrability. Hierarchies of equations determined by conservation laws.

Recommended BooksP.G. Drazin and R.S. Johnson, Solitons: An Introduction, CUP 1989, ISBN 0521336554T. Dauxois and M. Peyrard, Physics of Solitons, CUP 2006, ISBN 0521854210G. Eilenberger, Solitons: Mathematical Methods for Physicists, Springer 1981, ISBN 354010223XG.L. Lamb, Elements of Soliton Theory, Wiley 1980S. Nettel, Wave Physics, Springer 1995, ISBN 3540585044R. Remoissenet, Waves Called Solitons, Springer 1999, ISBN 3540659196M. Toda, Theory of Nonlinear Lattices, Springer [2nd Ed] 1988See also R.K. Bullough and P.J. Caudrey (eds), Solitons, Springer 1980G.B. Whitham, Linear and Nonlinear Waves, Wiley 1974

The book by Drazin and Johnson covers most of the course, and is available in paperback.

Preliminary Reading: Read chapter 1 of Drazin and Johnson, and study the exercises for that chap-ter (the answers are given at the end of the book!). Explore the website www.ma.hw.ac.uk/solitons/(in particular the movies and the pages on Scott-Russells soliton)

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Reading material relevant to biological applications: the module concentrates on the description ofvarious properties of solitons in integrable systems. However, there exist solitons, first observed byDavydov and Scott, that arise in the description of energy and charge transfer in biological systems.They are quite similar to the solitons studied in the bulk of the course although they are based onvarious versions of the discrete nonlinear Schroedinger equation, which is not ’integrable’. Afew lectures in the second term will be dedicated on the Davydov ideas and their applications inbiology. The references areA.S. Davydov, Solitons in Molecular Systems, (Dordrecht, Reidel, 1985)A.C. Scott, Phys. Reports 217, 1, (1992).

2.2.17 Dynamical Systems (38 lectures) Lectures as for MATH3091

Aim: To provide an introduction to modern analytical methods for nonlinear ordinary differentialequations in real variables.

Content Term 1: Introduction: Smooth direction fields in phase space. Existence, uniqueness andinitial-value dependence of trajectories. Autonomous Systems: Orbits. Phase portraits. Equilib-rium and periodic solutions. Orbital derivative, first integrals. Equilibrium Solutions: Linearisationand linear systems. Hartman-Grobman, stable-manifold theorems. Phase portraits for non-linearsystems, computation. Stability of equilibrium, Lyapunov functions.

Content Term 2: Periodic Solutions: Flow, section, maps, fixed points. Brouwers Theorem, peri-odic forcing, planar cycles. Poincare-Bendixson and related theorems. Orbital stability. Bifurca-tions: Hopf and other local bifurcations from equilibrium. Uses of bifurcations.

Recommended BooksD.K. Arrowsmith and C.M. Place, Dynamical Systems, Chapman & Hall 1992, ISBN 0412390809P.G. Drazin, Nonlinear Systems, CUP 1992, ISBN 0521406684P. Glendinning, Stability, Instability and Chaos, CUP 1994, ISBN 0521425662F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer (2nd Edition)1996, ISBN 3540609342

These are all paperback introductory undergraduate texts with plenty of examples. Their style,content and order of topics all differ, but each includes something on most of the course material.Any one is likely to be helpful and there is no best buy. Instead arrange with your friends to getdifferent ones, and share.

Preliminary Reading: Read the introduction at http://www.maths.dur.ac.uk/dma0rcj/PDF/prelude.pdf

2.2.18 Mathematical Biology (38 lectures) Lectures as for MATH3171

Aim: Study of non-linear differential equations in biological models, building on level 1 and 2Mathematics.

Content Term 1: Introduction to the Ideas of Applying Mathematics to Biological Problems Re-action Diffusion Equations and their Applications in Biology: Reaction diffusion and chemotaxismechanisms. Application of the classical diffusion equation to dispersal of insects.Realistic modeling of insect dispersal with a nonlinear diffusion equation. Application of a non-linear diffusion equation to patterns formed by herrings and gulls. Linear and nonlinear stability

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for the diffusion equation. Chemotaxis and slime mould aggregation.ODE Models in Biology: Enzyme kinetics. A little ODE stability theory. The chemostat andbacteria production.

Content Term 2: The Formation of Patterns in Nature: Pattern formation mechanisms, morpho-genesis. Questions such as how does a tiger get its stripes. Diffusion driven instability and patternformation. The famous work of Turing dealing with how patterns occur in nature. Conditionsunder which Turing instabilities will not form.Epidemic Models and the Spread of Infectious Diseases: Epidemic models. Spread of infectiousdiseases. Simple ODE model. Spatial spread of diseases. Spatial spread of rabies among foxes.Stability in epidemics and predator - prey models.

Recommended BooksJ.D. Murray, Mathematical Biology I. An Introduction, Springer, ISBN 0387952233J.D. Murray, Mathematical Biology II. Spatial models and biomedical applications, Springer,ISBN 0387952284L.A. Segel Modeling dynamic phenomena in molecular and cellular biology, Cambridge Uni-versity Press, ISBN 052127477XJ. Keener and J. Sneyd, Mathematical Physiology, Springer, ISBN 0387983613

None of these books covers the course entirely. However, the course is covered by all four. Segelsbook is easiest to read. Murrays are excellent. Keener and Sneyd is a very good account of moremedical applications of mathematics.

2.2.19 Partial Differential Equations (38 lectures) Lectures as for MATH3291

Aim: To develop a basic understanding of the theory and methods of solution for partial differen-tial equations, and of the ideas of approximate (numerical) solution to certain partial differentialequations.

Content Term 1: First-order equations and characteristics. Conservation laws. Systems of first-order equations, conservation laws and Riemann invariants. Hyperbolic systems and discontinuousderivatives. Acceleration waves. Classification of general second order quasi-linear equations andreduction to standard form for each type (elliptic, parabolic and hyperbolic).

Content Term 2: Energy methods for parabolic equations. Well-posed problems. Maximum princi-ples for parabolic equations. Finite difference solution to parabolic and elliptic equations. Stabilityand convergence for solution to finite difference equations. Iterative methods of solving Ax = b.

Recommended BooksJ. Ockendon, S. Howison, A. Lacey and A. Movchan, Applied Partial Differential Equations,revised edition, Oxford University Press 2003; ISBN 0198527713E.C. Zachmanoglou and D.W. Thoe, Introduction to Partial Differential Equations with Appli-cations, Dover 1986; ISBN 0486652513K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential Equations, secondedition, Cambridge University Press 2005; ISBN 0521607930G.D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods,third edition, Oxford University Press 1985; ISBN 0198596502A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge

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University Press 1996; ISBN 0521556554

The first two books listed are concerned with analytical aspects and are relevant to the first part ofthe module. The others are useful for the second term.

Preliminary ReadingFor the flavour of the first part of the course look at Chapter 1 of Ockendon et al. or Chapter III ofZachmanoglou and Thoe.

2.2.20 Statistical Methods (38 lectures) Lectures as for MATH3051

Aim: To provide a working knowledge of the theory, computation and practice of statistical meth-ods.

Content Term 1: Statistical Computing: Introduction to statistical software for data analysis, andfor reinforcing statistical concepts. Multivariate Analysis: Multivariate normal distribution, co-variance matrix, Mahalanobis distance, principal component analysis. Likelihood Estimation:Likelihood and scorefunction for multiparameter models, Fisher Information, confidence regions,method of support, LR tests, profile likelihood.

Content Term 2: Regression: General linear model: regression, analysis of variance, designed ex-periments, diagnostics, influence, outliers, transformations, variable selection, correlated errors,lack-of-fit tests. Generalised linear models: Framework, exponential families, likelihood and de-viance, standard errors and confidence intervals, prediction, analysis of deviance, residuals, over-dispersion.

Recommended BooksT.W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley 1984, ISBN 0471360910M. J. Crawley, Statistical Computing An Introduction to Data Analysis using S-Plus, Wiley2002, ISBN 0471560405L. Fahrmeir and G. Tutz, Multivariate Statistical Modeling based on Generalized Linear Mod-els (Second edition), Springer 2001, ISBN 9780387951874T. Hastie, and R. Tibsihirani and J. Friedmann, The Elements of Statistical Learning, Springer2001, ISBN 0387952845W.J. Krzanowski, An Introduction to Statistical Modeling, Arnold 1998, ISBN 0340691859J. Neter, M. Kutner, C. Nachtsheim,W.Wasserman, Applied Linear Statistical Methods (severaleditions with different combinations of authors 19742004), ISBN 0256117365Pawitan, J , In All Likelihood, Oxford 2001, ISBN 0198507658J.A. Rice, Mathematical Statistics and Data Analysis, Duxbury 1995, ISBN 0534209343S. Weisberg, Applied Linear Regression, Wiley 1985, ISBN 0471879576.

Preliminary ReadingChapters 3.1-3.3, 8, 9.1-9.4 (Michaelmas) and 12, 14 (Epiphany) in Rices book.

2.2.21 *Stochastic Processes (38 lectures) Lectures as for MATH4091

Aim: introduce mathematics students to the wide variety of models of systems in which sequencesof events are governed by probabilistic laws. Students completing this course should be equippedto read for themselves much of the vast literature on applications to problems in mathematical fi-

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nance, physics, engineering, chemistry, biology, medicine, psychology and many other fields.

Content Term 1: Probability Revision Conditional expectation, sigma fields. Examples of MarkovChains Branching processes, Gibbs sampler. Discrete Parameter Martingales The upcrossinglemma, almost sure convergence, the backward martingale, the optional sampling theorem, ex-amples and applications. Discrete Renewal Theory The renewal equation and limit theorems in thelattice case, examples.

Content Term 2: General Renewal Theory. The renewal equation and limit theorems in the continu-ous case, excess life, applications. The renewal reward model. Poisson Processes Poisson processon the line, relation to exponential distribution, marked/compound Poisson processes, Cramersruin problem, spatial Poisson processes. Continuous Time Markov Chains Kolmogorov equations,birth and death processes, simple queueing models. Topics Chosen From: stationary Gaussianprocesses, Brownian motion, percolation theory, contact process.

Recommended BooksS. M. Ross, Introduction to probability models, Academic Press, New York (1997); ISBN:0125980620S. Karlin and H. M. Taylor, A first course in stochastic processes, Academic Press, New York;ISBN10: 0123985528, ISBN13: 9780123985521.W. Feller, An introduction to probability and its applications, Volume I., Wiley; ISBN 13:9780471257097; ISBN 10: 0471257095 (hard but a classic).J. R. Norris, Markov chains, Cambridge University Press, 1998, ISBN 0521633966 (Paperback).

The book by Grimmett and Stirzaker is available in paperback and recommended for purchase.The book Probability and random processes by G. R. Grimmett and D. R. Strizaker (3rd ed., OUP2001) covers most topics discussed in the lectures.

Preliminary ReadingYour 1H probability notes. The books above also begin with reviews of probability theory, e.g.chapters 1-3 of Grimmett and Stirzaker. Also, D.R. Stirzaker, Elementary probability theory,CUP 1994. This has many worked examples and exercises, and covers some of the course as wellas the preliminaries.

Reading material relevant to biological applications: the concepts studied in this module couldbe readily applied to many situations of biological interests, for example how genetic variability isshaped by natural selection, demographic factors, and random genetic drift, as discussed in:

Richard Durrett, Probability models for DNA sequence evolution, Springer Verlag, 2nd ed.,(2008), XII, 432 p.,ISBN: 9780387781686http://www.springer.com/math/probability/book/978-0-387-78168-6

2.2.22 **Probability (38 lectures) Lectures as for MATH4131

Aim: designed to build a logical structure on probabilistic intuition; to study classical results suchas the Strong Law of Large Numbers, the Central Limit Theorem, and some applications; to discusssome modern developments in the subject. Students completing this course should be equippedto read for themselves much of the vast literature on applications to biology, physics, chemistry,

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mathematical finance, engineering and many other fields.

Content Term 1 Introductory examples: from finite to infinite spaces. Probability as Measure:s-fields. Measure and probability spaces. Main properties. Random Variables as measurablefunctions. Distributions. Generating and characteristic functions. Convergence almost surely, inprobability, in L2. Borel-Cantelli lemmas. Kolmogorov 0-1 law.

Content Term 2: General theory: probability spaces and random variables. Integration: Expecta-tion as integral. Inequalities. Monotone and dominated convergence. Limit results: Laws of largenumbers. Weak convergence. The central limit theorem. Large deviations. Topics Chosen From:Random graphs. Percolation. Ergodic theorems. Stochastic integral.

Recommended BooksG. R. Grimmett and D.R. Stirzaker, Probability and Random Processes, Clarendon Press, Ox-ford, also Oxford University Press, ISBN 0198572220.The book Probability: theory and examples by R. Durrett published by Duxbury Press, (2ndedition: 1996, ISBN 0534243185) extends and complements the course material.

Preliminary ReadingThe Grimmett-Stirzaker book has a review of basic probability in Chapters 1-4. Alternatively youcould look at: Y. A. Rozanov, Probability theory, a concise course, Dover, ISBN 0486635449(paperback).(This is inexpensive and covers the basics.)D. Stirzaker, Elementary Probability, Cambridge University Press. ISBN 0521833442 ( paper-back).(This has many interesting examples and exercises.)

Reading material relevant to biological applications: the concepts studied in this module couldbe readily applied to many situations of biological interests, for example how genetic variability isshaped by natural selection, demographic factors, and random genetic drift, as discussed in:

Richard Durrett, Probability models for DNA sequence evolution, Springer Verlag, 2nd ed.,(2008), XII, 432 p.,ISBN: 9780387781686http://www.springer.com/math/probability/book/978-0-387-78168-6

2.3 The Dissertation module

The student will research and write a dissertation on an advanced topic, under the guidance ofhis/her supervisor and a co-supervisor in a complementary discipline within the BSI, and the guid-ance notes provided.

The Dissertation represents 600 hours of SLAT (Student Learning Activity Time), of which 10 to15 are supervision hours.

2.3.1 Aims of the Dissertation

1. To assist students to develop creative and critical thinking, the ability to assemble materialfrom several sources and to write an extended report in an area at the interface betweenmathematics and biology, possibly including original investigations.

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2. To produce a dissertation that gives a coherent acount of the topic, presented in an original,well organised and appropriate manner.

2.3.2 Choosing a topic

A list of topics of interest to mathematicians and biologists, and which members of staff are willingto supervise will be circulated no later than week 15. Students wishing to investigate a topic noton the list may be allowed to do so provided a member of staff is willing to supervise them.

For the coming academic year, the topic list includes:

1. Regulatory network analysis in plant development.

Supervisor: Dr Junli Liu 2, Co-supervisor: Prof. Keith Lindsey 2.

Description: Hormone signalling systems coordinate plant growth and development througha range of complex interactions. The activities of plant hormones, such as auxin, ethyleneand cytokinin, depend on cellular context and exhibit interactions that can be either syner-gistic or antagonistic. An important question about understanding those interactions is howgenes act on the crosstalk between hormones to regulate plant growth. This project is to de-velop mathematical models based on differential equations to quantitatively understand andpredict the roles of the crosstalk.

2. Modelling the metabolism of herbicide and safener in plant.

Supervisor: Dr Junli Liu, Co-supervisor: Prof. Robert Edwards 1.

Description: Glutathione transferases, also referred to as glutathione S-transferases (GSTs),catalyse the conjugation of both herbicides and safeners in plant. They are central to thedetoxification of the herbicides. Experimental observations for decades have accumulatedrich information on the detoxifying processes of herbicides in plants and shown that inter-actions between GSTs and herbicides as well as safeners are complex. This project is todevelop kinetic models integrating the kinetics of enzyme-catalysed reactions with gene ex-pressions for quantitatively studying the metabolism of herbicide and safener in plant. It isaimed to understand how the metabolic flux is regulated and controlled.

3. Rate parameter inference in stochastic systems biology chemical reaction models.

Supervisor: Dr Ian Vernon 3, Co-supervisor: Prof. Michael Goldstein 3.

Description: Models of chemical reaction networks are used to describe many intracellularprocesses. Often, as the number of molecules involved is small (e.g. in a gene transcription

2Department of Biological and Biomedical Sciences3Department of Mathematical Sciences

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process), the stochastic or random nature of the system is evident. In this case, stochasticversions of the chemical reaction network models can be successfully used to represent andunderstand the system. These models contain several rate parameters, one for each proposedreaction in the network. If observed data is available, the main problem of interest is how tolearn about the rate parameters using both the model and the observations.

In this project the student will use advanced bayesian inference techniques to obtain poste-rior distributions of all rate parameters in such stochastic systems biology models. The mainmethod will be that of Markov Chain Monte Carlo (MCMC), a very powerful inference tech-nique that can be applied to a large class of problems. The student will learn various MCMCalgorithms, starting with the Gibbs and Hastings algorithms, and these will be employed onsimple network models where complete observations of the system are available. More ad-vanced techniques will then be used to handle the cases of incomplete data, and sparse data,specifically the technique of ’data augmentation’. Time permitting, more advanced modelswill be analysed using the developed MCMC machinery.

The knowledge the student will gain will be of use in performing inference in a wide classof problems both in Biomathematics and in several other scientific disciplines.

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4. Emulation Techniques as applied to Systems Biology Models.

Supervisor: Dr Ian Vernon, Co-supervisor: Prof. Michael Goldstein.

Description: Models of chemical reaction networks are used to describe many intracellularprocesses. These reaction network models can be deterministic (e.g. a set of differentialequation) or stochastic (simulations from random processes). Often the networks are verylarge and contain many rate parameters, one for each proposed reaction in the network.Understanding such networks can be difficult, as it can take a long time to simulate onerealization of the model (e.g. by numerically solving a system of differential equations,or by simulating a stochastic process). If observed data is available, the main problem ofinterest is how to learn about the rate parameters using both the model and the observations.

Often, the combination of long evaluation time and large number of rate parameters meansthat standard inference techniques cannot be successfully used. In this project the studentwill learn computer model techniques centred around the idea of Emulation. An Emulator isa statistical function that mimics the behaviour of a complex model, but which is very fast toevaluate. Emulators can then be used to perform inference, i.e. to learn about which choicesof rate constants would lead to a good match between model output and observed data.The student will attempt to emulate simple deterministic network models using GaussianProcess based emulation. More advanced emulation techniques (active variables, polynomialmean functions) will then be employed to handle larger deterministic networks of realisticsize. Time permitting, stochastic emulation methodology will be used to perform inferenceon stochastic models of varying complexity, allowing a comparison to standard inferencetechniques.

Emulation techniques are very general and can be used to represent, and therefore under-stand, a wide class of complex physical models, of either deterministic or stochastic nature.They have been used successfully in many scientific disciplines.

5. Diffusion in the cell.

Supervisor: Dr Bernard Piette 3, Co-supervisor: Dr Junli Liu

Description: Diffusion processes play an important role for the transport of small complexeswithin the cytoplasm and across the cell membrane. The aim of the MSc project will beto review the theory of diffusion at the molecular scale, Brownian motion, and meso-scale,diffusion equation.

6. Mathematical methods in system biology.

Supervisor: Dr Bernard Piette, Co-supervisor: Dr Junli Liu

Description: Systems biology is a biology-based inter-disciplinary study field that focuseson the systematic study of complex interactions in biological systems. Cell life is the resultof a large set of interdependency chemical reactions, diffusion processes an other processes

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that one must study as whole. The aim of the MSc project is to get acquainted with the princi-ple of systems biology and the mathematical methods that are used to describe such systems.

7. Frequency dependent chemotaxis and chemolocation.

Supervisor: Dr Buddhapriya Chakrabarti 3, Co-supervisor: Prof. Anne Taormina 3

Description: Unicellular organisms such as bacteria (as well as some multicellular organ-isms) undergo chemotaxis http://www.youtube.com/watch?v=I_xh-bkiv_c, a motionin which the organism senses the ambient chemical in solution and either moves up (e.g. insearch of food) or down its gradient (e.g. away from harmful chemicals). Several theorieshave been developed in the past to understand this behavior. A less explored mechanismis one in which the motile body responds not to the ambient chemicals present in solutionbut rather sends out a signal (let’s say releases a chemical A), which on reaching the targetsget converted to a different signal (say chemical B, via a surface chemical reaction) whichthen diffuses back to the motile body. The cell then moves sensing the ambient chemicalgradient of this diffused signal. The addition of this extra step results in an interesting fre-quency dependent chemotactic target selection http://arxiv.org/abs/0811.4468. Sofar the theory has been developed for a motile cell in the presence of static targets. We willexplore the phenomenon when the targets are motile.

Applications include understanding aggregation phenomena of (i) dictyostelium aggregationand formation of fruiting bodies, http://www.youtube.com/watch?v=Ql7i_TLUurM (ii)quorum sensing in bacterial populationshttp://en.wikipedia.org/wiki/Quorum_sensing and (iii) cancer metastasis.

8. Unzipping of DNA hairpins using translocation through nanopores.

Supervisor: Dr Buddhapriya Chakrabarti, Co-supervisor: Prof. Anne Taormina

Description: Translocation of single stranded DNA through biological and solid state poresof nanometer dimension http://www.youtube.com/watch?v=cEKKHZKunXk&feature=relatedhas received considerable attention in recent times due to their potential use in developingassays for rapid DNA sequencing http://www.nanoporetech.com/. From a fundamentalperspective this is a rich problem involving fluid flow and dynamics of polymers in con-finement. Experiments that study translocation of single stranded DNA through biologicalnanopores (α-hemolysin) observe a dependence of the translocation speed on which end ofthe DNA (3’ or 5’ end) threads the pore first. Coarse-grained theories and atomistic simula-tions have been developed to understand this phenomenonhttp://www.bu.edu/meller/PDFs/PhysRevE_77_031904.pdf, and http://www.bu.edu/meller/PDFs/PNAS_8-2005.pdf. Recent experiments have focused on unzipping of DNAhairpins using nanopores, which happens via a shear mode http://www.bu.edu/meller/PDFs/nl802218f1.pdf. We would explore the translocation dynamics of double strandedDNA that are being unzipped in the process using continuum models and meso-scale simu-lations.

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9. Novel optimization algorithms for protein crystallization

Supervisor: Dr Ehmke Pohl 4, Co-supervisor: Prof. Anne Taormina

Description: Protein crystallography is by far the most important and powerful method todetermine the 3-dimensional structure of biological macromolecules. The major bottleneckof the technique is the formation of suitable, well-ordered crystals. In spite of tremendousefforts to understand the underlying physical principles, crystallizations conditions cannot bepredicted a priori, for any given protein. Crystallization therefore remains a highly empiricalprocess that is based on iterations of hundreds or thousands of crystallization trials performedin a high-throughput mode. Therefore, new algorithms are needed to increase the chances ofsuccess and decrease the number of experiments required to obtain suitable crystals.

Crystallization can be viewed as a global minimization problem where dozens of physico-chemical parameters need to be varied in order to find the condition that produces suitablecrystals. These parameters can be roughly grouped in external physical variable such as tem-perature and crystallization setup, chemical parameters, such as pH, type and concentrationof the major crystallizing agent, type and concentration of various additives, and biologicalparameter including type and concentration of specific ligands, inhibitors or binding partner.

Due to the fact that no empirical function exists that can describe the crystallization be-havior and because crystallization experiments are typically performed in ultra-low volume(100nL) and high-throughput (192 different conditions per single plate) genetic algorithmmay provide a natural alternative to traditional statistical analysis. The goal of this projectis to implement and test such algorithms with direct application and feedback to test proteincrystals and real crystallization problems.

10. Machine vision

Supervisor: Dr Kasper Peeters2, Co-supervisor: Prof. Anne Taormina

Description: Making computers recognise the content of an image, instead of just processingit, is a hard problem with a wide variety of potential applications. An increasing number ofalgorithms is based on knowledge obtained directly from biological experiments. Examplesof well-known ideas of this type are neural networks (which mimic neuron connectivity inthe brain) or Gabor filters (which mimic the response of cells in the visual cortex). Severalother recent ideas, and the problems they intend to solve, are described in e.g. web.mit.edu/serre/www/publications/Serre_etal_PAMI07.pdf.

The goal of this project is to learn and implement some of these biology-inspired ideas formachine vision and analyse the underlying mathematics.

You choose a particular dissertation topic by the end of the second term (Epiphany) in consultationwith the Projects Director (Prof. Anne Taormina, room CM302), and possible dissertationsupervisors.

4Department of Chemistry

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Your supervisor will give you some suggested reading by the end of the second term. You shoulduse this to get some idea of your topic before your examinations in May/June. You must pass theseexaminations (as well as those occurring in January - see Section 4 for details) in order to continuewith your dissertation, for which you study your topic in some depth.

2.3.3 Details of how dissertation period is to be supervised

You should meet your supervisor fairly frequently at first, say once per week (allowing for absenceson vacation and examinations) and maybe less frequently once you are well embarked on thetopic. But you should make contact at least fortnightly during the third term. As well as obtainingthe supervisor’s advice, as it becomes necessary, you should produce samples of work for yoursupervisor’s comments. At a pre-agreed point near the end of the dissertation period, a draftdissertation should be given to the supervisor. It is not the supervisor’s job to proof-read yourdraft, but to give feedback on actual and intended content. You will then produce and submit thefinished dissertation.

2.3.4 Work back-up

Note the advice on backing-up and protecting your computer-based work that is given by the ITService in their handbook for students: Computing at Durham. Also, make sure to allow plenty oftime for printing etc., in case of equipment failures. Ignoring elementary precautions is not a validexcuse.

2.3.5 Length of the dissertation

The dissertation should be 40-60 A4 pages in length (with 1 inch margins, body text in 12ptnon-condensed type and normal baseline spacing at 14.4pt). The pages before the Introduction(or first chapter) are not counted. Appendices and graphical illustrations may be discounted withpermission of the Projects Director. An index, if present, need not be included in the page count.

2.3.6 Style and format for the dissertation

The dissertation should be produced in a suitable LaTeX format or a suitable equivalent (for lots ofinformation on LaTeX, see http://www.maths.dur.ac.uk/Ug/projects/resources/). The dissertationshould have:

• a front page including: the title, a description (A dissertation submitted in partial fulfilment ofthe requirements for admission to the degree of MSc in Biomathematics at Durham University),your full name and the month and year.• a table of contents• a bibliography• a reference list

(These last two could be combined if appropriate.)

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2.3.7 Assertion of authorship

You should assert that the dissertation is your own work except as acknowledged in the text. Thisis best done by including a page as follows:

“This dissertation is my own work, except where explicitly acknowledged by the giving of a refer-ence.”

Name: Type your full name.

Signed and dated: Please put your usual signature, together with the date.

2.3.8 Plagiarism

All sources must be acknowledged. Also, if you reproduce material word-for-word from anothersource, you must make a reference to the source at that point. Such reproduction should be lim-ited to small sections (typically less than a page in each instance), and to gain marks you mustdemonstrate understanding of the duplicated material, for example, by discussion or example.

The following is an extract from Volume I of the University Calendar:

In formal examinations and all assessed work prescribed in degree, diploma and certificate regula-tions, candidates should take care to acknowledge the work and opinions of others and avoid anyappearance of representing them as their own. Unacknowledged quotation or close paraphrasingof other people’s writing, amounting to the presentation of other persons’ thoughts or writings asone’s own, is plagiarism and will be penalized. In extreme cases, plagiarism may be classed as adishonest practice under Section IV2(a)(viii) of the General Regulations and may lead to expulsion.

2.3.9 Handing in

Two copies (spiral or comb bound so that they can be opened flat) of the dissertation should behanded in to the maths department office (CM 201) on or before the deadline. A receipt should beobtained. The second copy of the report will be made free of charge by the Mathematics Office ifthe top copy is brought before binding. You must also submit an electronic copy of your report asa pdf (or other by prior agreement) file attached to an e-mail to the Projects Director.

You should consult your supervisor and the 4H projects page (and associated links) for furtheradvice on the mechanical production of your dissertation.

The deadline for submission of the dissertation is 17:00 hrs on Friday 7th September 2012.

Exceptionally, in borderline cases, you may be asked to attend an oral examination, probably inOctober/November 2012.

3 Research Environment

As an MSc student in Biomathematics, you will have an opportunity to meet and discuss withmathematicians and scientists who are members of the Biophysical Sciences Institute (BSI). All

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at present are based in their ‘mother’ department (Biological and Medical Sciences, Chemistry,Engineering, Mathematical Sciences or Physics). Some of them will be involved in teaching youand/or supervising your dissertation.

A welcome party will be organized at the beginning of the academic year, where all BSI memberswho have a keen interest in the MSc in Biomathematics will be invited to meet all MSc students.This should help everyone, student or researcher, to establish some early links.

It is desirable that you make a real effort to interact with as many of these scientists as possi-ble. You are strongly encouraged to participate to seminars and workshops that are organizedby the BSI throughout the year. Details of the talks may be found by following the links fromhttp://www.dur.ac.uk/biophysical.sciences. The Department of Mathematical Sciences also runs aBiomathematics Seminar series, to which speakers from Durham and outside regularly contribute.On the day they are being given, talks are advertised on the department homepage(http://www.dur.ac.uk/mathematical.sciences/).

You will also contribute concretely to the BSI activities during a poster session we will organize inthe Easter term, where you will be presenting some of your work.

The BSI does not have a building of its own yet, and therefore, it is crucial that you know wherethe different departments involved in the BSI are located on campus. Below is a schematic map tohelp you.

11: Biological and Biomedical Sciences12: Physics; Ogden Centre for Fundamental

Physics13: Library (Main Section)14: Engineering/Computer Sciences/

Health and Safety Office15: Chemistry; Scarborough Lecture Theatre15: Information Technology Service15: Mathematical Sciences15: Natural Sciences40: Geography; Applebey Lecture Theatre41: Dawson Building42: Visitor Information Point43: Earth Sciences; Calman Learning Centre44: Psychology45: Mountjoy Research Centre

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Figure 2: 3-D map of the Science Site.

The researchers from Durham University directly involved in the teaching of the MSc are:

1. Dr Beth Bromley (Physics, e.h.c.bromley@durham.ac.uk) teaches part of Core Biomathe-matics II, Biological Physics II. Her research interests centre on the biomolecular design

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approach to synthetic biology.To learn more, see http://www.dur.ac.uk/physics/staff/profiles/?id=8289

2. Dr Buddhapriya Chakrabarti (Mathematical Sciences, buddhapriya.chakrabarti@durham.ac.uk)teaches part of Core Biomathematics II, Soft-condensed Matter inspired Biology. His re-search is in Biophysics and focuses on understanding the mechanical response and flowbehaviour of soft and fragile materials, especially biopolymers such as DNA and proteins.He uses a combination of analytical and numerical techniques of statistical physics to discerngeneral principles underlying complex behaviour in soft matter and cell biology.

3. Dr Stewart Clark (Physics, s.j.clark@durham.ac.uk) teaches Core Biomathematics I, Quan-tum Mechanics for Biomaterials. His research interests include the development and ap-plication of electronic structure methods for the prediction of properties of materials at theatomic level. Applications include calculation of the electronic, structural, vibrational andspectroscopic properties of bio-molecules. .To learn more, see http://www.dur.ac.uk/physics/staff/profiles/?id=1789

4. Prof. Roger Crouch (School of Engineering, r.s.crouch@durham.ac.uk) teaches Core Biomath-ematics I, Computational Mechanics. His research interests include the development of aninelastic finite deformation computational analysis capability for simulating collagen scaf-folds (tissue engineering), the examination of slip in fibrous muscle fabric through plasticitytheory and the development of an automated mesh-generator and load balancing algorithmfor 3D parallel finite element coupled fluid-structure interaction of the heart.To learn more, see http://www.dur.ac.uk/engineering/staff/profile/?username=des0rsc

5. Dr Suzanne Fielding (Physics, suzanne.fielding@durham.ac.uk) teaches part of Core Biomath-ematics II, Soft-condensed Matter inspired Biology. Her research is in soft condensed matterphysics, rheology and biologically active suspensions.To learn more, see http://www.dur.ac.uk/physics/staff/profiles/?id=7330

6. Prof. Keith Lindsey (Biological and Biomedical Sciences, keith.lindsey@durham.ac.uk)teaches part of Core Biomathematics II, Regulatory Networks in Biology. His research inter-ests include developmental genetics of plants and its biotechnological application.To learn more, see http://www.dur.ac.uk/biological.sciences/staff/profile/?username=dbl0kl

7. Dr Junli Liu (Biological and Biomedical Sciences, junli.liu@durham.ac.uk) teaches part ofCore Biomathematics II, Regulatory Networks in Biology. His research interests includesystems biology and mathematical modeling : theory and applications. Specific applicationsinclude modeling of signaling networks; modeling of metabolic networks, and modeling ofcytoskeleton dynamics..To learn more, see http://www.dur.ac.uk/biological.sciences/staff/profile/?username=dbl1jl1

8. Prof. Tom McLeish (Physics, t.c.b.mcleish@durham.ac.uk) teaches part of Core Biomath-ematics II, Soft-condensed Matter inspired Biology. He is the pro-vice chancellor for re-search and his research interests are in soft condensed matter physics, rheology and biologi-cal physics.To learn more, see http://www.dur.ac.uk/physics/staff/profiles/?id=6691

9. Dr Kasper Peeters (Mathematical Sciences, kasper.peeters@durham.ac.uk) teaches CoreBiomathematics I, Biological Physics I. His research interests include the dynamics of mi-crotubules and of viruses.To learn more, see http://maths.dur.ac.uk/users/kasper.peeters/

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10. Dr Bernard Piette (Mathematical Sciences, b.m.a.g.piette@durham.ac.uk) teaches part ofCore Biomathematics I, Modeling of Macrobiomolecule Dynamics. His research interestsinclude the mathematical modeling of the cytoskeleton, and microtubules in particular, aswell as processes where the cytoskeleton plays an important role.To learn more, see http://www.dur.ac.uk/mathematical.sciences/people/profile/?id=474

11. Dr Ehmke Pohl (Chemistry, ehmke.pohl@durham.ac.uk) teaches Core Biomathematics I,Protein Crystallography. His research aims to unravel the three-dimensional structures ofproteins associated with virulence and disease, using predominantly X-ray crystallography.To learn more, see http://www.dur.ac.uk/chemistry/staff/profile/?id=5500

12. Prof. Roy Quinlan (Biological and Biomedical Sciences, r.a.quinlan@durham.ac.uk), teachespart of Core Biomathematics I, Modeling of Macrobiomolecule Dynamics. His research in-terests include the cytoskeleton-chaperone complex and its role in the cellular responses toprotein aggregation induced in neurodegeneration, cardiomyopathy and cataract.To learn more, see http://www.dur.ac.uk/biological.sciences/about/staff/?mode=staff&id=36

13. Prof. Anne Taormina (Mathematical Sciences, anne.taormina@durham.ac.uk) teaches CoreBiomathematics II, Mathematical Virology. Her research interests include mathematical vi-rology and dynamics of protein architectures.To learn more, see http://www.maths.dur.ac.uk/ dma0at/Personal/

14. Dr Ian Vernon (Mathematical Sciences, i.r.vernon@durham.ac.uk) teaches Core Biomathe-matics I, Systems Biology and Bayesian Inference. His research interests include the mod-eling of intracellular chemical reaction networks as stochastic processes, in particular usingBayesian inference as applied to the rate constants of such reaction networks. He also adaptsdeterministic computer model calibration techniques to the stochastic case, and applies themto the above systems biology models.

15. Prof. Wojtek Zakrzewski (Mathematical Sciences, w.j.zakrzewski@durham.ac.uk) teachesCore Biomathematics II, Biological Physics II. His research interests include the mathemati-cal modelling of DNA and other proteins. He is also interested in charge and energy transferin many systems including biological ones.To learn more, see http://www.dur.ac.uk/mathematical.sciences/people/profile/?id=485

The Biomathematics III MSc module is composed of two optional units you choose amongst alist of seven undergraduate courses. These are taught by mathematicians in the Department ofMathematical Sciences, whose interests are less directly related to biological applications, butwhose expertise is extremely valuable in an interdisciplinary context.

4 Examinations and Assessment

4.1 Regulations for the taught MSc

The General Regulations for the taught MSc and the special regulations for the course describedin this booklet are printed in Volume II of the current version of the Durham University Calen-dar, which is available for consultation in the main library or in the Department of MathematicalSciences Office.

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4.2 University assessment process

Full details of the University procedures for Examinations and Assessment may be found in theTeaching and Learning Handbook (www.dur.ac.uk/teachingandlearning.handbook/)

4.3 Board of Examiners

The Board of Examiners is responsible for all assessment of the taught MSc in Biomathematics.The Chairman is Prof. Anne Taormina (room CM 302) and the Secretary is Dr Ostap Hryniv(Room CM 309).

4.4 Generalities on summative assessment of the MSc in Biomathematicsmodules

The MSc. in Biomathematics consists of four compulsory modules: three 40-credit (double) mod-ules of lecture courses (modules Core Biomathematics I, Core Biomathematics II and Biomathe-matics III) and a 60-credit (triple) module (Dissertation), see Section 2.1.

Core Biomathematics I is taught in the Michaelmas term and Core Biomathematics II is taught inthe Epiphany term. Biomathematics III is a long thin double module taught in Michaelmas andEpiphany. The Dissertation is prepared over the summer.

Core Biomathematics I is assessed in January, while Core Biomathematics II is assessed at thebeginning of the Easter term, and Biomathematics III is assessed in May/June. The dissertationis marked independently by two members of staff, and the final mark arrived at by a moderatingprocess, in the fourth week of September. All examination marks are subject to confirmation bythe External Examiner, and approval by the Board of Examiners.

Each module must be separately passed in order to complete the course successfully. The finalmark for the course is averaged from the marks achieved on the individual modules. The threedouble modules have weight 2/9 each, and the Dissertation module has weight 1/3.

4.5 Passing the course, distinction

(For the official version of the regulations please see the “Core regulations for modular taughtmasters degrees, postgraduate diplomas and postgraduate certificates”(http://www.dur.ac.uk/university.calendar/coreregsmtmd.pdf ).What follows is a brief resume.

• In order to PASS the MSc. it is necessary to pass each individual module, i.e. to score 50%or higher in each module.

• In order to be awarded a MERIT one must obtain an overall average of at least 60%, and failto qualify for the award of a distinction.

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• In order to be awarded a DISTINCTION one must obtain an overall average of at least 70%across all the modules taken, to the value of 180 credits, including the achievement of a markof 70% or more in the dissertation.

If you fail a taught module you can resit failed units (but only the following year), and you mustpostpone your dissertation until after you pass the resits. It is also possible to resubmit a faileddissertation. The maximum mark that you can be awarded for a resit or resubmission is 50%.

4.6 Assessment criteria

4.6.1 Assessment of double modules (Core Biomathematics I, Core Biomathematics II andBiomathematics III)

Each of these three modules is worth 40 credits. Core Biomathematics I and II are built on tailor-made postgraduate courses, while Biomathematics III is made of two undergraduate courses atlevel 3 or 4, chosen from a list of 7.

Marks are awarded in each of these three modules on the basis of:

• a three-hour examination paper for Core Biomathematics I (weight: 2/9)

• a three-hour examination for Core Biomathematics II consisting of a two and a half hourexam paper (weight: 5/27), a 20-minute [15 for presentation, 5 for discussion] oral presen-tation (weight: 2/81) and a 10-minute poster presentation (weight: 1/81)

• two 120-minute examination papers for Biomathematics III, one for each module taught byextraction within the module (weight: 2/9)

The examination for Core Biomathematics I is held in January, just before the start of the Epiphanyterm; the exam paper for Core Biomathematics II is held in the first week of the Easter term, whilethe presentation is assessed in Epiphany.

The exam papers for the courses taught by extraction are taken in May on the same day as theundergraduates.

Quality assurance mechanism: Marking to a template, vetting by a suitable member of the MScin Biomathematics Management Board and by the External Examiner.

The oral presentation and poster are assessed independently by the lecturer of the course ‘Com-municating Science’ within Core Biomathematics II, and another staff member. The poster willbe presented during a poster session of a Biophysical Sciences Institute event organised during theEaster term.

The oral presentation and poster comprise 17% of the marks for the Core Biomathematics II mod-ule. The final presentation mark, which is decided on the basis of the grades given by the twomarkers, is reviewed and confirmed by the Board of Examiners of the MSc programme.

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Guidelines for paper preparation:

• The three-hour examination paper for Core Biomathematics I contains a section for eachcourse in the first term. Each section contains one Section A-type and one Section B-typequestion 5. The examinations are not open-book; notes or books or other materials may notbe brought into the examination.

The rubric on the examination papers reads: full marks may be obtained for complete an-swers to all section A-type questions and three section B-type questions. Section B-typequestions carry twice as many marks as Section A-type ones.

Assessment criteria: Examination papers are marked quantitatively. Each Section A -typequestion carries ten marks, and each Section B-type question carries 20 marks distributedaccording to the setter’s marking scheme, and printed on the examination paper.

• The two and a half hour paper for Core Biomathematics II contains a section for each coursein the second term. Each section contains one Section A-type and one section B-type ques-tion, except Communicating Science which does not have a section B-type question. Theexaminations are not open-book; notes or books or other materials may not be brought intothe examination.

The rubric on the examination papers reads: full marks may be obtained for complete an-swers to all section A-type questions and two section B-type questions. Section B-type ques-tions carry twice as many marks as Section A-type ones.

Assessment criteria: Examination papers are marked quantitatively. Each Section A -typequestion carries ten marks, and each Section B-type question carries 20 marks distributedaccording to the setter’s marking scheme, and printed on the examination paper.

• The 120-minute examination paper for each extraction module in Biomathematics III hasfour Section B-type questions, one being compulsory. The examinations are not open-book;notes or books or other materials may not be brought into the examination.

The rubric on the examination papers reads: full marks may be obtained for complete an-swers to the compulsory question and two more questions.

Assessment criteria: Examination papers are marked quantitatively. Each question carries20 marks distributed according to the setter’s marking scheme; they are printed on the ex-amination paper.

5Section A questions are straightforward, covering a spread of topics between them, possibly in several disjointparts. It is expected that a student who has followed the course diligently would score 75% or better. Section B ques-tions are more demanding than Section A questions, allowing better students to demonstrate their superior knowledge,technique and flair.

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Guidelines for the assessment of the oral presentation and the poster presentation:

Oral presentation (20 marks)

1. Timing well-judged (2 marks)

2. Substantial content, at the right level (4 marks)

3. Introduction, logical development, conclusion (4 marks)

4. Clear delivery, fluent and enthusiastic (4marks)

5. Adequate and appropriate visual aids (3 marks)

6. Speaker in command of the material (3 marks)

Poster presentation (10 marks)

1. Fitting title, with authorship details (1 mark)

2. Structure logical and easy to follow (2 marks)

3. Substantial content, at the right level (2 marks)

4. Effective use and suitable balance of equations, figures, tables and text (2 marks)

5. Good typography (1 marks)

6. Visually attractive overall impression (2 marks)

4.6.2 Assessment of the dissertation module (Dissertation)

Marks are awarded for this module on the basis of a dissertation.

Quality assurance mechanism: independent marking by two appropriate members of staff, one ofthem being the supervisor of the dissertation; marks moderated by the MSc course director. TheExternal Examiner also reads the dissertation.

Assessment criteria:

The following guidelines describe features expected for a distinction or a pass, and characteristicsof a failing project. Projects may exhibit features in different ranges, in which case a reasonablebalance should be sought. These features are those one might look for in a project, not thosea project must necessarily possess. The mark given, and the weighting of marks for differentcharacteristics, is at the discretion of the marker.

Marks are awarded according to the following scheme:

Examiners are provided with a mark form for each dissertation marked. Examiners must provide,on that form, a brief rationale for the mark awarded, making explicit reference to the assessmentcriteria given below. This is for the benefit of external and other examiners. Examiners shouldnot write on the dissertation itself.

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70-100

• The dissertation is well organised into sections and appendices, with appropriate intro-duction, conclusion, and table of contents. The notation, diagrams, graphs and tablesare well chosen and used fittingly. A full bibliography is supplied and citations areproperly made. Grammar, spelling and typography are correct.

• Excellent command of expression and logical argument in a skillfully structured report.

• Superior evaluation and integration of existing literature.

• Evidence of significant insight and original thought in dealing with the critical issues.

• Evidence of originality in terms of new insights into a possibly well-established area.

• Evidence that the candidate has mastered substantial new material.

Overall: Look for evidence of originality and that the student has mastered advanced mate-rial, and at the level of novelty, insight and flair.

90-100: The student shows excellence in all criteria, substantial evidence of originality inapproach and interpretation, confident mastery of the content and complexity of the topic,and abundant evidence of background research. The student worked highly independently,with mastery of highly advanced material.

80-89: The student shows excellence in most criteria and a high degree of competence inthe others. There is good evidence of originality in approach and interpreting, mastery ofthe content and complexity of the topic, and abundant evidence of background research. Thestudent worked highly independently and shows understanding of advanced material. Thewritten report is of, or near, publication quality.

70-79: The student shows a high degree of competence in all the criteria, but does not meetthe requirements for a strong distinction.

50 - 69

• The dissertation is reasonably well organised into sections and appendices, with ap-propriate introduction, conclusion, and table of contents. The notation is suitable, butshows some inconsistencies. Diagrams, graphs and tables are presented adequately.A reasonable bibliography is supplied, but some citations may be missing. Grammar,spelling and typography show occasional lapses.

• The dissertation is competently written, logically argued and adequately organised.

• The evaluation and integration of the existing literature is sound without being excel-lent.

• Reasonable insight and some evidence of original thought in dealing with the criticalissues.

• Evidence that the candidate has mastered some new material.

60-69: Most of the above criteria are satisfied. The presentation is solid and competentwithout being of distinction quality. The candidate shows some insight, and has masteredmaterial at an advanced level.

50-59: Some more substantial errors in presentation or organisation of the material. Newmaterial is covered, but the discussion tends to be more descriptive than evaluative, andarguments are often disjointed. Little evidence of original thinking.

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Fail, 0-49

• The report is badly organised and lacks features such as an appropriate introduction, aconclusion, a table of contents, a bibliography. The notation is inadequate. Diagrams,graphs and tables are badly drawn or badly presented. There are serious lapses ingrammar, spelling and typography.

• The work is very poorly written and shows a serious inability to structure and presenta logical argument.

• Coverage of the necessary literature is inadequate, with little information provided rel-evant to the claims made, or conclusions drawn, within the project.

• Serious misunderstanding of key concepts and issues.

• Little or no evidence that the candidate has mastered new material.

4.7 Formative continuous assessment

Under the general regulations of the University with regard to the keeping of terms, you are re-quired to complete written work to a standard satisfactory to the Chairman of the Board of Studies.In practice this means that you must hand in at least 75% of written work on time at a standard ofgrade C or better (see table below). To ensure this, your performance is monitored by the CourseDirector. You are required to submit work before the deadline for submission. No credit is givenfor late work unless there is a prior arrangement with the lecturer.

The purpose of the continuous assessment of coursework is to help you at each stage of the learningprocess. It is designed to encourage effort all year long and provides manageable milestones, inpreparation for the summative assessment of end of year examinations. Course lecturers provideproblems of an appropriate standard and length to the students, as well as assessment templates(model solutions) to the markers.

Each script will be returned to you with the grade written on it. The interpretation of grades is asin the table below.

The returned scripts should indicate clearly where errors and gaps in arguments occur, and the na-ture of errors. They should give brief indications as to the approach required, bearing in mind thatmodel solutions for all set problems will be provided to students by lecturers shortly after the mark-ing has occurred. The lecturer makes relevant model solutions available to students via the coursewebpage or/and Durham On-Line (DUO) shortly after they have submitted their assignments.

Remark: A grade C is deemed acceptable. D/E or a failure to hand in work is a demerit. If say 4questions of equal standard are set and 2 are answered very well and 2 are not tackled at all thenthere is close to 50% attainment, resulting in grade C.

In all cases, performance at marked written work can provide useful evidence for the Board ofExaminers if examination performance is adversely affected by illness or other circumstances.

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Grade Equivalent Mark Quality

A ≥ 80% Essentially complete and correct workB 60%—79% Shows understanding,

but contains a small number of errors or gapsC 40%—59% Clear evidence of a serious attempt at the work,

showing some understanding, but with important gapsD 20%—39% Scrappy work, bare evidence of understanding

or significant work omittedE <20% No understanding or little real attempt made

4.8 Calculators

Generally, calculators may be needed or permitted in a number of Maths modules and in the corre-sponding examinations. In the interest of fairness, the Board of Studies in Mathematical Scienceshas decided that only the simplest scientific types are allowed. In particular, you are not allowed totake to an examination any calculator which is programmable, can display graphics, has facilitiesfor text storage or communications and can evaluate integrals or solve linear equations.

For details follow the links ‘Teaching→ Exam info’ from the Department’s home-page.

4.9 Plagiarism, cheating and collusion

Working with your fellow students is perfectly acceptable, but joint work should be declared assuch. The University has a strict policy against plagiarism and other forms of cheating, a state-ment of which may be found in the Teaching and Learning Section in Volume I of your Faculty’sUndergraduate Handbook.

Plagiarism includes• The verbatim copying of another’s work without acknowledgement.• The close paraphrasing of another’s work by simply changing a few words, or altering the orderof the presentation, without acknowledgement.• Unacknowledged quotation of phrases from another’s work.• The deliberate and detailed presentation of another’s concept as one’s own.

Cheating includes• Communication with or copying from any other student during an examination.• Communication during an examination with any person other than a properly authorised invigi-lator or another authorised member of staff.• Introducing any written or printed material into the examination room unless expressly permittedby the Board of Examiners in Mathematical Sciences or course regulations.• Introducing any electronically stored information into the examination room, unless expresslypermitted by the Board of Examiners in Mathematical Sciences or course regulations.• Gaining access to unauthorised material during or before an examination.• The provision or assistance in the provision of false evidence or knowledge or understanding inexaminations.

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Collusion includes• The collaboration, without official approval, between two or more students in the preparation andproduction of work which is ultimately submitted by each in an identical, or substantially similar,form and/or represented by each to be the product of his or her individual efforts.• The unauthorised co-operation between a student and another person in the preparation andproduction of work which is presented as the student’s own.

4.10 Illness and Examinations

The Board of Examiners has discretion to take mitigating circumstances into account when makinga final decision on a student’s performance and class of degree. You must inform the Board ofExaminers before they meet, using the Mitigating Circumstances form, which can be obtainedfrom your college or downloaded from www.durham.ac.uk/˜dac0www4/6a21.doc.

Supporting evidence such as a doctor’s certificate, or other evidence from an independent profes-sional such as a counsellor or members of DUSSD, should be submitted with the form if availableand appropriate.

Students considering claiming Mitigating Circumstances are advised to read Section 6 of theTeaching and Learning Handbook of the University of Durham, accessible on-line under the ad-dress www.dur.ac.uk/˜dac0www4/index6.pdf. The relevant section is:6.1.4.14.4. Evidence for Boards of Examiners.

4.11 Award of degrees

Recommendations for the award of degrees are made by the Board of Examiners when all themarks are available. The Board of Examiners may exercise discretion and take account of specialor exceptional circumstances which may have affected a candidate’s performance and for whichthere is evidence. The views of the External Examiner are particularly influential in the case ofdisagreement on the mark to be awarded for a particular unit of assessment or on the final award.

5 Further Learning and Teaching details

5.1 Sources of advice

You may discuss any problems with the MSc Course Director (Prof. Anne Taormina, room CM302), though difficulties with particular units are best discussed, in the first instance, with the lec-turer concerned. Other people to turn to for help or information are the Director of PostgraduateStudies (Prof. Michael Farber, room CM 209), and, in the departmental office, the Secretaryfor Postgraduate Affairs (Mrs Fiona Giblin) and the Departmental Secretary (Mrs RachelDuke-Parker ). If you have a problem which cannot be solved by any of these people, the Headof Department (Prof P. Mansfield, room CM 210, p.r.w.mansfield@durham.ac.uk) should beapproached. There is also a formal University grievance procedure.

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5.2 Private study

Each 40-credit MSc module is defined as a study unit comprising 400 hours of SLAT (StudentLearning Activity Time) per annum. The total ‘contact time’ that a student spends in lectures,tutorials, etc. amounts to around 30% of the total SLAT. You would be wise to plan how best to usethe remaining 70% (280 hours, i.e., 28 hours per week in Michaelmas for Core Biomathematics I,28 hours per week in Epiphany for Core Biomathematics II, and 12.8 hours per week of a 22-weekacademic for Biomathematics III). This time is allocated within the module to be spent, not onlyin preparing submitted work, but in private study of the lecture course material and in revision.You are advised to organise your time in such a way that you are able to devote a number ofhours each week to reviewing your lecture notes, reading around the subject and working throughexercises extra to those which have been set by the lecturer. By so doing you will be developingyour study and personal management skills and be giving yourself the best opportunity to gain afirm understanding of the topics as they unfold. By attending to any difficulties or misconceptionsyou have as the course progresses, you will be in an excellent position at the end of the course tomake the most of your revision time. Planning and preparation are the key to reducing examinationstress.

5.3 Set work, handing in and help

You should attempt all the work set for the units you are taking. In particular, you should attemptand hand in all work set for handing in. If you are having difficulty with a particular unit you canand should, in the first instance, ask the lecturer concerned for help as soon as possible. You coulddo this immediately after a lecture, by calling on the lecturer concerned in his or her office or byemail. You can also ask your supervisor for guidance. Please refer to Section 4.7 for the minimumrequirements for the University’s ‘keeping of term’ regulations.

5.4 Computers, ICT and DUO

You are expected to use the internet — i.e., e-mail and the World-Wide Web (WWW) — andfacilities are provided by the Information Technology Service (ITS). You should take advantageof ITS instruction courses to make sure that you have a basic acquaintance with computers. Theweb-address is www.dur.ac.uk/ITS.

The Maths Department web-address is www.dur.ac.uk/mathematical.sciences/ and a valu-able link is ‘Teaching’. Here besides lecture and tutorial timetables you will find material providedby lecturers. For this they may use ‘Durham University Online’ (DUO).

DUO is a virtual learning environment which is a collection of on-line resources including linksto web pages, lecture notes and exercise sheets/solutions, communication tools like email andassessment features such as formative quizzes. Your login area on DUO is where you can accessall on-line course materials offered by your lecturers.

Soon after your registration details have been entered onto the University’s student records system(Banner), you will automatically be enrolled by the Learning Technologies Team at the IT Serviceon the DUO courses related to the two optional mathematics modules that you are taking. Detailsof how to logon to the DUO system are given at duo.dur.ac.uk and in the IT Service publication

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‘Computing at Durham’. Individual lecturers will inform you about its use for their courses fromtime to time during the year. The Department will also make use of the Announcements area inDUO to pass on important information to you so please get into the habit of logging in at leasttwice a week.

5.5 Timetabling and other information

Timetables giving details of places and times for your lectures are available on Departmental web-pages and on noticeboards in the first floor corridor of the Department.

The times of the MMath lectures can be found on the 3H and 4H noticeboards, and on the Web viathe pageshttp://www.maths.dur.ac.uk/php/ug.php3?honours=3http://www.maths.dur.ac.uk/php/ug.php3?honours=4.

The times of the Core Biomathematics I and II lectures will be published on the webpages in duecourse.

Teaching staff often send you important information by e-mail to your local @durham.ac.uk ad-dress, so you should scan your mailbox regularly.

5.6 Staff-Student consultation and feedback

The Department has several methods of Staff-Student consultation and feedback. At the end ofeach of the first two terms you will be asked to fill in a questionnaire on your taught units. Yourresponses will be considered initially by the Course Director and then by the Management Boardfor the MSc in Biomathematics.

Postgraduate students have two representatives on the department’s Postgraduate Studies Commit-tee, and one representative on the department’s Board of Studies. They will be pleased to raise anyissue that you bring to their attention.

The MSc in Biomathematics has a representative on the Department’s Staff-Student ConsultativeCommittee, which meets once in each of the first two terms.

Over the Christmas vacation you will be asked to use a suitable mathematics typesetting pro-gram (preferably LaTeX) to produce up to two pages, including some mathematics, outlining yourprogress in the first term. This will also help you prepare for writing up your summer dissertation(for lots of information on LaTeX, see http://www.maths.dur.ac.uk/Ug/projects/resources/).

Over the Easter vacation you will be asked to produce a report of at most four pages (again,preferably using LaTeX) describing your progress, prior to a short supportive interview just afterthe start of the third term with two members of the academic staff.

If you have concerns about teaching which are not covered by these meetings and questionnaires,contact can be made directly with the Course Director.

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5.7 Absence and illness

If you fail to hand in written work because of illness you must ask your College to inform theDepartment. If you fail to hand in written work for the above, or any other, reasons you shouldcontact the Course Director as soon as possible.

If your academic performance is significantly affected by circumstances beyond your control — forinstance, illness or bereavement — at any time during your course especially in the period leadingup to or during an examination period, you might wish to bring these mitigating circumstances tothe attention of the Board of Examiners. See section 4.10 for more detail.

5.8 Students with special needs

The University is committed to full compliance with the aims of the Special Educational Needs andDisability Act 2001. Once a student has been accepted for a course of study, the University acceptsa responsibility to ensure appropriate provision for that student throughout his/her course. Studentswith disabilities can expect to be integrated into the normal University environment. They areencouraged and helped to be responsible for their own learning and so achieve their full academicpotential.

Durham University Service for Students with Disabilities (DUSSD) aims to provide appropriatecare and support for all Durham students with a disability, dyslexia, medical or mental healthcondition which significantly affects study. DUSSD can advise you and organise special academicfacilities if you have a disability and need some help. They will try to provide whatever support isnecessary to enable you to study effectively and to make full use of your opportunities at University.This help will be specific and appropriate to you and relevant to the courses you choose.

Special arrangements and facilities may well be required by disabled students when taking ex-aminations. These might include extra reading time or a separate quiet room and are intended tominimise the effects of disability, which are often exacerbated by examination conditions. DUSSDorganises all the requisite examination concessions for hearing-impaired, visually-impaired anddyslexic students. DUSSD also makes recommendations to departments for students with otherdisabilities who have regular support from the Service.

For further advice, or to obtain a copy of the University’s Disability Statement, please contactDurham University Service for Students with Disabilities (DUSSD), Pelaw House, Leazes Road,Durham, DH1 1TA, Tel: 0191 334 8115 (Voice and Minicom),Email: disabilities.service@durham.ac.uk.

6 Practicalities

6.1 Getting started

There will be an informal meeting with the MSc Course Director on Monday October 4th, startingat 1:00pm. in the department Coffee Room (CM 211) This will be a chance to pick up informationon the postgraduate lecture courses and other matters.

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There are several administrative matters that must be sorted out at the beginning of the academicyear which it would be wise to complete before lectures begin on Thursday October 7th.

• You will need to complete your registration form and obtain your campus card (which will beneeded to gain access to the University Library and a number of other University buildings, andto borrow books from the University Library.) At the same time you should be given your username and password for a computer account with the University’s ITS Service.

• You should go to the departmental office (CM 201) where you will be informed about the ar-rangements for a work-space.

• There is a pigeonhole in the Coffee Room (CM 211) for mail.

• You should register for departmental computing facilities (see below).

6.2 Useful contacts

The first point of contact for issues referring to a particular lecture course should be the relevantlecturer - either immediately after a lecture, or by visiting the office of the lecturer, or by e-mail.For more general questions or difficulties you are welcome to consult the Course Director.Course Director: Prof. Anne Taormina (CM 302) anne.taormina@durham.ac.ukRegistration and timetabling: Prof. Anne Taormina (CM 302) anne.taormina@durham.ac.ukDepartment computing officer: Mr. M. Short (CM 331) mark.short@durham.ac.ukDepartment postgraduate secretary: Ms F. Giblin (CM 201) f.l.giblin@durham.ac.uk

6.3 The University Library

This is located on the Science Site close to the Department of Mathematical Sciences. It containsa large selection of books and journals of interest to mathematical scientists. To borrow books youwill require a campus card.

The main bookshop in Durham is Waterstones on Saddler St. which carries a limited selection ofappropriate texts; other titles are generally available by order.

The department has a small research library (the Collingwood Library) in CM217.

6.4 Computing facilities

The main university computing facilities are run by the Information Technology Service (ITS). Youshould have been registered automatically for an ITS account when completing your UniversityRegistration and obtaining your campus card (see above). In case of any problems or if you needany further information about the University’s computing facilities, you should visit the ITS Help-Desk which is situated on the ground floor of the same building as the Mathematics Department.The University maintains a number of clusters of PCs and Unix machines. One such cluster islocated in a room adjacent to the ITS Help-Desk.

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Also, please ask Dr Sharry Borgan to add you to the department list of MSc students, and, whenyou have made your choice of optional modules (within the MSc module Biomathematics III), askDr Borgan to add you to the e-mail lists of students taking those modules.

The department has some computers (linked to the department network) in CM217, which you arewelcome to use.

Section 5.4 contains further details about the computing facilities on offer.

6.5 Smoking and Mobile Phones

Please note that smoking is forbidden by law in any building in the University. Also, mobiles mustalways be switched off in classroom.

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