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5000-level modules

MT5098 Group Dissertation for MSc Programmes (MSc programmes only)
MT5099 Dissertation for MSc Programmes (MSc programmes only)
MT5611 Advanced Symbolic Computation
MT5613 Advanced History of Mathematics (MSc programmes only)
MT5701 Advanced Statistical Inference
MT5751 Estimating Animal Abundance
MT5758 Applied Multivariate Analysis 
MT5761 Statistical Modelling
MT5762 Introductory Data Analysis (MSc programmes only)
MT5763 Software for Data Analysis
MT5764 Advanced Data Analysis
MT5765 Medical Statistics
MT5802 Advanced Analytical Techniques
MT5806 Advanced Computational Techniques
MT5809 Advanced Fluid Dynamics
MT5810 Advanced Solar Theory
MT5821 Advanced Combinatorics
MT5823 Semigroup Theory
MT5824 Topics in Groups
MT5825 Measure and Probability Theory 
MT5827 Lie Algebras
MT5830 Hyperbolic Geometry
MT5831 Advanced Bayesian Inference
MT5836 Galois Theory
MT5837 Ergodic Theory and Dynamical Systems
MT5852  Mathematical Biology 2
MT5990 Independent Study Module
MT5991 Professional Skills for Mathematical Scientists
MT5999 Advanced Project in Mathematics/Statistics (final year of MMath or MPhys degrees only)


ID5059 Knowledge Discovery and Datamining


ID5059  Knowledge Discovery and Datamining

Credits 15.0
Semester 2
Academic year 2018/9
Timetable 11.00 am Mon (odd weeks), Wed and Fri
Description

Contemporary data collection can be automated and on a massive scale e.g. credit card transaction databases. Large databases potentially carry a wealth of important information that could inform business strategy, identify criminal activities, characterise network faults etc. These large scale problems may preclude the standard carefully constructed statistical models, necessitating highly automated approaches. This module covers many of the methods found under the banner of "Datamining", building from a theoretical perspective but ultimately teaching practical application. Topics covered include: historical/philosophical perspectives, model selection algorithms and optimality measures, tree methods, bagging and boosting, neural nets, and classification in general. Practical applications build sought-after skills in programming (typically R, SAS or python).

Prerequisites
Antirequisites
Lectures and tutorials Lectures, seminars, tutorials and practical classes.
Assessment 2-hour Written Examination = 60%, Coursework = 40%
Module coordinator Dr T W Kelsey
Lecturer Dr T W Kelsey, Dr R Hoffmann

In 2018/19 this interdisciplinary module is taught by the School of Computer Science.


MT5098  Group Dissertation for MSc Programme/s

Credits 60
Semester Full Year
Academic year 2018/19
Timetable To be arranged
Description

This module is a group-based dissertation which is supervised by members of the teaching staff who will advise on the choice of subject and provide guidance and structure throughout the progress of the dissertation. This module results in an individually written and submitted dissertation of not more than 15,000 words. This dissertation may also include an agreed collaboratively written group report, but this report will constitute no more than 30% of the module grade. Each student is assessed taking into account both individual and group submissions.

Prerequisites Students must be enrolled on the msc programme in the applied statistics and data mining.
Antirequisites You cannot take this module if you take MT5099
Lectures and tutorials 1-hour supervision (x 13 weeks)
Assessment Dissertation = 100%
Module coordinator Dr J Mitchell
Lecturer


MT5099  Dissertation for MSc Programme/s

Credits 60.0
Semester Whole Year
Academic year 2018/9
Timetable At times to be arranged with the supervisor.
Description

Student dissertations will be supervised by members of the teaching staff who will advise on the choice of subject and provide guidance throughout the progress of the dissertation. The completed dissertation must be no more than 15,000 words.

Prerequisites
Antirequisites
Lectures and tutorials Individual supervision
Assessment
Module coordinator Dr J D Mitchell
Lecturer


MT5611  Advanced Symbolic Computation

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 9.00 am Mon (odd weeks), Wed and Fri
Description

This module aims to enable students to use a computer as a tool in their other modules and to turn naturally to a computer when solving mathematical problems. The module aims to illustrate the following points: computation allows one to conduct mathematical experiments; computation allows one to collect data about a problem being studied. This is similar to the way other scientists work. It is easier to try several different approaches to a problem and see which works. The computer is not intelligent; intelligence comes from the user. The user thinks, the user interprets, the computer calculates. Students will undertake a more substantial project than that required for MT4111.

Prerequisites at least one MT4000-level module
Antirequisites MT4111
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 practical session (weeks 2 - 11).
Assessment 2-hour Written Examination = 55%, Coursework: Project = 45%
Module coordinator Dr L S Theran
Lecturer Dr L S Theran

MT5611 runs in alternate years.


MT5613  Advanced Topics in the History of Mathematics

Credits 20.0
Semester 1
Academic year 2019/20
Timetable 12.00 noon Mon (odd), Wed & Fri.
Description

The overall aim of the module is to give students an insight into the historical development of mathematics and an opportunity to research into one particular topic in some depth. This module is taught in parallel with MT4501.

Prerequisites
Antirequisites
Lectures and tutorials 2 lectures and 1 tutorial.
Assessment Written Examination = 34% (2 x 1-hour class tests), Coursework: Project = 66%
Module coordinator TBC
Lecturer TBC

MT5613 runs in alternate years.  It is only available to students registered on a taught postgraduate MSc programme in the School of Mathematics and Statistics.


MT5701  Advanced Statistical Inference

Credits 20.0
Semester 2
Academic year -
Timetable 10.00 am Mon (odd weeks), Wed and Fri
Description

This module consists of MT4606 with the addition of directed reading on more advanced aspects of the subject and a requirement to write a review essay on an aspect of the subject. The syllabus includes: comparison of point estimators; the Rao-Blackwell Theorem; distribution theory; Fisher information and the Cramer-Rao lower bound; maximum likelihood estimation; hypothesis-testing; confidence sets.

Prerequisites MT3507 and any MT4000-level module
Antirequisites MT4606
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 0.5 tutorial (weeks 2 - 11).
Assessment 2-hour Written Examination = 75%, Coursework: Project = 25%
Module coordinator TBC
Lecturer TBC

MT5701 runs in alternate years.

It last ran in 2017/18. It is not expected to run again.


MT5751  Estimating Animal Abundance

Credits 15.0
Semester 2
Academic year 2018/9
Timetable 12.00 noon Mon (odd), Wed and Fri
Description

The module will introduce students to the main types of survey method for wildlife populations. It will cover simple methods in some detail and provide students with a conceptual framework for building understanding of more advanced methods. By the end of the course, students will be able to identify an appropriate assessment method for a given population, be able to design a simple survey to assess the population, and perform simple analyses of survey data. Students will get experience in using the methods via computer practical sessions involving design and analyses of surveys conducted by computer simulation.

Prerequisites (MT3507 or MT3508) and any MT4000-level module
Antirequisites
Lectures and tutorials 1.5 hrs lecture, 1 hr practical, 0.5 hr tutorial (weeks 1 - 10)
Assessment 2-hour Written Examination = 50%, Coursework = 50%
Module coordinator Dr R Glennie
Lecturer Dr R Glennie

MT5751 runs in alternate years.

Reading list

  • Efford M.G., and R.M. Fewster. 2013.  Estimating population size by spatially explicit capture–recapture. Oikos 122: 918–928.
  • MacKenzie, D.I., J.D. Nichols, J.A. Royle, K.H. Pollock, J.E. Hines and L.L. Bailey. 2006. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Elsevier, San Diego, USA.


MT5758  Applied Multivariate Analysis

Credits 15.0
Semester 2
Academic year 2018/9
Timetable 11.00 am Mon (even weeks), Tue and Thu
Description

This module provides introductory and advanced training in the applied analysis of multivariate data. The module emphasis is upon practical analysis of data and the extraction of answers from real-life data. Basic theory is given covering matrix algebra, metrics and general measures of similarity. The most common and fundamental methods including dimension reduction and classification are covered e.g. Multivariate Analysis of Variance, Principal Components Analysis, multidimensional scaling, Factor Analysis, clustering methods. The practical component of the module focuses on analysis of real data using the commercial software tools Excel, SAS and SPSS.

Prerequisites Acceptance on to MMath Statistics or MMath Mathematics programmes
Antirequisites MT4609
Lectures and tutorials 2.5 lectures (weeks 1 - 10), and 4 tutorials and 4 project group meetings over the semester.
Assessment 2-hour Written Examination = 50%, Coursework = 50%
Module coordinator Dr J B Illian
Lecturer Dr J B Illian


MT5761  Statistical Modelling

Credits 15.0
Semester 1
Academic year 2018/19
Timetable Mon, Tues, Thur, Fri 3:00 - 4:00 (lectures), Tues, Thur 4:00 - 5:00 (practicals)
Description

This applied statistics module covers the main aspects of linear models (LMs) and generalized linear models (GLMs). In each case the course describes model specification, various options for model selection, model assessment and tools for diagnosing model faults. Common modelling issues such as collinearity and residual correlation are also addressed, and as a consequence of the latter the Generalized Least squares (GLS) method is described. The GLM component has emphasis on models for count data and presence/absence data while GLMs for multinomial (sometimes called choice-based models) are also covered for nominal and ordinal response outcomes. The largest part of the course material is taught inside an environmental impact assessment case study with reality-based research objectives. Political and medical examples are used to illustrate the multinomial models.

Prerequisites At least one of MT4113, MT4527, MT4528, MT4530, MT4531, MT4537, MT4539, MT4606, MT4608, MT4609, MT4614.
Antirequisites MT4607, MT5753
Lectures and tutorials 4 lectures (x 5 weeks), 2 practicals (x 5 weeks)
Assessment 2-hour Written Examination = 50%, Coursework = 50%
Module coordinator Dr V M Popov
Lecturer Dr V M Popov


MT5762  Introductory Data Analysis

Credits 15.0
Semester 1
Academic year 2018/19
Timetable Mon, Tue, Fri 2:00 - 3:30, Thur 3:30 - 5:00
Description

This module provides coverage of essential statistical concepts and analysis methods relevant to commercial analysis. Specifically: the different types of data and their numerical/graphical treatment; basic probability theory and concepts of inference; fundamental statistical concepts with particular emphasis on sampling issues; basic statistical models and tests; linear models; introductory computer-intensive inference. This module is a short intensive course and is a core, preliminary, requirement for the MSc in Applied Statistics and Datamining. It covers material essential for study of the more advanced statistical methods encountered in subsequent modules.

Prerequisites
Antirequisites MT5756
Lectures and tutorials Four 1.5-hour lectures (x 5 weeks)
Assessment Coursework = 100%
Module coordinator Dr C R Donovan
Lecturer Dr D Donovan, Dr L A S Scott-Hayward

This module is not available to Undergraduate students.


MT5763  Software for Data Analysis

Credits 15.0
Semester 1
Academic year 2018/19
Timetable Mon, Tues, Fri 3:30 - 4:30 (lectures). Mon, Tues, Fri 4:30 - 5:30 (Practicals)
Description

This module covers the practical computing aspects of statistical data analysis, focussing on packages most widely used in the commercial sector (R, SAS, SPSS & Excel). We cover the accessing, manipulation, checking and presentation of data (visual and numerical). We fit various statistical models to data, with subsequent assessment, interpretation and presentation. Good practice and 'reproducible research' is covered, as is computer intensive inference and big data considerations. This module is a short intensive course and is a core, preliminary, requirement for the MSc in Applied Statistics and Datamining and the MSc in Data Intensive Analysis. It covers material essential for study of the more advanced statistical methods encountered in subsequent modules.

Prerequisites MT1007 or MT3507 or MT3508 or be taking MT5762
Antirequisites MT5756
Lectures and tutorials Three 2-hour lecture/practical classes (x 5 weeks)
Assessment Coursework = 100%
Module coordinator Dr C R Donovan
Lecturer Dr C R Donovan


MT5764  Advanced Data Analysis

Credits 15.0
Semester 2
Academic year 2018/19
Timetable Mon 12:00-1:00 Weeks 2, 4, 5, 8, 10 Tues, Thur 12:00-2:00, Weeks 1-10 (lectures) Tues 2:00 - 3:00 Weeks 2-9 (practicals)
Description

This module covers modern modelling methods for situations where the data fails to meet the assumptions of common statistical models and simple remedies do not suffice. This represents a lot of real world data. Methods covered include: nonlinear models; basic splines and Generalised Additive Models; LASSO and the Elastic Net; models for non-independent errors and random effects. Pragmatic data imputation is covered with associated issues. Computer intensive inference is considered throughout. Practical applications build sought-after skills in R and the commercial packages SAS.

Prerequisites MT4607 or MT5753 or MT5761
Antirequisites MT5757
Lectures and tutorials 2.5 hours of lectures lectures (Weeks 1 - 10) and 8 practicals over the semester.
Assessment 2-hour Written Examination = 60%, Coursework = 40%
Module coordinator TBC
Lecturer TBC


MT5765  Medical Statistics

Credits 15.0
Semester 2
Academic year 2018/19
Timetable 10am Mon (odd weeks), Wed, Fri
Description

This module will cover a number of topics in medical statistics, that are important areas both in terms of methodological development and application. The main topic covered will be Survival Analysis, with others selected from Meta-analysis, Power calculations, Prospective vs Observational studies, Sequential analyses, Clinical trials.

Prerequisites MT3507 or MT3508
Antirequisites
Lectures and tutorials 2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)
Assessment Coursework = 35%, 2-hour Written Examination = 65%
Module coordinator Prof A G Lynch
Lecturer Prof A G Lynch


MT5802  Advanced Analytical Techniques

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 12.00 noon Mon (odd weeks), Wed and Fri
Description

This module introduces students to some further important applied analytic techniques such as Variational Calculus, Integral equations and transforms, and the theory of Steepest Descent.

Prerequisites MT3503
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2-hour Written Examination = 75%, Coursework = 25%
Module coordinator Dr C V Tran
Lecturer Dr C V Tran

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module, MT5842 Advanced Analytical Techniques.


MT5806  Advanced Computational Techniques

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 12.00 noon Mon (even weeks), Tue and Thu
Description

This module introduces students to some of the ideas, techniques and constraints that underpin modern approaches to the numerical modeling of physical processes that may be described by partial differential equations. Students will gain expertise in implementing standard methods and will submit a short dissertation together with a portfolio of computational work.

Prerequisites MT3802 and MT4112
Antirequisites
Lectures and tutorials 2 lectures (weeks 1 - 10) and a typical average of 0.5 hours of project supervisions (weeks 2 - 11)
Assessment Coursework = 100%
Module coordinator Dr S J Brooks
Lecturer Dr S J Brooks

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module MT5846 Advanced Computational Techniques.


MT5809  Advanced Fluid Dynamics

Credits 20.0
Semester 1
Academic year 2018/9
Timetable 11.00 am Mon (odd weeks), Wed and Fri
Description

This module will examine current research in fluid dynamics, with a particular focus on meteorology and oceanography. The large-scale atmosphere and oceans behave quite unlike a 'classical' fluid owing to the presence of stable density stratification and rotation. As a result, the fluid motion is dominated by slow, 'vortical' or eddying motions (like cyclones) which generally spin slower than the Earth. Superimposed on this slow motion are relatively fast wave-like motions analogous to surface waves on a pond. These lectures describe the mathematical basis of these fundamentally different types of motion, and furthermore illustrate the increasingly important role of computer modelling in this research.

Prerequisites MT4509
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator Dr J N Reinaud
Lecturer Dr J N Reinaud

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module MT5849 Geophysical Fluid Dynamics.


MT5810  Advanced Solar Theory

Credits 20.0
Semester 1
Academic year 2018/9
Timetable 12.00 noon Mon (even weeks), Tue and Thu
Description

The object of this module is to describe the magnetohydrodynamic processes at work in the Sun, using modern techniques of applied mathematics, and to discuss the latest theories in relation to aspects of current research within the School.

Prerequisites MT4510
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator Prof A W Hood
Lecturer Prof A W Hood

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module, MT5850 Advanced Solar Theory.


MT5821  Advanced Combinatorics

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 12.00 noon Mon (odd weeks), Wed and Fri
Description

Combinatorics underlies and interacts many topics in discrete mathematics including group theory, statistical design, and statistical mechanics, as well as being a lively subject in its own right. The module will give students a good grounding in the techniques and will engage students with research-level problems. It is designed to make a wide area of combinatorics available to students.

Prerequisites MT4514 or MT4516
Antirequisites
Lectures and tutorials 2.5-hour lectures (weeks 1 - 10) and 1-hour tutorial (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator Prof P J Cameron
Lecturer Prof P J Cameron

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module MT5861 Advanced Combinatorics, which will run in Semester 1.

Syllabus

A selection from the following will be covered.  It is envisaged that the module in a given year will cover one of the following areas:

  1. Enumerative combinatorics: basic counting, formal power series and their calculus, recurrence relations, q-analogues, group action and cycle index, species, asymptotic results.
  2. Graphs, codes and designs: strongly regular graphs, t-designs, optimality for block designs, codes and weight enumerators, matroids and Tutte polynomial, MacWilliams relations.
  3. Projective and polar spaces: geometry of vector spaces, combinatorics of projective planes, sesquilinear and quadratic forms and their classification, diagram geometry, classical groups.

Reading list

Strand 1:

  • Alan Slomson, Introduction to combinatorics, Chapman and Hall;
  • Richard Stanley, Enumerative Combinatorics, CUP.

Strand 2:

  • Cameron and van Lint, Graphs, Codes, Designs and their Links, CUP.

Strand 3:

  • Artin, Geometric Algebra, Interscience;
  • Taylor, The Classical Groups, Heldemann.


MT5823  Semigroups

Credits 20.0
Semester 2
Academic year -
Timetable 9.00 am Mon (odd weeks), Wed and Fri
Description

The general aim of this module is to introduce students to semigroup theory, which is the study of sets with one associative binary operation defined on them. In the process, the common aims and concerns of abstract algebra will be emphasised and illustrated by drawing comparisons between semigroups, groups and rings.

Prerequisites MT4003 or MT3505 or MT4517
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10), 1 tutorial and 1 examples class (weeks 2 - 11).
Assessment 2-hour Written Examination = 75%, Coursework = 25%
Module coordinator TBC
Lecturer TBC

MT5823 runs in alternate years.

It last ran in 2017/18. From 2019/20 it will be replaced by a new 15-credit module, MT5863 Semigroups.


MT5824  Topics in Groups

Credits 20.0
Semester 1
Academic year 2018/19
Timetable 10.00 am Mon (odd weeks), Wed and Fri
Description

The overall aim of this module is to build on the foundations established in MT4003/MT4603, and take the students further into this important and beautiful branch of mathematics. More specifically, through a selection of topics, some of which will be of current research interest in St Andrews, it will introduce students to advanced techniques of handling groups and classifying them.

Prerequisites MT4003
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10), 1 tutorial and 1 examples class (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator Dr C P Bleak
Lecturer Dr C P Bleak

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module MT5864 Topics in Groups.


MT5825  Measure and Probability Theory

Credits 20.0
Semester 1
Academic year 2018/19
Timetable 11.00 am Mon (odd weeks), Wed and Fri
Description

This module introduces some of the powerful techniques and ideas of modern mathematical analysis and mathematical probability theory that are important both in analysis in its own right and in its many applications in mathematics and science. The module will include topics such as: measure theory, the mathematical foundations for probability theory, law of large numbers. Mathematical analysis and the use of probabilistic methods in analysis is one of the active research areas within the School, and the choice of topics will reflect current activity.

Prerequisites MT3502 or MT4004
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2-hour Written Examination = 75%, Coursework = 25%
Module coordinator Dr M J Todd
Lecturer Dr M J Todd

This module runs each year.

From 2019/20 it will be replaced by a new 15-credit module MT5865 Measure and Probability Theory.


MT5827  Lie Algebras

Credits 20.0
Semester 2
Academic year TBC
Timetable 11.00 am Mon (odd weeks), Wed and Fri
Description

The aim of this module is to classify the semi-simple Lie algebras over an algebraically closed field. Lie algebra has important applications to theoretical physics and is used in the classification of finite simple groups.

Prerequisites MT3501 and (MT3505 or MT4003 or MT4517)
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator TBC
Lecturer TBC

MT5827 runs in alternate years.  It is not expected to run from 2019/20 onwards.


MT5830  Hyperbolic Geometry

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 10.00 am Mon (odd weeks), Wed and Fri
Description

We study two dimensional hyperbolic space, which is a fundamental example of a non-Euclidean metric space. Hyperbolic space has a rich structure and many counter intuitive properties and this module will focus on the geometry of this space, including a detailed study of the geodesic structure, the group of isometries, and the actions of Fuchsian groups which lead to beautiful tilings and fractal limit sets. We will combine ideas from analysis, geometry and group theory, with a strong emphasis on visual intuition.

Prerequisites MT2505 and MT3502 and MT3503
Antirequisites MT5828
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2.5-hour Written Examination = 100%
Module coordinator Dr J M Fraser
Lecturer Dr J M Fraser

MT5830 runs in alternate years.

From 2020/21 onwards it will be replaced by a new 15-credit module MT5870 Hyperbolic Geometry.

Syllabus

The choice of specific topics covered and the balance between them may change from year to year. The topics will be chosen from:

  1. The Poincare disk model: the hyperbolic metric, group of isometries, basic hyperbolic geometry
  2. The upper half-plane model: Gauss-Bonnet Theorem, the Cayley transformation, the modular group
  3. Hyperbolic isometries: classification via fixed points and trace analysis
  4. Fuchsian groups: fundamental domains, Poincare's theorem, limit sets, the Poincare series


MT5831  Advanced Bayesian Inference

Credits 20.0
Semester 1
Academic year 2018/9
Timetable 10.00 am Mon (even weeks), Tue and Thu
Description

This module consists of MT4531 with an additional project which will give consideration to some more advanced aspects of the theory or to the application of Bayesian techniques. This may involve either directed reading or the use of the computer for simulation or data-based analyses. The syllabus includes Bayes' theorem, inference for Normal samples; univariate Normal linear regression; principles of Bayesian computational, Markov chain Monte Carlo - theory and applications.

Prerequisites MT3507 or MT3508
Antirequisites MT4531
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 8 tutorials/practical classes over semester.
Assessment 2-hour Written Examination = 60%, Coursework = 40%
Module coordinator Dr M Papathomas
Lecturer Dr M Papathomas

This module runs every year.


MT5836  Galois Theory

Credits 20.0
Semester 2
Academic year 2018/9
Timetable 11.00 am Mon (odd weeks), Wed and Fri
Description

Galois theory is one of the most beautiful areas of mathematics, establishing a remarkable connection between the theory of polynomial equations and their roots and group theory. The subject brings together ideas from the theory of groups and fields in a powerful way, culminating in Galois' fundamental theorem. There are many applications of the work, for example demonstrating that certain ruler and compass constructions are impossible, and that there is no general formula for the solution of quintic equations.

Prerequisites MT3505 or MT4517
Antirequisites MT5826
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 10 tutorials/practical classes over semester.
Assessment 2.5-hour Written Examination = 100%
Module coordinator Dr M Quick
Lecturer Dr M Quick

MT5836 runs in alternate years. From 2020/21 onwards it will be replaced by a new 15-credit module MT5876 Galois Theory.

Syllabus

  • Polynomial equations and their roots.
  • Review of rings, fields, rings of polynomials, factorisation.
  • Field extensions, splitting fields, algebraic closure
  • Galois correspondences and the main theorem.
  • Soluble groups.
  • Solution of equations by radicals, insolubility of the quintic.
  • Further applications.

Reading list

  • John M Howie, Fields and Galois Theory, Springer
  • Ian Stewart, Galois Theory, Chapman & Hall
  • D J H Garling, A Course in Galois Theory, Cambridge University Press
  • J B Fraleigh, A First Course in Abstract Algebra, Addison-Wesley


MT5837  Ergodic Theory and Dynamical Systems

Credits 20.0
Semester 2
Academic year -
Timetable 9.00 am - 10.00 am Mon (even teaching weeks), Tue, Thu
Description

This module introduces the modern ergodic theory approach to understanding chaotic dynamical systems. Topics include recurrence, consequences of ergodicity, entropy, the structure of the space of invariant measures and unique ergodicity. This will give students an insight into a thriving field of mathematics, which is at the core of the research interests of many faculty in the Pure Division in the School of Mathematics and Statistics.

Prerequisites MT5825
Antirequisites
Lectures and tutorials 2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)
Assessment 2.5-hour Written Examination = 100%
Module coordinator Dr M Todd
Lecturer Dr M Todd

MT5837 runs in alternate years. It last ran in 2017/18.

From 2019/20 it will be replaced by a new 15-credit module MT5877 Ergodic Theory and Dynamical Systems.

Syllabus

The balance of the course is likely to change from year to year, but will consist of topics around the following.

  • Introduction to basic dynamical systems, examples
  • Poincaré Recurrence Theorem, Birkhoff's Ergodic Theorem, applications
  • Entropy of a measure preserving transformation, and applications (eg Kolmogorov Sinai Theorem)
  • The space of invariant measures

Reading list

The main textbook will be Walters' book. This and other useful books are listed below.

  • An Introduction to Ergodic Theory, Peter Walters, Springer
  • Ergodic Theory with a View Towards Number Theory, M. Einsiedler and T. Ward, Springer
  • Introduction to the modern theory of dynamical systems, A. Katok, B. Hasselblatt, Cambridge University Press, 1995
  • Ergodic Theory, K. Petersen, Cambridge University Press, 1983
  • Concepts and Results in Chaotic Dynamics, P. Collet and J.-P. Eckmann, Springer


MT5852  Mathematical Biology 2

Credits 20.0
Semester 1
Academic year 2018/9
Timetable 9.00 am Mon (odd weeks), Wed and Fri
Description

This module will explore real world applications of mathematics to biological and medical problems e.g. cell movement, pattern formation in animal coat markings, spread of diseases (AIDS, measles). The mathematical techniques used in the modelling will be nonlinear partial differential equations. The module will be useful to students who wish to specialise in Applied Mathematics in their degree programme.

Prerequisites MT3504
Antirequisites
Lectures and tutorials 2.5 lectures (weeks 1 - 10) and 1 tutorial (weeks 2 - 11).
Assessment 2-hour Written Examination = 90%, Coursework (Class Test) = 10%
Module coordinator Dr T Lorenzi
Lecturer Dr T Lorenzi

This module runs each year. From 2019/20 it will be replaced by a new 15-credit module MT5853 Mathematical Biology 2.

Syllabus

  • Introduction to partial differential equation (PDE) modelling in biology; the diffusion equation; reaction-diffusion equations; Fisher’s equation and travelling wave solutions of reaction-diffusion equations; chemotaxis models of cell movement; the Keller-Segel equations.
  • Turing pre-pattern theory; the Gierer-Meinhardt activator-inhibitor system; diffusion-driven instability; applications to animal coat marking; the Mechano-Chemical theory of pattern formation; applications to morphogenesis.
  • Epidemic models and the spread of disease; applications to measles, AIDS and other sexually transmitted diseaes; spatial spread of epidemics; applications to the Black Death and rabies.

Reading List

  • N.F. Britton, Essential Mathematical Biology, (Springer 2003).
  • J.D. Murray, Mathematical Biology I: An Introduction, (Springer, 3rd ed. 2003).
  • J.D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, (Springer, 3rd ed. 2003).
  • L. Edelstein-Keshet, Mathematical Models in Biology, (SIAM Classics in Applied Mathematics, SIAM Publishing 2005).


MT5990  Independent Study Module

Credits 20.0
Semester Either
Academic year 2018/9
Timetable To be arranged.
Description

This module provides the opportunity for a student to study an Advanced topic as a reading course under the supervision of a member of staff. The topic will be disjoint from those available in other modules.

Prerequisites Permission from the Head of School
Antirequisites
Lectures and tutorials Typically 1 hour project supervisions.
Assessment Coursework = 100%
Module coordinator Dr A L Wilmot-Smith
Lecturer

This module runs in each semester every year.

From 2019/20 it will be replaced by a new 15-credit module MT5590 Independent Study Module.


MT5991  Professional Skills for Mathematical Scientists

Credits 30.0
Semester Whole Year
Academic year 2018/9
Timetable To be arranged.
Description

This module encompasses a range of skills, both generic and topic specific, together with taught components aimed at providing an appreciation of both breadth and depth of research areas in Pure or Applied Mathematics. The precise programme of study, together with the identification of the relevant software expertise required, will be determined in consultation with the student's supervisor.

Prerequisites
Antirequisites
Lectures and tutorials Varies. Typically 1 project supervision per week over whole year.
Assessment Coursework = 100%
Module coordinator Dr J D Mitchell
Lecturer n/a


MT5999  Advanced Project in Mathematics / Statistics

Credits 40.0
Semester Whole Year
Academic year 2018/9
Timetable To be arranged.
Description

This is a more substantial project which, for MMath students, will replace the existing Honours project. The project will be chosen from an approved list of topics. The student will be required to investigate a topic in some depth, submit a report by the end of April and give a presentation.

Prerequisites Entry to an MPhys or MMath programme
Antirequisites
Lectures and tutorials Typically and on average, 40 mins of project supervisions per week over whole year
Assessment Coursework = 100%: Project = 80%, Presentation = 20%
Module coordinator Prof N Ruskuc
Lecturer

This module runs every year.

From 2019/20 it will be replaced by a new 30-credit module MT5599 Advanced Project in Mathematics/Statistics.

Booklet for MT5999 MMath Honours projects 2018-2019 (PDF, 702 KB)

and the Project allocation form 2018-2019 (PDF, 71 KB) 

 

Booklet for MT5999 MMath Honours projects 2017-2018 (PDF, 457 KB)