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Mathematics |
The Dual Honours Mathematics course at Keele is taken by students who are also studying a variety of other courses from the sciences, the humanities and social sciences. There is also a Single Honours Mathematics course. Students whose main interests might be in non-scientific subjects are encouraged to broaden their general education by taking a module in Mathematics or Statistics. Modules are available to fit a wide variety of previous mathematical attainment, and for this reason, it is important to select appropriate modules which closely match the student’s programme of study without becoming excessively demanding.
Of the Level I modules, MAT-10005, 10012, 10013, 10014, 10015, 10016, 10017, 10018 and 10023 assume a high level of school or college algebra and calculus: these modules are aimed at students who would expect to complete a degree in which Mathematics forms a substantial part. The modules MAT-10019 AND 10020 in Mathematics and MAT-10022 in Statistics are part of the Complementary Studies Programme, and are designed for students with a more limited background in the subject.
Modules in Mathematics are taught mainly through lectures and Example Classes, and students are expected to submit solutions to problems on a regular basis for the coursework component. Most modules finish with a written examination at the end of the semester. Mathematics has a PC laboratory, which is available to students.
NB: Because of variations in staff availability and research interests from time to time, certain courses may not run in particular semesters. Erasmus, Exchange and Study Abroad students please confirm availablility with the School when applying.
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-10025 | Mathematical Methods I | C | M | 7.5 | 15 | |
| This module develops students' skills in mathematical techniques, mainly in differentiation and integration. It begins by revising the standard elementary functions and their properties and continues with the revision of basic results and techniques in differentiation. There then follows sections on Taylor series and on complex numbers. The module next revises basic results and techniques in integration. Finally there is material concerning functions of more than one variable, partial differentiation, the chain rule and maxima and minima. | ||||||
| MAT-10031 | Foundations of Analysis | C | M | 7.5 | 15 | |
| This module is intended as an introduction to rigour in Mathematics. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module comprises a development of real analysis and covers the real number system, sequences, series and limits. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-10028 | Probability & Operational Research | C | M | 7.5 | 15 | |
| The first part of this module is an introduction to the axiomatic treatment of probability and to random variables. The second part presents the basic theory of linear programming problems and the Simplex method for solving them. | ||||||
| MAT-10029 | Mathematical Methods II | C | M | 7.5 | 15 | |
| This module continues from Mathematical Methods I and provides further techniques in calculus as well as an introduction to matrix and vector algebra. Topics will include matrix algebra, elementary row operations, solving linear equations, determinants, eigenvalues and eigenvectors, diagonalisation of matrices, three dimensional vector algebra and geometry, lines and planes, general vector algebra, linear independence and bases; double integration, first order differential equations: separable and linear equations, second order differential equations with constant coefficients. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-20008 | Differential Equations | C | M | 7.5 | 15 | |
| The aim of the module is to develop mathematical techniques and focuses on methods of solving ordinary differential equations. The topics include: solutions to first-order equations, higher order linear equations, power series methods, graphical aspects of differential equations, Fourier series and Laplace transforms. 2 hours lectures & 1 hour examples/laboratory class | ||||||
| MAT-20009 | Analysis and Abstract Algebra | C | M | 7.5 | 15 | |
| The aims of this module are to build upon the first year analysis course in order to develop a rigorous theory of functions of a real variable, and to introduce abstraction in mathematics through the study of abstract algebra. The module includes: limits of functions of a real variable, continuity, differentiation and Riemann integration; equivalence relations, elementary group theory, applications to number theory, modulo arithmetic, and an introduction to rings and fields. 3 hours lectures & 1 hour examples class | ||||||
| MAT-20011 | Mathematics - Study Abroad I | O | C | 7.5 | 15 | |
| MAT-20012 | Mathematics - Study Abroad II | O | C | 7.5 | 15 | |
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-20004 | Complex Variable I and Vector Calculus | C | M | 7.5 | 15 | |
| This module contains a course on vector calculus and a first course in functions of a complex variable. The topics covered include: complex functions, analytic functions, Cauchy’s theorems, complex power series, singularities, the residue theorem, contour integration, differentiation of vectors, differential operators, integration of vectors, the divergence theorem and Stokes’ theorem. | ||||||
| MAT-20005 | Dynamics | O | M | 7.5 | 15 | |
| The module is an introduction to dynamics with applications mainly to systems which can be modelled by particle dynamics. The topics investigated include: Newton’s laws, momentum, kinetic and potential energy, projectiles, simple harmonic motion, springs, the pendulum, rocket motion, planetary and satellite orbits, linear theory of oscillations, normal modes. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20006 | Stochastic Processes | O | M | 7.5 | 15 | |
| The aim of this module is to examine the mathematics of random processes with particular reference to biological and social sciences. The course will include: revision of probability and distribution theory, difference equations, Markov chains, branching and Poisson processes, birth and death processes, queues, reliability and lifetime distributions. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20010 | Linear and Metric Spaces | O | M | 7.5 | 15 | |
| The aim of this module is to introduce the concept of an abstract vector (linear) space, and then the concept of a metric space. The module builds on the knowledge of analysis and matrix algebra gained from MAT-10015, 10016 and 20009. The module includes: vector spaces, subspaces, bases and dimension, linear transformations, inner products and norms, metric spaces, convergence, topological ideas, completeness and contraction mappings. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20013 | Mathematics - Study Abroad III | O | C | 7.5 | 15 | |
| MAT-20014 | Mathematics - Study Abroad IV | O | C | 7.5 | 15 | |
| MAT-20016 | Mathematical Modelling | O | M | 7.5 | 15 | |
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-30002 | Non-linear Differential Equations | O | M | 7.5 | 15 | |
| Systems that evolve in time can often be modelled by differential equations. There are countless examples of such systems from the physical world including the weather, climate change, stock markets, the economy, population dynamics, mechanical systems, etc. The great variety of behaviours exhibited by these systems is reflected in the solutions to the corresponding differential equations. This module introduces a number of methods for identifying and classifying various types of behaviour in various types of differential equation. While linear differential equations model some processes, the majority are described by nonlinear equations, and it is these that display the greatest diversity of behaviour. However, very few nonlinear differential equations have exact solutions. Nevertheless, a great deal of insight can be obtained from qualitative methods. This module focuses on geometric methods for constructing phase plane representations of dynamics and perturbation methods for obtaining approximate solutions. With these tools it is then possible to examine the changes in behaviour that can occur when a parameter is varied, and bifurcation theory is introduced to describe this. The relation between the evolution of differential equations and the evolution of maps is explained, and more exotic behaviour, like period doubling and chaos, are then studied in terms of the dynamics of maps. | ||||||
| MAT-30003 | Partial Differential Equations | O | M | 7.5 | 15 | |
| This module provides an introduction to analytical methods for solving partial differential equations (PDEs). Throughout the module focuses on PDEs in two independent variables, although generalisation to three, or more, independent variables is briefly discussed. The module begins by introducing the method of characteristics for solving first order linear and quasi-linear PDEs. This is followed by the classification of linear second order PDEs into hyperbolic, parabolic or elliptic type, with a detailed treatment of the reduction to canonical form in each case. Thereafter, the module introduces the separation of variables technique and transform methods to solve the wave, diffusion, Laplace and Poisson equations. These PDEs are frequently encountered in many branches of applied mathematics, including fluid dynamics, mathematical biology, financial mathematics and electromagnetism. Finally the module introduces the technique of eigenfunction expansions for solving inhomogeneous PDEs, and the powerful technique of Green’s functions. | ||||||
| MAT-30005 | Relativity | O | M | 7.5 | 15 | |
| Relativity is a theory of space and time. It consists of two fundamentally different areas, that is, Special Relativity and General Relativity. Special Relativity was first proposed by Einstein in 1905 and is concerned with the connection between observations made in frames of reference that move with constant velocity relative to each other. It has many practical applications in situations which involve extremely high speeds. General Relativity was first proposed by Einstein in 1916 and incorporates non-uniform motion. Its main applications lie in gravitation theory, including astrophysics and cosmology. This module gives an introduction to both Special and General Relativity from a mainly mathematical point of view. The standard applications to physical problems are given, but experimental details are kept to a minimum. | ||||||
| MAT-30008 | Mathematical Programming | O | M | 7.5 | 15 | |
| Mathematical programming involves maximizing or minimizing a real function of several variables subject to a list of constraints. It is a major branch of Operational Research, where the formulation is typically a model of an organizational problem; although there are many applications in the social and natural sciences and also in other areas of mathematics. The module studies the mathematical underpinnings of various algorithms for solving different classes of problem, with a strong emphasis on linearity. Some specific applications are mentioned, but the module deals primarily with theory and methods. The work builds upon the account of the Simplex method given in MAT - 10005; this material will be assumed. | ||||||
| MAT-30009 | Discrete Mathematics | O | M | 7.5 | 15 | |
| This module contains a selection of topics in Discrete Mathematics. The motivation is to show how real projective geometry may be generalised to geometries over any field, and then applied, in the case of finite fields, to solve problems in the construction of combinatorial designs and error-correcting codes. Approximately equal emphasis is placed on theory and applications. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||
| MAT-30021 | Numerical Analysis | O | M | 7.5 | 15 | |
| This module is concerned with the analysis of numerical methods, concentrating on how to select a suitable method and analyse the results produced, rather than on programming the methods themselves. Substantial use is made of technology in terms of existing teaching packages, computer algebra and hand held technologies, all of which provide transferable skills. There are regular computer laboratory sessions at which students will be expected to use any and all of the methods introduced in lectures. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-30001 | Graph Theory | O | M | 7.5 | 15 | |
| This module introduces the concept of a graph as a pictorial representation of a symmetric relation. A variety of topics are investigated and, for each one, at least one of the major theorems is proved. The emphasis is on pure graph theory although a significant number of applications are explored via worked examples and coursework. | ||||||
| MAT-30004 | Fluid Mechanics | O | M | 7.5 | 15 | |
| The module is a first course in fluid mechanics, designed for students with no previous knowledge of the subject. Although previous acquaintance with vectors and differential equations would be helpful, the lecturer will offer revision of the required parts of these subjects as the module progresses. | ||||||
| MAT-30006 | Logic | O | M | 7.5 | 15 | |
| The aim of the module is to introduce mathematical concepts for examining philosophical questions about the nature of mathematics as a whole. It attempts to present a sophisticated perspective on mathematics in a way that is accessible to undergraduates. The first half of the module concerns the subject-matter of mathematics. The thesis is developed that all mathematical objects can be understood as sets; set theory is developed in an informal axiomatic spirit, based on Gödel’s notion of transfinite iteration of the ‘set of’ operation. The second half examines mathematical reasoning, which is formalised as predicate calculus and studied metamathematically. The basic apparatus of formal semantics is introduced, and issues such as completeness and categoricity are surveyed informally. | ||||||
| MAT-30010 | Complex Variable II | O | M | 7.5 | 15 | |
| This module revises and consolidates the material of MAT - 20004: Complex Variable I, before studying further applications of contour integration and the Residue Theorem. It then provides an introduction to conformal mappings, together with some of their applications, in particular their application in determining harmonic functions in two-dimensional regions. The module also covers certain analytical aspects of complex functions. | ||||||
| MAT-30011 | Waves | O | M | 7.5 | 15 | |
| The module aims to give an account of the underlying mathematical theory that describes the behaviour of waves. The mathematical development of the subject is combined with a discussion of applications, for example musical instruments. The module material is illuminated by small demonstrations and by computer-generated animations of wave processes. The topics include: the wave equation, waves on stretched strings, waves on membranes, waves on beams, sound waves, and waves in liquids with a free surface. | ||||||
| MAT-30013 | Group Theory | O | M | 7.5 | 15 | |
| This module builds on the Group Theory introduced in MAT - 20009 to develop some of the mathematics underlying the classification of finite groups. This culminates in a proof of Sylow’s First Theorem which offers a partial converse to Lagrange’s Theorem proved in MAT - 20009. The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented. | ||||||
| MAT-30014 | Medical Statistics | O | M | 7.5 | 15 | |
| This module illustrates the application of statistical techniques to health related research. Methods are applied using data from real-life studies, with particular emphasis placed on cancer studies. No prior knowledge of medicine or biology is required. The module commences with a revision of hypothesis testing procedures. This is followed by three main topics: clinical trials, survival analysis and epidemiology. Clinical trials are immensely important for evaluating the relative effectiveness of different treatments, and their design and analysis are considered in-depth. Survival analysis looks at the features and analysis of data from studies of patients with a potentially fatal disease. Epidemiology explores the distribution of disease in a population and discusses studies for assessing whether there is a possible association between a factor (such as, smoking, eating beef, using a mobile phone) and the subsequent development of a disease. | ||||||
| # | MAT-30016 | Project II | O | C | 7.5 | 15 |
| There is available in the Department a list of possible projects and supervisors. The nature of the project depends of the topic, but students are required to submit a report and to give an oral presentation on their work both of which will be assessed. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-10025 | Mathematical Methods I | C | M | 7.5 | 15 | |
| This module develops students' skills in mathematical techniques, mainly in differentiation and integration. It begins by revising the standard elementary functions and their properties and continues with the revision of basic results and techniques in differentiation. There then follows sections on Taylor series and on complex numbers. The module next revises basic results and techniques in integration. Finally there is material concerning functions of more than one variable, partial differentiation, the chain rule and maxima and minima. | ||||||
| MAT-10031 | Foundations of Analysis | C | M | 7.5 | 15 | |
| This module is intended as an introduction to rigour in Mathematics. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module comprises a development of real analysis and covers the real number system, sequences, series and limits. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-10028 | Probability & Operational Research | C | M | 7.5 | 15 | |
| The first part of this module is an introduction to the axiomatic treatment of probability and to random variables. The second part presents the basic theory of linear programming problems and the Simplex method for solving them. | ||||||
| MAT-10029 | Mathematical Methods II | C | M | 7.5 | 15 | |
| This module continues from Mathematical Methods I and provides further techniques in calculus as well as an introduction to matrix and vector algebra. Topics will include matrix algebra, elementary row operations, solving linear equations, determinants, eigenvalues and eigenvectors, diagonalisation of matrices, three dimensional vector algebra and geometry, lines and planes, general vector algebra, linear independence and bases; double integration, first order differential equations: separable and linear equations, second order differential equations with constant coefficients. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-20008 | Differential Equations | C | M | 7.5 | 15 | |
| The aim of the module is to develop mathematical techniques and focuses on methods of solving ordinary differential equations. The topics include: solutions to first-order equations, higher order linear equations, power series methods, graphical aspects of differential equations, Fourier series and Laplace transforms. 2 hours lectures & 1 hour examples/laboratory class | ||||||
| MAT-20009 | Analysis and Abstract Algebra | C | M | 7.5 | 15 | |
| The aims of this module are to build upon the first year analysis course in order to develop a rigorous theory of functions of a real variable, and to introduce abstraction in mathematics through the study of abstract algebra. The module includes: limits of functions of a real variable, continuity, differentiation and Riemann integration; equivalence relations, elementary group theory, applications to number theory, modulo arithmetic, and an introduction to rings and fields. 3 hours lectures & 1 hour examples class | ||||||
| MAT-20011 | Mathematics - Study Abroad I | O | C | 7.5 | 15 | |
| MAT-20012 | Mathematics - Study Abroad II | O | C | 7.5 | 15 | |
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-20004 | Complex Variable I and Vector Calculus | C | M | 7.5 | 15 | |
| This module contains a course on vector calculus and a first course in functions of a complex variable. The topics covered include: complex functions, analytic functions, Cauchy’s theorems, complex power series, singularities, the residue theorem, contour integration, differentiation of vectors, differential operators, integration of vectors, the divergence theorem and Stokes’ theorem. | ||||||
| MAT-20005 | Dynamics | O | M | 7.5 | 15 | |
| The module is an introduction to dynamics with applications mainly to systems which can be modelled by particle dynamics. The topics investigated include: Newton’s laws, momentum, kinetic and potential energy, projectiles, simple harmonic motion, springs, the pendulum, rocket motion, planetary and satellite orbits, linear theory of oscillations, normal modes. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20006 | Stochastic Processes | O | M | 7.5 | 15 | |
| The aim of this module is to examine the mathematics of random processes with particular reference to biological and social sciences. The course will include: revision of probability and distribution theory, difference equations, Markov chains, branching and Poisson processes, birth and death processes, queues, reliability and lifetime distributions. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20010 | Linear and Metric Spaces | O | M | 7.5 | 15 | |
| The aim of this module is to introduce the concept of an abstract vector (linear) space, and then the concept of a metric space. The module builds on the knowledge of analysis and matrix algebra gained from MAT-10015, 10016 and 20009. The module includes: vector spaces, subspaces, bases and dimension, linear transformations, inner products and norms, metric spaces, convergence, topological ideas, completeness and contraction mappings. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20013 | Mathematics - Study Abroad III | O | C | 7.5 | 15 | |
| MAT-20014 | Mathematics - Study Abroad IV | O | C | 7.5 | 15 | |
| MAT-20016 | Mathematical Modelling | O | M | 7.5 | 15 | |
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-30002 | Non-linear Differential Equations | O | M | 7.5 | 15 | |
| Systems that evolve in time can often be modelled by differential equations. There are countless examples of such systems from the physical world including the weather, climate change, stock markets, the economy, population dynamics, mechanical systems, etc. The great variety of behaviours exhibited by these systems is reflected in the solutions to the corresponding differential equations. This module introduces a number of methods for identifying and classifying various types of behaviour in various types of differential equation. While linear differential equations model some processes, the majority are described by nonlinear equations, and it is these that display the greatest diversity of behaviour. However, very few nonlinear differential equations have exact solutions. Nevertheless, a great deal of insight can be obtained from qualitative methods. This module focuses on geometric methods for constructing phase plane representations of dynamics and perturbation methods for obtaining approximate solutions. With these tools it is then possible to examine the changes in behaviour that can occur when a parameter is varied, and bifurcation theory is introduced to describe this. The relation between the evolution of differential equations and the evolution of maps is explained, and more exotic behaviour, like period doubling and chaos, are then studied in terms of the dynamics of maps. | ||||||
| MAT-30003 | Partial Differential Equations | C | M | 7.5 | 15 | |
| This module provides an introduction to analytical methods for solving partial differential equations (PDEs). Throughout the module focuses on PDEs in two independent variables, although generalisation to three, or more, independent variables is briefly discussed. The module begins by introducing the method of characteristics for solving first order linear and quasi-linear PDEs. This is followed by the classification of linear second order PDEs into hyperbolic, parabolic or elliptic type, with a detailed treatment of the reduction to canonical form in each case. Thereafter, the module introduces the separation of variables technique and transform methods to solve the wave, diffusion, Laplace and Poisson equations. These PDEs are frequently encountered in many branches of applied mathematics, including fluid dynamics, mathematical biology, financial mathematics and electromagnetism. Finally the module introduces the technique of eigenfunction expansions for solving inhomogeneous PDEs, and the powerful technique of Green’s functions. | ||||||
| MAT-30005 | Relativity | O | M | 7.5 | 15 | |
| Relativity is a theory of space and time. It consists of two fundamentally different areas, that is, Special Relativity and General Relativity. Special Relativity was first proposed by Einstein in 1905 and is concerned with the connection between observations made in frames of reference that move with constant velocity relative to each other. It has many practical applications in situations which involve extremely high speeds. General Relativity was first proposed by Einstein in 1916 and incorporates non-uniform motion. Its main applications lie in gravitation theory, including astrophysics and cosmology. This module gives an introduction to both Special and General Relativity from a mainly mathematical point of view. The standard applications to physical problems are given, but experimental details are kept to a minimum. | ||||||
| MAT-30008 | Mathematical Programming | O | M | 7.5 | 15 | |
| Mathematical programming involves maximizing or minimizing a real function of several variables subject to a list of constraints. It is a major branch of Operational Research, where the formulation is typically a model of an organizational problem; although there are many applications in the social and natural sciences and also in other areas of mathematics. The module studies the mathematical underpinnings of various algorithms for solving different classes of problem, with a strong emphasis on linearity. Some specific applications are mentioned, but the module deals primarily with theory and methods. The work builds upon the account of the Simplex method given in MAT - 10005; this material will be assumed. | ||||||
| MAT-30009 | Discrete Mathematics | O | M | 7.5 | 15 | |
| This module contains a selection of topics in Discrete Mathematics. The motivation is to show how real projective geometry may be generalised to geometries over any field, and then applied, in the case of finite fields, to solve problems in the construction of combinatorial designs and error-correcting codes. Approximately equal emphasis is placed on theory and applications. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||
| MAT-30021 | Numerical Analysis | O | M | 7.5 | 15 | |
| This module is concerned with the analysis of numerical methods, concentrating on how to select a suitable method and analyse the results produced, rather than on programming the methods themselves. Substantial use is made of technology in terms of existing teaching packages, computer algebra and hand held technologies, all of which provide transferable skills. There are regular computer laboratory sessions at which students will be expected to use any and all of the methods introduced in lectures. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-30001 | Graph Theory | O | M | 7.5 | 15 | |
| This module introduces the concept of a graph as a pictorial representation of a symmetric relation. A variety of topics are investigated and, for each one, at least one of the major theorems is proved. The emphasis is on pure graph theory although a significant number of applications are explored via worked examples and coursework. | ||||||
| MAT-30004 | Fluid Mechanics | O | M | 7.5 | 15 | |
| The module is a first course in fluid mechanics, designed for students with no previous knowledge of the subject. Although previous acquaintance with vectors and differential equations would be helpful, the lecturer will offer revision of the required parts of these subjects as the module progresses. | ||||||
| MAT-30006 | Logic | O | M | 7.5 | 15 | |
| The aim of the module is to introduce mathematical concepts for examining philosophical questions about the nature of mathematics as a whole. It attempts to present a sophisticated perspective on mathematics in a way that is accessible to undergraduates. The first half of the module concerns the subject-matter of mathematics. The thesis is developed that all mathematical objects can be understood as sets; set theory is developed in an informal axiomatic spirit, based on Gödel’s notion of transfinite iteration of the ‘set of’ operation. The second half examines mathematical reasoning, which is formalised as predicate calculus and studied metamathematically. The basic apparatus of formal semantics is introduced, and issues such as completeness and categoricity are surveyed informally. | ||||||
| MAT-30010 | Complex Variable II | O | M | 7.5 | 15 | |
| This module revises and consolidates the material of MAT - 20004: Complex Variable I, before studying further applications of contour integration and the Residue Theorem. It then provides an introduction to conformal mappings, together with some of their applications, in particular their application in determining harmonic functions in two-dimensional regions. The module also covers certain analytical aspects of complex functions. | ||||||
| MAT-30011 | Waves | O | M | 7.5 | 15 | |
| The module aims to give an account of the underlying mathematical theory that describes the behaviour of waves. The mathematical development of the subject is combined with a discussion of applications, for example musical instruments. The module material is illuminated by small demonstrations and by computer-generated animations of wave processes. The topics include: the wave equation, waves on stretched strings, waves on membranes, waves on beams, sound waves, and waves in liquids with a free surface. | ||||||
| MAT-30013 | Group Theory | O | M | 7.5 | 15 | |
| This module builds on the Group Theory introduced in MAT - 20009 to develop some of the mathematics underlying the classification of finite groups. This culminates in a proof of Sylow’s First Theorem which offers a partial converse to Lagrange’s Theorem proved in MAT - 20009. The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented. | ||||||
| MAT-30014 | Medical Statistics | O | M | 7.5 | 15 | |
| This module illustrates the application of statistical techniques to health related research. Methods are applied using data from real-life studies, with particular emphasis placed on cancer studies. No prior knowledge of medicine or biology is required. The module commences with a revision of hypothesis testing procedures. This is followed by three main topics: clinical trials, survival analysis and epidemiology. Clinical trials are immensely important for evaluating the relative effectiveness of different treatments, and their design and analysis are considered in-depth. Survival analysis looks at the features and analysis of data from studies of patients with a potentially fatal disease. Epidemiology explores the distribution of disease in a population and discusses studies for assessing whether there is a possible association between a factor (such as, smoking, eating beef, using a mobile phone) and the subsequent development of a disease. | ||||||
| # | MAT-30016 | Project II | O | C | 7.5 | 15 |
| There is available in the Department a list of possible projects and supervisors. The nature of the project depends of the topic, but students are required to submit a report and to give an oral presentation on their work both of which will be assessed. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-10025 | Mathematical Methods I | C | M | 7.5 | 15 | |
| This module develops students' skills in mathematical techniques, mainly in differentiation and integration. It begins by revising the standard elementary functions and their properties and continues with the revision of basic results and techniques in differentiation. There then follows sections on Taylor series and on complex numbers. The module next revises basic results and techniques in integration. Finally there is material concerning functions of more than one variable, partial differentiation, the chain rule and maxima and minima. | ||||||
| MAT-10031 | Foundations of Analysis | C | M | 7.5 | 15 | |
| This module is intended as an introduction to rigour in Mathematics. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module comprises a development of real analysis and covers the real number system, sequences, series and limits. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-10028 | Probability & Operational Research | C | M | 7.5 | 15 | |
| The first part of this module is an introduction to the axiomatic treatment of probability and to random variables. The second part presents the basic theory of linear programming problems and the Simplex method for solving them. | ||||||
| MAT-10029 | Mathematical Methods II | C | M | 7.5 | 15 | |
| This module continues from Mathematical Methods I and provides further techniques in calculus as well as an introduction to matrix and vector algebra. Topics will include matrix algebra, elementary row operations, solving linear equations, determinants, eigenvalues and eigenvectors, diagonalisation of matrices, three dimensional vector algebra and geometry, lines and planes, general vector algebra, linear independence and bases; double integration, first order differential equations: separable and linear equations, second order differential equations with constant coefficients. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-20008 | Differential Equations | C | M | 7.5 | 15 | |
| The aim of the module is to develop mathematical techniques and focuses on methods of solving ordinary differential equations. The topics include: solutions to first-order equations, higher order linear equations, power series methods, graphical aspects of differential equations, Fourier series and Laplace transforms. 2 hours lectures & 1 hour examples/laboratory class | ||||||
| MAT-20009 | Analysis and Abstract Algebra | C | M | 7.5 | 15 | |
| The aims of this module are to build upon the first year analysis course in order to develop a rigorous theory of functions of a real variable, and to introduce abstraction in mathematics through the study of abstract algebra. The module includes: limits of functions of a real variable, continuity, differentiation and Riemann integration; equivalence relations, elementary group theory, applications to number theory, modulo arithmetic, and an introduction to rings and fields. 3 hours lectures & 1 hour examples class | ||||||
| MAT-20011 | Mathematics - Study Abroad I | O | C | 7.5 | 15 | |
| MAT-20012 | Mathematics - Study Abroad II | O | C | 7.5 | 15 | |
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-20004 | Complex Variable I and Vector Calculus | C | M | 7.5 | 15 | |
| This module contains a course on vector calculus and a first course in functions of a complex variable. The topics covered include: complex functions, analytic functions, Cauchy’s theorems, complex power series, singularities, the residue theorem, contour integration, differentiation of vectors, differential operators, integration of vectors, the divergence theorem and Stokes’ theorem. | ||||||
| MAT-20005 | Dynamics | O | M | 7.5 | 15 | |
| The module is an introduction to dynamics with applications mainly to systems which can be modelled by particle dynamics. The topics investigated include: Newton’s laws, momentum, kinetic and potential energy, projectiles, simple harmonic motion, springs, the pendulum, rocket motion, planetary and satellite orbits, linear theory of oscillations, normal modes. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20006 | Stochastic Processes | O | M | 7.5 | 15 | |
| The aim of this module is to examine the mathematics of random processes with particular reference to biological and social sciences. The course will include: revision of probability and distribution theory, difference equations, Markov chains, branching and Poisson processes, birth and death processes, queues, reliability and lifetime distributions. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20010 | Linear and Metric Spaces | O | M | 7.5 | 15 | |
| The aim of this module is to introduce the concept of an abstract vector (linear) space, and then the concept of a metric space. The module builds on the knowledge of analysis and matrix algebra gained from MAT-10015, 10016 and 20009. The module includes: vector spaces, subspaces, bases and dimension, linear transformations, inner products and norms, metric spaces, convergence, topological ideas, completeness and contraction mappings. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20013 | Mathematics - Study Abroad III | O | C | 7.5 | 15 | |
| MAT-20014 | Mathematics - Study Abroad IV | O | C | 7.5 | 15 | |
| MAT-20016 | Mathematical Modelling | O | M | 7.5 | 15 | |
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-10025 | Mathematical Methods I | C | M | 7.5 | 15 | |
| This module develops students' skills in mathematical techniques, mainly in differentiation and integration. It begins by revising the standard elementary functions and their properties and continues with the revision of basic results and techniques in differentiation. There then follows sections on Taylor series and on complex numbers. The module next revises basic results and techniques in integration. Finally there is material concerning functions of more than one variable, partial differentiation, the chain rule and maxima and minima. | ||||||
| MAT-10027 | Introduction to Data Analysis and Statistical Software | EP | C | 7.5 | 15 | |
| This module is an introduction to all aspects of data analysis. It begins by explaining the importance of the rigourous techniques necessary for reliable and valid statistical analysis using a typical statistical software package, MINITAB. Although the emphasis is on the practical applications of statistical techniques, the theory of probability and random variables studied elsewhere is drawn upon, to underpin the ideas and methods encountered. The first part of the module concentrates on graphical and numerical methods for exploring data and on gaining familiarity with MINITAB. Formal approaches to modelling and making inferences are covered in the second part. Case studies are used throughtout to demonstrate how statistical methods can be applied in practice. | ||||||
| MAT-10030 | Topics in Pure Mathematics | C | C | 7.5 | 15 | |
| This module introduces ideas and techniques in three areas of pure mathematics: number theory, geometry and polynomials. Topics include: Fibonacci numbers and chaos, projective geometry and topology, and the search for solutions to cubic, quartic and quintic equations. | ||||||
| MAT-10031 | Foundations of Analysis | C | M | 7.5 | 15 | |
| This module is intended as an introduction to rigour in Mathematics. It begins by discussing mathematical statements and the meaning and basic strategies of proof. This is followed by a short exposition of naive set theory and by a careful treatment of the notion of a function. The remainder of the module comprises a development of real analysis and covers the real number system, sequences, series and limits. | ||||||
| MAT-10033 | Introduction to Mathematical Software | O | C | 7.5 | 15 | |
| This module introduces students to the latest developments in computerised mathematics systems, using the advanced mathematical software, Mathematica, throughout, and shows how the software can be used to solve complex mathematical and scientific problems. The module begins by examining the structure of common mathematical functions in Mathematica and introducing some basic Mathematica commands to plot, differentiate and integrate functions. It goes on to look at how Mathematica works with complex numbers, equations, vectors and matrices. Next, methods for investigating the solutions of differential equations and recurrence relations in Mathematica are examined. Lastly, using the material covered in the module, Mathematica is applied to some real problems in mathematics. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-10027 | Introduction to Data Analysis and Statistical Software | O | C | 7.5 | 15 | |
| This module is an introduction to all aspects of data analysis. It begins by explaining the importance of the rigourous techniques necessary for reliable and valid statistical analysis using a typical statistical software package, MINITAB. Although the emphasis is on the practical applications of statistical techniques, the theory of probability and random variables studied elsewhere is drawn upon, to underpin the ideas and methods encountered. The first part of the module concentrates on graphical and numerical methods for exploring data and on gaining familiarity with MINITAB. Formal approaches to modelling and making inferences are covered in the second part. Case studies are used throughtout to demonstrate how statistical methods can be applied in practice. | ||||||
| MAT-10027 | Introduction to Data Analysis and Statistical Software | EP | C | 7.5 | 15 | |
| This module is an introduction to all aspects of data analysis. It begins by explaining the importance of the rigourous techniques necessary for reliable and valid statistical analysis using a typical statistical software package, MINITAB. Although the emphasis is on the practical applications of statistical techniques, the theory of probability and random variables studied elsewhere is drawn upon, to underpin the ideas and methods encountered. The first part of the module concentrates on graphical and numerical methods for exploring data and on gaining familiarity with MINITAB. Formal approaches to modelling and making inferences are covered in the second part. Case studies are used throughtout to demonstrate how statistical methods can be applied in practice. | ||||||
| MAT-10028 | Probability & Operational Research | C | M | 7.5 | 15 | |
| The first part of this module is an introduction to the axiomatic treatment of probability and to random variables. The second part presents the basic theory of linear programming problems and the Simplex method for solving them. | ||||||
| MAT-10029 | Mathematical Methods II | C | M | 7.5 | 15 | |
| This module continues from Mathematical Methods I and provides further techniques in calculus as well as an introduction to matrix and vector algebra. Topics will include matrix algebra, elementary row operations, solving linear equations, determinants, eigenvalues and eigenvectors, diagonalisation of matrices, three dimensional vector algebra and geometry, lines and planes, general vector algebra, linear independence and bases; double integration, first order differential equations: separable and linear equations, second order differential equations with constant coefficients. | ||||||
| MAT-10032 | Introduction to Mathematical Modelling and Dynamics | C | M | 7.5 | 15 | |
| The aim of the module is to introduce the application of mathematics in the modelling of physical systems. The module includes applications of first and second order differential equations and an introduction to dynamics. The topics investigated include: Newton’s Laws, momentum, kinetic and potential energy, projectiles, simple harmonic motion, springs, pendulums, rocket motion, planetary and satellite orbits, together with other physical processes modelled through first and second order differential equations. It is envisaged that upon successful completion of this module, a student will have gained skills in problem solving and also skills in translating a verbal problem into mathematics, solving the resulting equations and interpreting the solutions. | ||||||
| MAT-10033 | Introduction to Mathematical Software | O | C | 7.5 | 15 | |
| This module introduces students to the latest developments in computerised mathematics systems, using the advanced mathematical software, Mathematica, throughout, and shows how the software can be used to solve complex mathematical and scientific problems. The module begins by examining the structure of common mathematical functions in Mathematica and introducing some basic Mathematica commands to plot, differentiate and integrate functions. It goes on to look at how Mathematica works with complex numbers, equations, vectors and matrices. Next, methods for investigating the solutions of differential equations and recurrence relations in Mathematica are examined. Lastly, using the material covered in the module, Mathematica is applied to some real problems in mathematics. | ||||||
| MAT-10033 | Introduction to Mathematical Software | EP | C | 7.5 | 15 | |
| This module introduces students to the latest developments in computerised mathematics systems, using the advanced mathematical software, Mathematica, throughout, and shows how the software can be used to solve complex mathematical and scientific problems. The module begins by examining the structure of common mathematical functions in Mathematica and introducing some basic Mathematica commands to plot, differentiate and integrate functions. It goes on to look at how Mathematica works with complex numbers, equations, vectors and matrices. Next, methods for investigating the solutions of differential equations and recurrence relations in Mathematica are examined. Lastly, using the material covered in the module, Mathematica is applied to some real problems in mathematics. | ||||||
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-20002 | Statistical Inference I | C | M | 7.5 | 15 | |
| This module builds on MAT-10005 to provide the theoretical background for statistical applications to be studied in later modules as well as illustrating how statistical theory is put into practice in a variety of hypothesis testing situations. The topics covered are: Distributions of functions of random variables, sampling theory, properties of point estimators, maximum likelihood, method of moments, interval estimation, hypothesis testing, Neyman-Pearson lemma, and some parametric and nonparametric tests. 3 hours lectures & 1 hour examples class | ||||||
| MAT-20003 | Operational Research II | O | M | 7.5 | 15 | |
| The module represents a wide variety of techniques for solving quantitative problems arising in management and everyday life. The topics include: the transportation problem, dynamic programming, critical path analysis, scheduling, reliability, replacement and inventory models. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20008 | Differential Equations | C | M | 7.5 | 15 | |
| The aim of the module is to develop mathematical techniques and focuses on methods of solving ordinary differential equations. The topics include: solutions to first-order equations, higher order linear equations, power series methods, graphical aspects of differential equations, Fourier series and Laplace transforms. 2 hours lectures & 1 hour examples/laboratory class | ||||||
| MAT-20009 | Analysis and Abstract Algebra | C | M | 7.5 | 15 | |
| The aims of this module are to build upon the first year analysis course in order to develop a rigorous theory of functions of a real variable, and to introduce abstraction in mathematics through the study of abstract algebra. The module includes: limits of functions of a real variable, continuity, differentiation and Riemann integration; equivalence relations, elementary group theory, applications to number theory, modulo arithmetic, and an introduction to rings and fields. 3 hours lectures & 1 hour examples class | ||||||
| MAT-20011 | Mathematics - Study Abroad I | O | C | 7.5 | 15 | |
| MAT-20012 | Mathematics - Study Abroad II | O | C | 7.5 | 15 | |
| MAT-20015 | Numerical Methods | O | M | 7.5 | 15 | |
| Topics include: the solution of algebraic equations, numerical quadrature, the numerical solution of differential equations including the Euler and Runge-Kutta methods, the solution of linear equations by direct and iterative methods, and numerical methods for determining eigenvalues and eigenvectors. 2 hours lectures & 1 hour examples class. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-20004 | Complex Variable I and Vector Calculus | C | M | 7.5 | 15 | |
| This module contains a course on vector calculus and a first course in functions of a complex variable. The topics covered include: complex functions, analytic functions, Cauchy’s theorems, complex power series, singularities, the residue theorem, contour integration, differentiation of vectors, differential operators, integration of vectors, the divergence theorem and Stokes’ theorem. | ||||||
| MAT-20006 | Stochastic Processes | C | M | 7.5 | 15 | |
| The aim of this module is to examine the mathematics of random processes with particular reference to biological and social sciences. The course will include: revision of probability and distribution theory, difference equations, Markov chains, branching and Poisson processes, birth and death processes, queues, reliability and lifetime distributions. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20010 | Linear and Metric Spaces | C | M | 7.5 | 15 | |
| The aim of this module is to introduce the concept of an abstract vector (linear) space, and then the concept of a metric space. The module builds on the knowledge of analysis and matrix algebra gained from MAT-10015, 10016 and 20009. The module includes: vector spaces, subspaces, bases and dimension, linear transformations, inner products and norms, metric spaces, convergence, topological ideas, completeness and contraction mappings. 2 hours lectures & 1 hour examples class | ||||||
| MAT-20013 | Mathematics - Study Abroad III | O | C | 7.5 | 15 | |
| MAT-20014 | Mathematics - Study Abroad IV | O | C | 7.5 | 15 | |
| MAT-20016 | Mathematical Modelling | C | M | 7.5 | 15 | |
| Semester 1 | C/O | TYP | ECTS | CATS | ||
| MAT-30002 | Non-linear Differential Equations | O | M | 7.5 | 15 | |
| Systems that evolve in time can often be modelled by differential equations. There are countless examples of such systems from the physical world including the weather, climate change, stock markets, the economy, population dynamics, mechanical systems, etc. The great variety of behaviours exhibited by these systems is reflected in the solutions to the corresponding differential equations. This module introduces a number of methods for identifying and classifying various types of behaviour in various types of differential equation. While linear differential equations model some processes, the majority are described by nonlinear equations, and it is these that display the greatest diversity of behaviour. However, very few nonlinear differential equations have exact solutions. Nevertheless, a great deal of insight can be obtained from qualitative methods. This module focuses on geometric methods for constructing phase plane representations of dynamics and perturbation methods for obtaining approximate solutions. With these tools it is then possible to examine the changes in behaviour that can occur when a parameter is varied, and bifurcation theory is introduced to describe this. The relation between the evolution of differential equations and the evolution of maps is explained, and more exotic behaviour, like period doubling and chaos, are then studied in terms of the dynamics of maps. | ||||||
| MAT-30003 | Partial Differential Equations | C | M | 7.5 | 15 | |
| This module provides an introduction to analytical methods for solving partial differential equations (PDEs). Throughout the module focuses on PDEs in two independent variables, although generalisation to three, or more, independent variables is briefly discussed. The module begins by introducing the method of characteristics for solving first order linear and quasi-linear PDEs. This is followed by the classification of linear second order PDEs into hyperbolic, parabolic or elliptic type, with a detailed treatment of the reduction to canonical form in each case. Thereafter, the module introduces the separation of variables technique and transform methods to solve the wave, diffusion, Laplace and Poisson equations. These PDEs are frequently encountered in many branches of applied mathematics, including fluid dynamics, mathematical biology, financial mathematics and electromagnetism. Finally the module introduces the technique of eigenfunction expansions for solving inhomogeneous PDEs, and the powerful technique of Green’s functions. | ||||||
| MAT-30005 | Relativity | O | M | 7.5 | 15 | |
| Relativity is a theory of space and time. It consists of two fundamentally different areas, that is, Special Relativity and General Relativity. Special Relativity was first proposed by Einstein in 1905 and is concerned with the connection between observations made in frames of reference that move with constant velocity relative to each other. It has many practical applications in situations which involve extremely high speeds. General Relativity was first proposed by Einstein in 1916 and incorporates non-uniform motion. Its main applications lie in gravitation theory, including astrophysics and cosmology. This module gives an introduction to both Special and General Relativity from a mainly mathematical point of view. The standard applications to physical problems are given, but experimental details are kept to a minimum. | ||||||
| MAT-30008 | Mathematical Programming | O | M | 7.5 | 15 | |
| Mathematical programming involves maximizing or minimizing a real function of several variables subject to a list of constraints. It is a major branch of Operational Research, where the formulation is typically a model of an organizational problem; although there are many applications in the social and natural sciences and also in other areas of mathematics. The module studies the mathematical underpinnings of various algorithms for solving different classes of problem, with a strong emphasis on linearity. Some specific applications are mentioned, but the module deals primarily with theory and methods. The work builds upon the account of the Simplex method given in MAT - 10005; this material will be assumed. | ||||||
| MAT-30009 | Discrete Mathematics | O | M | 7.5 | 15 | |
| This module contains a selection of topics in Discrete Mathematics. The motivation is to show how real projective geometry may be generalised to geometries over any field, and then applied, in the case of finite fields, to solve problems in the construction of combinatorial designs and error-correcting codes. Approximately equal emphasis is placed on theory and applications. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||
| MAT-30021 | Numerical Analysis | O | M | 7.5 | 15 | |
| This module is concerned with the analysis of numerical methods, concentrating on how to select a suitable method and analyse the results produced, rather than on programming the methods themselves. Substantial use is made of technology in terms of existing teaching packages, computer algebra and hand held technologies, all of which provide transferable skills. There are regular computer laboratory sessions at which students will be expected to use any and all of the methods introduced in lectures. | ||||||
| Semester 2 | C/O | TYP | ECTS | CATS | ||
| MAT-30001 | Graph Theory | O | M | 7.5 | 15 | |
| This module introduces the concept of a graph as a pictorial representation of a symmetric relation. A variety of topics are investigated and, for each one, at least one of the major theorems is proved. The emphasis is on pure graph theory although a significant number of applications are explored via worked examples and coursework. | ||||||
| MAT-30004 | Fluid Mechanics | O | M | 7.5 | 15 | |
| The module is a first course in fluid mechanics, designed for students with no previous knowledge of the subject. Although previous acquaintance with vectors and differential equations would be helpful, the lecturer will offer revision of the required parts of these subjects as the module progresses. | ||||||
| MAT-30006 | Logic | O | M | 7.5 | 15 | |
| The aim of the module is to introduce mathematical concepts for examining philosophical questions about the nature of mathematics as a whole. It attempts to present a sophisticated perspective on mathematics in a way that is accessible to undergraduates. The first half of the module concerns the subject-matter of mathematics. The thesis is developed that all mathematical objects can be understood as sets; set theory is developed in an informal axiomatic spirit, based on Gödel’s notion of transfinite iteration of the ‘set of’ operation. The second half examines mathematical reasoning, which is formalised as predicate calculus and studied metamathematically. The basic apparatus of formal semantics is introduced, and issues such as completeness and categoricity are surveyed informally. | ||||||
| MAT-30010 | Complex Variable II | O | M | 7.5 | 15 | |
| This module revises and consolidates the material of MAT - 20004: Complex Variable I, before studying further applications of contour integration and the Residue Theorem. It then provides an introduction to conformal mappings, together with some of their applications, in particular their application in determining harmonic functions in two-dimensional regions. The module also covers certain analytical aspects of complex functions. | ||||||
| MAT-30011 | Waves | O | M | 7.5 | 15 | |
| The module aims to give an account of the underlying mathematical theory that describes the behaviour of waves. The mathematical development of the subject is combined with a discussion of applications, for example musical instruments. The module material is illuminated by small demonstrations and by computer-generated animations of wave processes. The topics include: the wave equation, waves on stretched strings, waves on membranes, waves on beams, sound waves, and waves in liquids with a free surface. | ||||||
| MAT-30013 | Group Theory | O | M | 7.5 | 15 | |
| This module builds on the Group Theory introduced in MAT - 20009 to develop some of the mathematics underlying the classification of finite groups. This culminates in a proof of Sylow’s First Theorem which offers a partial converse to Lagrange’s Theorem proved in MAT - 20009. The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented. | ||||||
| MAT-30014 | Medical Statistics | O | M | 7.5 | 15 | |
| This module illustrates the application of statistical techniques to health related research. Methods are applied using data from real-life studies, with particular emphasis placed on cancer studies. No prior knowledge of medicine or biology is required. The module commences with a revision of hypothesis testing procedures. This is followed by three main topics: clinical trials, survival analysis and epidemiology. Clinical trials are immensely important for evaluating the relative effectiveness of different treatments, and their design and analysis are considered in-depth. Survival analysis looks at the features and analysis of data from studies of patients with a potentially fatal disease. Epidemiology explores the distribution of disease in a population and discusses studies for assessing whether there is a possible association between a factor (such as, smoking, eating beef, using a mobile phone) and the subsequent development of a disease. | ||||||
| # | MAT-30016 | Project II | O | C | 7.5 | 15 |
| There is available in the Department a list of possible projects and supervisors. The nature of the project depends of the topic, but students are required to submit a report and to give an oral presentation on their work both of which will be assessed. | ||||||
| # | MAT-30019 | Dissertation & Communication Skills in Mathematics | O | C | 7.5 | 15 |
| This module allows students to acquire and demonstrate skills in compiling a dissertation and preparing an oral presentation for each of two approved topics in mathematics. | ||||||