Students preparing for their graduation ceremony at Canterbury Cathedral

Mathematics and its Applications with an Industrial Placement - MSc

2018

Studying Mathematics at postgraduate level gives you a chance to begin your own research, develop your own creativity and be part of a long tradition of people investigating analytic, geometric and algebraic ideas.

2018

Overview

This programme allows you to further enhance your knowledge, creativity and computational skills in core mathematical subjects and their applications giving you a competitive advantage in a wide range of mathematically based careers. The modules, which are designed and taught by internationally known researchers, are accessible, relevant, interesting and challenging.

 

About the School of Mathematics, Statistics and Actuarial Science (SMSAS)

The School has a strong reputation for world-class research as indicated by our results in the latest Research Excellence Framework (REF). Postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School.

The Research Excellence Framework (REF) 2014 rated 72% of the School's research output as International Quality or above. The School is in the top 25 in the UK when considered on weighted GPA.

The Mathematics Group also has an excellent track record of winning research grants from the Engineering and Physical Sciences Research Council (EPSRC), the Royal Society, the EU, the London Mathematical Society and the Leverhulme Trust.

National ratings

In the Research Excellence Framework (REF) 2014, research by the School of Mathematics, Statistics and Actuarial Science was ranked 25th in the UK for research power and 100% or our research was judged to be of international quality.

An impressive 92% of our research-active staff submitted to the REF and the School’s environment was judged to be conducive to supporting the development of world-leading research.

Course structure

At least one modern application of mathematics is studied in-depth by each student. Mathematical computing and open-ended project work forms an integral part of the learning experience. There are opportunities for outreach and engagement with the public on mathematics.

The programme provides opportunities for students to develop and demonstrate knowledge and understanding, qualities, skills and other attributes in the following areas:

  1. Applications of mathematical theories, methods and techniques
  2. The power of generalisation, abstraction and logical argument
  3. Nonlinear and noncommutative phenomena
  4. Geometric, algebraic and analytic thinking
  5. Mathematical computation

Your placement

Placements normally commence shortly after completion of Stage 1 of the MSc (June) or after completion of the short dissertation (August) and vary in length from three months to 50 weeks, extending the MSc programme to between 15 and 24 months.  The start date and duration depend on the employer. Students on a longer placement module (i.e. 6, 9 or 12 months) can transfer to a shorter module if the placement arrangement changes unavoidably once the student has embarked on it, but if a student cannot complete the minimum of three months placement he/she will be required to transfer to the MSc programme without a placement. Placements may be undertaken in the UK or overseas (the University does not guarantee every student will find a placement.  Those who do not secure a placement will be transferred to the MSc programme without a placement).

The placement consists of two modules: Industrial Placement Experience and Industrial Placement Report. Four versions of the Experience module exist to cover placements of different lengths. The Experience module is assessed as pass/fail only and the Report module is graded on a categorical scale.

Modules

The following modules are indicative of those offered on this programme. This list is based on the current curriculum and may change year to year in response to new curriculum developments and innovation.  Most programmes will require you to study a combination of compulsory and optional modules. You may also have the option to take modules from other programmes so that you may customise your programme and explore other subject areas that interest you.

Modules may include Credits

The aim of this module is to equip students with the skills needed to communicate efficiently the findings of a recent piece of research. This module is supported by a series of workshops covering various forms of written and oral communication. Each student will chose a topic in mathematics, statistics or financial mathematics from a published list on which to base their three coursework assessments which include a scientific writing assessment and an oral presentation.

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15

Students spend a period doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied earlier during their degree programme. Employer evaluation, personal and professional reviews and on-line blogs are assessed.

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30

Students spend a period of time doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their MSc programme.

The work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of the module.

Participation in this module is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students completing the taught component of their studies. The University does not guarantee that every student will find a placement.

Students who do not obtain a placement will be required to transfer to the appropriate programme without an Industrial Placement.

Read more
30

Students spend a period of time doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their MSc programme.

The work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of the module.

Participation in this module is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students completing the taught component of their studies. The University does not guarantee that every student will find a placement.

Students who do not obtain a placement will be required to transfer to the appropriate programme without an Industrial Placement.

Read more
60

Students spend a period of time doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their MSc programme.

The work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of the module.

Participation in this module is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students completing the taught component of their studies. The University does not guarantee that every student will find a placement.

Students who do not obtain a placement will be required to transfer to the appropriate programme without an Industrial Placement.

Read more
90

Students spend a period of time doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their MSc programme.

The work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of the module.

Participation in this module is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students completing the taught component of their studies. The University does not guarantee that every student will find a placement.

Students who do not obtain a placement will be required to transfer to the appropriate programme without an Industrial Placement.

Read more
120

Discrete mathematics has found new applications in the encoding of information. Online banking requires the encoding of information to protect it from eavesdroppers. Digital television signals are subject to distortion by noise, so information must be encoded in a way that allows for the correction of this noise contamination. Different methods are used to encode information in these scenarios, but they are each based on results in abstract algebra. This module will provide a self-contained introduction to this general area of mathematics.

Syllabus: Modular arithmetic, polynomials and finite fields. Applications to

• orthogonal Latin squares,

• cryptography, including introduction to classical ciphers and public key ciphers such as RSA,

• "coin-tossing over a telephone",

• linear feedback shift registers and m-sequences,

• cyclic codes including Hamming,

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15

Most differential equations which arise from physical systems cannot be solved explicitly in closed form, and thus numerical solutions are an invaluable way to obtain information about the underlying physical system. The first half of the module is concerned with ordinary differential equations. Several different numerical methods are introduced and error growth is studied. Both initial value and boundary value problems are investigated. The second half of the module deals with the numerical solution of partial differential equations. The syllabus includes: initial value problems for ordinary differential equations; Taylor methods; Runge-Kutta methods; multistep methods; error bounds and stability; boundary value problems for ordinary differential equations; finite difference schemes; difference schemes for partial differential equations; iterative methods; stability analysis.

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15

Combinatorial games, game trees, strategy, classification of positions. Two-player zero-sum games, security levels, pure and mixed strategies, von Neumann's minimax theorem. Solving zero-sum two player games using linear programming. Arbitrary sum games, utility, and matrix games. Nash equilibrium, Nash equilibrium theorem, applications, and cooperation. Multi-player games, coalitions, and the Shapley value.

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15

This module provides an introduction to the study of orthogonal polynomials and special functions. They are essentially useful mathematical functions with remarkable properties and applications in mathematical physics and other branches of mathematics. Closely related to many branches of analysis, orthogonal polynomials and special functions are related to important problems in approximation theory of functions, the theory of differential, difference and integral equations, whilst having important applications to recent problems in quantum mechanics, mathematical statistics, combinatorics and number theory. The emphasis will be on developing an understanding of the structural, analytical and geometrical properties of orthogonal polynomials and special functions. The module will utilise physical, combinatorial and number theory problems to illustrate the theory and give an insight into a plank of applications, whilst including some recent developments in this field. The development will bring aspects of mathematics as well as computation through the use of MAPLE and a discussion of elliptic and theta functions.

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15

The module is intended to serve as an introduction to point-set topology, focusing on examples and applications. This will also enhance other modules by providing examples and concepts relevant to Functional Analysis, Algebra and Mathematical Physics.

The syllabus will include but is not restricted to topics from the following list:

• Basic definitions and examples (Euclidean and discrete spaces and non-metrizable examples such as the finite complement topology)

• Continuity and convergence in general topological spaces (especially related to the examples above)

• Product topology, subspace topology, quotient topology (including real and complex projective spaces)

• Compactness, including comparing different characterisations of compactness

• Homotopy and paths

• Homeomorphisms and homotopy equivalence, contractibility

• Connectedness and path-connectedness

• Winding number

• Fixed point theorems

In addition, for level 7 students:

• Advanced topic such as a topological proof of the Fundamental Theorem of Algebra; simply connected spaces.

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15

Groups arise naturally in many areas of mathematics as well as in chemistry and physics. A concrete way to approach groups is by representing them as a group of matrices, in which explicit computations are easy. This approach has been very fruitful in developing our understanding of groups over the last century. It also helps students to understand aspects of their mathematical education in a broader context, in particular concepts from earlier modules (From Geometry to Algebra/Groups and Symmetries and Linear Algebra) have been amalgamated into more general and powerful tools.

This module will provide a rigorous introduction to the main ideas and notions of groups and representations. It will also have a strong computational strand: a large part of the module will be devoted to explicit computations of representations and character tables (a table of complex numbers associated to any finite group).

Syllabus:

1. Review of basic group theory (including matrix groups, the symmetric groups, permutation groups and symmetry groups, subgroups, conjugacy, normal subgroups and quotient groups, homomorphisms, group actions);

2. A concrete approach to groups via representations (including examples via group actions and the language modules);

3. Irreducible representations, Maschke's theorem, Schur's lemma;

4. Characters and their basic properties;

5. Character tables: theory and computations for small groups. Consequences.

In addition, for level 7 students:

6. Simple groups, composition series and the Jordan--Hölder theorem.

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Over a century ago, the Norwegian mathematician Sophus Lie made a simple but profound observation: each well-known method for solving a class of ordinary differential equations (ODEs) uses a change of variables that exploits symmetries of the class. Lie went on to develop this idea into a systematic method for attacking the problem of solving unknown differential equations. Essentially, one can use mathematical tools to force a given differential equation to reveal whether or not it has certain symmetries – provided it has, they can be used to simplify or solve the equation. This module is designed to enable students to understand the mathematics behind Lie's methods and to become proficient in using these powerful tools.

The following topics are covered.

Introduction: Symmetries of geometrical objects, symmetries of some first-order ODEs, solution via symmetries.

Lie symmetries of first-order ODEs: The infinitesimal generator, canonical coordinates, invariant points, Lie symmetries and standard solution methods.

How to find Lie symmetries: The linearized symmetry condition, solution of overdetermined systems, the Lie algebra of point symmetry generators.

Solution of higher-order ODEs: Solvability, differential invariants, reduction of order, invariant solutions.

In addition, for level 7 students:

Advanced topic: This will be selected from the following:

• Symmetry methods for PDEs.

• First integrals and dynamical symmetries.

• Discrete symmetries of ODEs

• Symmetries of difference equations.

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Linear PDEs. Dispersion relations. Review of d'Alembert's solutions of the wave equation.

Quasi-linear first-order PDEs. Total differential equations. Integral curves and integrability conditions. The method of characteristics.

Shock waves. Discontinuous solutions. Breaking time. Rankine-Hugoniot jump condition. Shock waves. Rarefaction waves. Applications of shock waves, including traffic flow.

General first-order nonlinear PDEs. Charpit's method, Monge Cone, the complete integral.

Nonlinear PDEs. Burgers' equation; the Cole-Hopf transformation and exact solutions. Travelling wave and scaling solutions of nonlinear PDEs. Applications of travelling wave and scaling solutions to reaction-diffusion equations. Exact solutions of nonlinear PDEs. Applications of nonlinear waves, including to ocean waves (e.g. rogue waves, tsunamis).

Level 7 Students only. Further applications of shock waves and nonlinear waves.

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Matrix theory: Hermitian and symmetric matrices, spaces of these matrices and the associated inner product, diagonalization, orthonormal basis of eigenvectors, spectral properties, positive definite matrices and their roots

Hilbert space theory: inner product spaces and Hilbert spaces, L^2 and l^2 spaces, orthogonality, bases, Gram-Schmidt procedure, dual space, Riesz representation theorem

Linear operators: the space of bounded linear operators with the operator norm, inverse and adjoint operators, Hermitian operators, infinite matrices, spectrum, compact operators, Hilbert-Schmidt operators, the spectral theorem for compact Hermitian operators.

Additional topics, especially for level 7 students may include:

- the Rayleigh quotient and variational characterisations of eigenvalues,

- the functional calculus,

- applications to Sturm-Liouville systems.

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15

The equations studied in this module will be ordinary differential systems, especially Hamiltonian systems. The aim of this subject area is to obtain and study numerical solutions of these systems that preserve specific qualitative and geometric properties. For certain differential equations, these geometric methods can be far superior to standard numerical methods. The syllabus includes: A review of basic numerical methods, variational methods and Hamiltonian mechanics; Properties that numerical methods can preserve (first integrals, symplecticity, time reversibility); Geometric numerical methods (modified Euler and Runge-Kutta methods, splitting methods); Use and misuse of the various notions of error.

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15

There is growing interest in applying the methods of algebraic topology to data analysis, sensor networks, robotics, etc. The module will develop the necessary elements of algebra and topology, and investigate how these techniques are used in various applications. The syllabus will include: an introduction to manifolds, CW complexes and simplicial complexes; an investigation of the elements of homotopy theory; an exploration of homological and computational methods; applications such as homological sensor networks and topological data analysis.

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15

Quantum mechanics provides an accurate description of nature on a subatomic scale, where the standard rules of classical mechanics fail. It is an essential component of modern technology and has a wide range of fascinating applications. This module introduces some of the key concepts of quantum mechanics from a mathematical point of view. Outline syllabus: why classical mechanics fails; the Schrödinger equation and interpretation of the wavefunction; applications of quantum mechanics.

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15

In this module we will study plane algebraic curves and the way that they arise in applications to other parts of mathematics and physics. Examples include the use of elliptic functions to solve problems in mechanics (e.g. the pendulum, or Euler's equations for rigid body motion), spectral curves of separable Hamiltonian systems, and algebraic curves over finite fields that are used in cryptography. The geometrical properties of a curve are not altered by coordinate transformations, so it is important to identify quantities that are invariant under such transformations. For curves, the most basic invariant is the genus, which is most easily understood in terms of the topology of the associated Riemann surface: it counts the number of handles or “holes”. The case of genus zero (corresponding to the Riemann sphere) is well understood, but curves of genus one (also known as elliptic curves) lead to some of the most interesting and difficult problems in modern number theory.

• Review of basic results from complex analysis and topology;

• Riemann surfaces and plane curves in complex affine and projective space;

• The genus of a curve: degree-genus and Riemann-Hurwitz formulae;

• Genus one: elliptic curves and their group structure; elliptic functions and elliptic integrals, with applications;

• Higher genus: functions, divisors and differentials on algebraic curves; Riemann-Roch theorem; example: hyperelliptic curves.

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Teaching and Assessment

Coursework involving complex problems testing numerical, analytical, geometric, algebraic and logical skills; Computer assignments using specific mathematical software packages discussed in the computing classes; written unseen examinations; Independent dissertation and project.

Continuation to Industrial Placement

Commencement of the placement is conditional on progression to Stage 2, as determined at the interim examination board in June under the same rules as for the programme without a placement.

The placement consists of two modules: Industrial Placement Experience and Industrial Placement Report. Four versions of the Experience module exist to cover placements of different lengths. The Experience module is assessed as pass/fail only and the Report module is graded on a categorical scale.

Programme aims

This programme aims to:

  • provide a Master’s level mathematical education of excellent quality, informed by research and scholarship
  • provide an opportunity to enhance your mathematical creativity, problem-solving skills and advanced computational skills
  • provide an opportunity for you to enhance your oral communication, project design and basic research skills
  • provide an opportunity for you to experience and engage with a creative, research-active professional mathematical environment
  • produce graduates of value to the region and nation by offering you opportunities to learn about mathematics in the context of its application.

Learning outcomes

Knowledge and understanding

You will gain knowledge and understanding of:

  • the applications of mathematical theories, methods and techniques
  • the power of generalisation, abstraction and logical argument
  • the processes and pitfalls of mathematical approximation 
  • nonlinear phenomena
  • geometric thinking
  • non-commutative phenomena
  • algebraic thinking
  • analytic thinking
  • mathematical computation.

Intellectual skills

You develop intellectual skills in:

  • problem solving: the ability to work with self-direction and originality in tackling and solving problems, as well as an ability to provide an analytic approach to mathematical problem-solving
  • independent critical reading of technical material
  • independent creative mathematical inquiry: to develop an understanding of how techniques of research and enquiry are used to create and interpret mathematical knowledge, to show initiative in the application of knowledge
  • logical argument: the ability to formulate detailed rigorous arguments and to deal with complex issues both systematically and creatively.

Subject-specific skills

You gain subject-specific skills in:

  • using mathematical typesetting (LaTeX)
  • the ability to communicate with clarity to both a mathematian and a non-specialist audience
  • carrying out symbolic computation (eg Maple) for deriving further conclusions
  • carrying out numerical computation (eg Matlab) for acquiring further information.

Transferable skills

You will gain the following transferable skills:

  • oral and written communication: the ability to communicate technical material, ideas and results to specialist and non-specialist audiences
  • project design: to independently plan, implement and complete a project to professional level
  • basic research: to be able to select and critically evaluate appropriate material from a variety of sources, be able to use appropriate IT tools, be able to write a literature survey, to investigate a mathematical topic in-depth
  • organisational, decision-making, self-management and time-management skills, including the ability to manage your own learning and self-development, and to plan and implement tasks autonomously
  • practical experience of the application in a working environment of knowledge and skills gained through academic study.

Careers

A postgraduate degree in Mathematics is a flexible and valuable qualification that gives you a competitive advantage in a wide range of mathematically oriented careers. Our programmes enable you to develop the skills and capabilities that employers are looking for including problem-solving, independent thought, report-writing, project management, leadership skills, teamworking and good communication.

Many of our graduates have gone on to work in international organisations, the financial sector, and business. Others have found postgraduate research places at Kent and other universities.

Study support

Postgraduate resources

The University’s Templeman Library houses a comprehensive collection of books and research periodicals. Online access to a wide variety of journals is available through services such as ScienceDirect and SpringerLink. The School has licences for major numerical and computer algebra software packages. Postgraduates are provided with computers in shared offices in the School. The School has two dedicated terminal rooms for taught postgraduate students to use for lectures and self-study.

Support

The School has a well-established system of support and training, with a high level of contact between staff and research students. There are two weekly seminar series: The Mathematics Colloquium at Kent attracts international speakers discussing recent advances in their subject; the Friday seminar series features in-house speakers and visitors talking about their latest work. These are supplemented by weekly discussion groups. The School is a member of the EPSRC-funded London Taught Course Centre for PhD students in the mathematical sciences, and students can participate in the courses and workshops offered by the Centre. The School offers conference grants to enable research students to present their work at national and international conferences.

Dynamic publishing culture

Staff publish regularly and widely in journals, conference proceedings and books. Among others, they have recently contributed to: Advances in Mathematics; Algebra and Representation Theory; Journal of Physics A; Journal of Symbolic Computations; Journal of Topology and Analysis. Details of recently published books can be found within the staff research interests.

Global Skills Award

All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme. The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.  

Entry requirements

A first or second class honours degree in a subject with a significant mathematical content (or equivalent). Students not meeting the entry requirement may take the two year full-time International Master’s in Mathematics and its Applications.

All applicants are considered on an individual basis and additional qualifications, and professional qualifications and experience will also be taken into account when considering applications. 

International students

Please see our International Student website for entry requirements by country and other relevant information for your country. 

English language entry requirements

The University requires all non-native speakers of English to reach a minimum standard of proficiency in written and spoken English before beginning a postgraduate degree. Certain subjects require a higher level.

For detailed information see our English language requirements web pages. 

Need help with English?

Please note that if you are required to meet an English language condition, we offer a number of pre-sessional courses in English for Academic Purposes through Kent International Pathways.

Research areas

Nonlinear differential equations

The research on nonlinear differential equations primarily studies algorithms for their classification, normal forms, symmetry reductions and exact solutions. Boundary value problems are studied from an analytical viewpoint, using functional analysis and spectral theory to investigate properties of solutions. We also study applications of symmetry methods to numerical schemes, in particular the applications of moving frames.

Painlevé equations

Current research on the Painlevé equations involves the structure of hierarchies of rational, algebraic and special function families of exact solutions, Bäcklund transformations and connection formulae using the isomonodromic deformation method. The group is also studying analogous results for the discrete Painlevé equations, which are nonlinear difference equations.

Mathematical biology

Artificial immune systems use nonlinear interactions between cell populations in the immune system as the inspiration for new computer algorithms. We are using techniques of nonlinear dynamical systems to analyse the properties of these systems.

Quantum integrable systems

Current research on quantum integrable systems focuses on powerful exact analytical and numerical techniques, with applications in particle physics, quantum information theory and mathematical physics.

Topological solitons

Topological solitons are stable, finite energy, particle-like solutions of nonlinear wave equations that arise due to the general topological properties of the nonlinear system concerned. Examples include monopoles, skyrmions and vortices. This research focuses on classical and quantum behaviour of solitons with applications in various areas of physics including particle, nuclear and condensed matter physics. The group employs a wide range of different techniques including numerical simulations, exact analytic solutions and geometrical methods.

Algebra and representation theory

A representation of a group is the concrete realisation of the group as a group of transformations. Representation theory played an important role in the proof of the classification of finite simple groups, one of the outstanding achievements of 20th-century algebra. Representations of both groups and algebras are important in diverse areas of mathematics, such as statistical mechanics, knot theory and combinatorics.

Algebraic topology

In topology, geometry is studied with algebraic tools. An example of an algebraic object assigned to a geometric phenomenon is the winding number: this is an integer assigned to a map of the n-dimensional sphere to itself. The methods used in algebraic topology link in with homotopy theory, homological algebra and modern category theory.

Invariant theory

Invariant theory has its roots in the classical constructive algebra of the 19th century and motivated the development of modern algebra by Hilbert, Noether, Weyl and others. There are natural applications and interactions with algebraic geometry, algebraic topology and representation theory. The starting point is an action of a group on a commutative ring, often a ring of polynomials on several variables. The ring of invariants, the subring of fixed points, is the primary object of study. We use computational methods to construct generators for the ring of invariants, and theoretical methods to understand the relationship between the structure of the ring of invariants and the underlying representation.

Financial mathematics

Research includes work on financial risk management, asset pricing and optimal asset allocation, along with models to improve corporate financial management.

Staff research interests

Full details of staff research interests can be found on the School's website.

Professor Peter A Clarkson: Professor of Mathematics

Soliton theory, in particular the Painlevé equations, and Painlevé analysis. Asymptotics, Bäcklund transformations, connection formulae and exact solutions for nonlinear ordinary differential and difference equations, in particular the Painlevé equations and discrete Painlevé equations. Orthogonal polynomials and special functions, in particular nonlinear special functions such as the Painlevé equations. Symmetry reductions and exact solutions of nonlinear partial differential equations, in particular using nonclassical and generalized techniques.

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Dr Clare Dunning: Senior Lecturer in Applied Mathematics

Exactly solvable models in mathematical physics; integrable quantum field theory and spectral theory of ordinary differential equations.

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Professor Peter Fleischmann: Professor of Pure Mathematics

Representation theory and structure theory of finite groups; constructive invariant theory; applied algebra and discrete mathematics.

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Dr Steffen Krusch: Lecturer in Applied Mathematics

Topological solitons in mathematical physics, in particular the classical and quantum behaviour of Skyrmions.

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Dr Stephane Launois: Reader in Pure Mathematics

Non-commutative algebra and non-commutative geometry, in particular, quantum algebras and links with their (semi-)classical counterparts: enveloping algebras and Poisson algebras.

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Dr Bas Lemmens: Senior Lecturer in Mathematics

Nonlinear (functional) analysis, dynamical systems theory and metric geometry. In particular, the theory of monotone dynamical systems and its applications, and the geometry of Hilbert's metric spaces.

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Dr Ana F. Loureiro: Lecturer in Mathematics

Orthogonal polynomials; special functions and integral transforms; some aspects of combinatorics and approximation theory.

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Professor Elizabeth L Mansfield: Professor of Mathematics

Nonlinear differential and difference equations; variational methods; moving frames and geometric integration.

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Dr Jaideep S Oberoi: Lecturer in Finance

Identification and quantification of liquidity risk in financial markets and the implications of incomplete information for asset price co-variation.

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Dr Rowena E Paget: Lecturer in Pure Mathematics

Representation theory of groups and algebras, with emphasis on algebras possessing a quasihereditary or cellular structure, such as the group algebras of symmetric groups, Brauer algebras and other diagram algebras.

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Dr Constanze Roitzheim: Lecturer in Mathematics

Stable homotopy theory, in particular model categories and chromatic homotopy theory; homological algebra; A-infinity algebras.

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Dr R James Shank: Reader in Mathematics

The invariant theory of finite groups and related aspects of commutative algebra, algebraic topology and representation theory.

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Dr Huamao Wang: Lecturer in Finance

Developing mathematical models; numerical methods and practical application of portfolio optimisation; derivative pricing and hedging; risk management based on stochastic calculus, optimal control, filtering and simulation.

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Dr Jing Ping Wang: Reader in Applied Mathematics

Geometric and algebraic properties of nonlinear partial differential equations; test and classification of integral systems and asymptotic normal forms of partial differential equations.

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Dr Ian Wood: Lecturer in Mathematics

Analysis of PDEs and spectral theory, in particular, the study of spectral properties of non-self adjoint operators via boundary triples and M-functions (generalised Dirichlet-to-Neumann maps), regularity to solutions of PDEs in Lipschitz domains and waveguides in periodic structures.

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Dr Chris F Woodcock: Senior Lecturer in Pure Mathematics

P-adic analogues of classical functions; commutative algebra; algebraic geometry; modular invariant theory.

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Fees

The 2018/19 annual tuition fees for this programme are:

Mathematics and its Applications with an Industrial Placement - MSc at Canterbury:
UK/EU Overseas
Full-time

For students continuing on this programme fees will increase year on year by no more than RPI + 3% in each academic year of study except where regulated.* If you are uncertain about your fee status please contact information@kent.ac.uk

General additional costs

Find out more about general additional costs that you may pay when studying at Kent. 

Funding

Search our scholarships finder for possible funding opportunities. You may find it helpful to look at both: