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Working at a frontier of mathematics that intersects with cutting edge research in physics. Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics.
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Working at a frontier of mathematics that intersects with cutting edge research in physics.

Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.

Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.

At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.

See the website http://www.ru.nl/masters/mathematics/physics### Why study Mathematical Physics at Radboud University?

- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.

- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).

- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.

- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.

- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.

- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.### Career prospects

Mathematicians are needed in all industries, including the industrial, banking, technology and service industry and also within management, consultancy and education. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills. ### Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad indeed and is why many graduates of a Master’s in Mathematics find work very quickly.

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

- Teacher (at all levels from middle school to university)

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst### PhD positions

Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world. ### Our research in this field

The research of members of the Mathematical Physics Department, emphasise operator algebras and noncommutative geometry, Lie theory and representation theory, integrable systems, and quantum field theory. Below, a small sample of the research our members pursue.

Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.

Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:

1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.

2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

See the website http://www.ru.nl/masters/mathematics/physics

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Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.

Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.

At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.

See the website http://www.ru.nl/masters/mathematics/physics

- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).

- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.

- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.

- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.

- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

- Teacher (at all levels from middle school to university)

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.

Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:

1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.

2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

See the website http://www.ru.nl/masters/mathematics/physics

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The Department of Mathematics offers graduate courses leading to M.Sc., and eventually to Ph.D., degree in Mathematics. The Master of Science program aims to provide a sound foundation for the students who wish to pursue a research career in mathematics as well as other related areas.
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The Department of Mathematics offers graduate courses leading to M.Sc., and eventually to Ph.D., degree in Mathematics. The Master of Science program aims to provide a sound foundation for the students who wish to pursue a research career in mathematics as well as other related areas. The department emphasizes both pure and applied mathematics. Research in the department covers algebra, number theory, combinatorics, differential equations, functional analysis, abstract harmonic analysis, mathematical physics, stochastic analysis, biomathematics and topology. ### Current faculty projects and research interests:

• Ring Theory and Module Theory, especially Krull dimension, torsion theories, and localization

• Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories

• Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology

• Algebraic Number Theory, especially rings of algebraic integers

• Iwasawa Theory of Galois representations and their deformations Euler and Kolyvagin systems, Equivariant Tamagawa Number

Conjecture

• Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems

• Graph theory, in particular number of cycles in 2-factorizations of complete graphs

• Coding theory, especially relation of designs to codes

• Random graphs, in particular, random proximity catch graphs and digraphs

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

• Banach algebras, especially the structure of the second Arens duals of Banach algebras

• Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group

• Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces

• Differential geometric, topologic, and algebraic methods used in quantum mechanics

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

• Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis)

• Graph Theory (probabilistic investigation of graphs emerging from computational geometry)

• Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis)

• Classification and Pattern Recognition (with applications in mine field and face detection)

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

• p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties

• Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings

• Symplectic topology and geometry, Seiberg-Witten theory, Floer homology

• Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry

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• Algebraic Theory of Lattices, especially their dimensions (Krull, Goldie, Gabriel, etc.) with applications to Grothendieck categories and module categories equipped with torsion theories

• Field Theory, especially Galois Theory, Cogalois Theory, and Galois cohomology

• Algebraic Number Theory, especially rings of algebraic integers

• Iwasawa Theory of Galois representations and their deformations Euler and Kolyvagin systems, Equivariant Tamagawa Number

Conjecture

• Combinatorial design theory, in particular metamorphosis of designs, perfect hexagon triple systems

• Graph theory, in particular number of cycles in 2-factorizations of complete graphs

• Coding theory, especially relation of designs to codes

• Random graphs, in particular, random proximity catch graphs and digraphs

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

• Banach algebras, especially the structure of the second Arens duals of Banach algebras

• Abstract Harmonic Analysis, especially the Fourier and Fourier-Stieltjes algebras associated to a locally compact group

• Geometry of Banach spaces, especially vector measures, spaces of vector valued continuous functions, fixed point theory, isomorphic properties of Banach spaces

• Differential geometric, topologic, and algebraic methods used in quantum mechanics

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

• Inference on Random Graphs (with emphasis on modeling email and internet traffic and clustering analysis)

• Graph Theory (probabilistic investigation of graphs emerging from computational geometry)

• Statistics (analysis of spatial data and spatial point patterns with applications in epidemiology and ecology and statistical methods for medical data and image analysis)

• Classification and Pattern Recognition (with applications in mine field and face detection)

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

• p-adic methods in arithmetical algebraic geometry, Ramification theory of arithmetic varieties

• Topology of low-dimensional manifolds, in particular Lefschetz fibrations, symplectic and contact structures, Stein fillings

• Symplectic topology and geometry, Seiberg-Witten theory, Floer homology

• Foliation and Lamination Theory, Minimal Surfaces, and Hyperbolic Geometry

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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications.
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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines. ### Why this programme

-The University of Glasgow’s School of Mathematics and Statistics is ranked 4th in Scotland (Complete University Guide 2015).

-The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.

-You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.

-You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.

-Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.

-With a 94% overall student satisfaction in the National Student Survey 2014, the School of Mathematics and Statistics combines both teaching excellence and a supportive learning environment.### Programme structure

Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)

-Algebraic & geometric topology

-Continuum mechanics & elasticity

-Differential geometry

-Fluid mechanics

-Functional analysis

-Further complex analysis

-Galois theory

-Mathematical biology

-Mathematical physics

-Numerical methods

-Number theory

-Partial differential equations

-Topics in algebra

Level-M courses (20 credits)

-Advanced algebraic & geometric topology

-Advanced differential geometry & topology

-Advanced functional analysis

-Advanced methods in differential equations

-Advanced numerical methods

-Biological & physiological fluid mechanics

-Commutative algebra & algebraic geometry

-Elasticity

-Fourier analysis

-Further topics in group theory

-Lie groups, lie algebras & their representations

-Magnetohydrodynamics

-Operator algebras

-Solitons

-Special relativity & classical field theory

SMSTC courses (20 credits)

-Algebra 1

-Algebra 2

-Applied analysis and PDEs 1

-Applied analysis and PDEs 2

-Applied mathematical methods 1

-Applied mathematical methods 2

-Geometry and topology 1

-Geometry and topology 2

-Mathematical modelling 1

-Mathematical modelling 2

-Pure analysis 1

-Pure analysis 2.

The project titles are offered each year by academic staff and so change annually### Career prospects

Career opportunities are diverse and varied and include academia, teaching, industry and finance.

Graduates of this programme have gone on to positions such as:

-Maths Tutor at a university.

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-The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.

-You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.

-You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.

-Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.

-With a 94% overall student satisfaction in the National Student Survey 2014, the School of Mathematics and Statistics combines both teaching excellence and a supportive learning environment.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)

-Algebraic & geometric topology

-Continuum mechanics & elasticity

-Differential geometry

-Fluid mechanics

-Functional analysis

-Further complex analysis

-Galois theory

-Mathematical biology

-Mathematical physics

-Numerical methods

-Number theory

-Partial differential equations

-Topics in algebra

Level-M courses (20 credits)

-Advanced algebraic & geometric topology

-Advanced differential geometry & topology

-Advanced functional analysis

-Advanced methods in differential equations

-Advanced numerical methods

-Biological & physiological fluid mechanics

-Commutative algebra & algebraic geometry

-Elasticity

-Fourier analysis

-Further topics in group theory

-Lie groups, lie algebras & their representations

-Magnetohydrodynamics

-Operator algebras

-Solitons

-Special relativity & classical field theory

SMSTC courses (20 credits)

-Algebra 1

-Algebra 2

-Applied analysis and PDEs 1

-Applied analysis and PDEs 2

-Applied mathematical methods 1

-Applied mathematical methods 2

-Geometry and topology 1

-Geometry and topology 2

-Mathematical modelling 1

-Mathematical modelling 2

-Pure analysis 1

-Pure analysis 2.

The project titles are offered each year by academic staff and so change annually

Graduates of this programme have gone on to positions such as:

-Maths Tutor at a university.

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The fields of graphics, vision and imaging increasingly rely on one another.
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The fields of graphics, vision and imaging increasingly rely on one another. This unique and timely MSc provides training in computer graphics, geometry processing, virtual reality, machine vision and imaging technology from world-leading experts, enabling students to specialise in any of these areas and gain a grounding in the others. ### Degree information

Graduates will understand the basic mathematical principles underlying the development and application of new techniques in computer graphics and computer vision and will be aware of the range of algorithms and approaches available, and be able to design, develop and evaluate algorithms and methods for new problems, emerging technologies and applications.

Students undertake modules to the value of 180 credits.

The programme consists of four core modules (60 credits), four optional modules (60 credits) and a research project (60 credits).

Core modules

-Mathematical Methods, Algorithmics and Implementation

-Image Processing

-Computer Graphics

-Research Methods

Optional modules

-Machine Vision

-Graphical Models

-Virtual Environments

-Geometry of Images

-Advanced Modelling, Rendering and Animation

-Inverse Problems in Imaging

-Computation Modelling for Biomedical Imaging

-Computational Photography and Capture

-Acquisition and Processing of 3D Geometry

Dissertation/report

All students undertake an independent research project related to a problem of industrial interest or on a topic near the leading edge of research, which culminates in a 60–80 page dissertation.

Teaching and learning

The programme is delivered through a combination of lectures and tutorials. Lectures are often supported by laboratory work with help from demonstrators. Student performance is assessed by unseen written examinations, coursework and a substantial individual project.### Careers

Graduates are ready for employment in a wide range of high-technology companies and will be able to contribute to maintaining and enhancing the UK's position in these important and expanding areas. The MSc provides graduates with the up-to-date technical skills required to support a wealth of research and development opportunities in broad areas of computer science and engineering, such as multimedia applications, medicine, architecture, film animation and computer games. Our market research shows that the leading companies in these areas demand the deep technical knowledge that this programme provides. Graduates have found positions at global companies such as Disney, Sony and Siemens. Others have gone on to PhD programmes at MIT, Princeton University, and Eth Zurich.

Top career destinations for this degree:

-Senior Post-Doctoral Research Associate, University of Oxford

-Software Engineer, Sengtian Software

-Graduate Software Engineer, ARM

-IT Officer, Nalys

-MSc in Computer Games and Entertainment, Goldsmiths, University of London

Employability

UCL Computer Science was one of the top-rated departments in the country, according to the UK Government's most recent research assessment exercise, and our graduates have some of the highest employment rates of any university in the UK. This degree programme also provides a foundation for further PhD study or industrial research.### Why study this degree at UCL?

UCL Computer Science contains some of the world's leading researchers in computer graphics, geometry processing, computer vision and virtual environments.

Research activities include geometric acquisition and 3D fabrication, real-time photo-realistic rendering, mixed and augmented reality, face recognition, content-based image-database search, video-texture modelling, depth perception in stereo vision, colour imaging for industrial inspection, mapping brain function and connectivity and tracking for SLAM (simultaneous localisation and mapping).

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Students undertake modules to the value of 180 credits.

The programme consists of four core modules (60 credits), four optional modules (60 credits) and a research project (60 credits).

Core modules

-Mathematical Methods, Algorithmics and Implementation

-Image Processing

-Computer Graphics

-Research Methods

Optional modules

-Machine Vision

-Graphical Models

-Virtual Environments

-Geometry of Images

-Advanced Modelling, Rendering and Animation

-Inverse Problems in Imaging

-Computation Modelling for Biomedical Imaging

-Computational Photography and Capture

-Acquisition and Processing of 3D Geometry

Dissertation/report

All students undertake an independent research project related to a problem of industrial interest or on a topic near the leading edge of research, which culminates in a 60–80 page dissertation.

Teaching and learning

The programme is delivered through a combination of lectures and tutorials. Lectures are often supported by laboratory work with help from demonstrators. Student performance is assessed by unseen written examinations, coursework and a substantial individual project.

Top career destinations for this degree:

-Senior Post-Doctoral Research Associate, University of Oxford

-Software Engineer, Sengtian Software

-Graduate Software Engineer, ARM

-IT Officer, Nalys

-MSc in Computer Games and Entertainment, Goldsmiths, University of London

Employability

UCL Computer Science was one of the top-rated departments in the country, according to the UK Government's most recent research assessment exercise, and our graduates have some of the highest employment rates of any university in the UK. This degree programme also provides a foundation for further PhD study or industrial research.

Research activities include geometric acquisition and 3D fabrication, real-time photo-realistic rendering, mixed and augmented reality, face recognition, content-based image-database search, video-texture modelling, depth perception in stereo vision, colour imaging for industrial inspection, mapping brain function and connectivity and tracking for SLAM (simultaneous localisation and mapping).

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Mathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life.
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Mathematics is at the heart of advances in science, engineering and technology, as well as being an indispensable problem-solving and decision-making tool in many other areas of life. This MSc course enables you to delve deeply into particular aspects of pure and applied mathematics, through a wide choice of modules in fascinating areas such as fractal geometry, coding theory and analytic theory. You’ll complete your MSc with a piece of independent study, exploring the history of modern geometry, advances in approximation theory, variational methods applied to eigenvalue problems, or algebraic graph theory and culminating in a dissertation on the topic of your choice.

Key features of the course

•Ideal for mathematically inclined scientists and engineers as well as mathematicians

•Extends your knowledge and refines your abilities to process information accurately, and critically analyse and communicate complex ideas

•Develops an enhanced skill set that will put you at an advantage in careers as diverse as mathematics, education, computer science, economics, engineering and finance.

•The most popular MSc in mathematics in the UK.

This qualification is eligible for a Postgraduate Loan available from Student Finance England. For more information, see Fees and funding

Course details

You can take a number of different routes towards your qualification - see the full module list for all options.

Modules

The modules in this qualification are categorised as entry, intermediate and dissertation. Check our website for start dates as some modules are not available for study every year.

Entry:

• Calculus of variations and advanced calculus (M820)

• Analytic number theory I (M823)

Intermediate:

• Nonlinear ordinary differential equations (M821)

• Applied complex variables (M828) - next available in October 2017 and following alternate years

• Analytic number theory II (M829) - next available in October 2018 and following alternate years

• Approximation theory (M832) - next available in October 2018 and following alternate years

• Advanced mathematical methods (M833) - next available in October 2017 and following alternate years

• Fractal geometry (M835) - next available in October 2017 and following alternate years

• Coding theory (M836) - next available in October 2018 and following alternate years

• Dissertation: Dissertation in mathematics (M840)

Module study order:

•You must normally pass at least one entry level module before studying an intermediate module.

•You must pass Analytic number theory I (M823) before studying Analytic number theory II (M829).

•You must normally pass four modules before studying the Dissertation in mathematics (M840).

•Some topics for the dissertation have prerequisite modules

Otherwise within each category modules may be studied in any order, and you may register for a module while studying a pre-requisite for that module (i.e. before you know whether you have passed the pre-requisite module or not).

To gain this qualification, you need 180 credits as follows:

150 credits from this list:

Optional modules

• Advanced mathematical methods (M833)

• Analytic number theory I (M823)

• Analytic number theory II (M829)

• Applied complex variables (M828)

• Approximation theory (M832)

• Calculus of variations and advanced calculus (M820)

• Coding theory (M836)

• Fractal geometry (M835)

• Nonlinear ordinary differential equations (M821)

Plus

Compulsory module

Dissertation in mathematics (M840)

The modules quoted in this description are currently available for study. However, as we review the curriculum on a regular basis, the exact selection may change over time.### Credit transfer

For this qualification, we do not allow you to count credit for study you have already done elsewhere.

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Key features of the course

•Ideal for mathematically inclined scientists and engineers as well as mathematicians

•Extends your knowledge and refines your abilities to process information accurately, and critically analyse and communicate complex ideas

•Develops an enhanced skill set that will put you at an advantage in careers as diverse as mathematics, education, computer science, economics, engineering and finance.

•The most popular MSc in mathematics in the UK.

This qualification is eligible for a Postgraduate Loan available from Student Finance England. For more information, see Fees and funding

Course details

You can take a number of different routes towards your qualification - see the full module list for all options.

Modules

The modules in this qualification are categorised as entry, intermediate and dissertation. Check our website for start dates as some modules are not available for study every year.

Entry:

• Calculus of variations and advanced calculus (M820)

• Analytic number theory I (M823)

Intermediate:

• Nonlinear ordinary differential equations (M821)

• Applied complex variables (M828) - next available in October 2017 and following alternate years

• Analytic number theory II (M829) - next available in October 2018 and following alternate years

• Approximation theory (M832) - next available in October 2018 and following alternate years

• Advanced mathematical methods (M833) - next available in October 2017 and following alternate years

• Fractal geometry (M835) - next available in October 2017 and following alternate years

• Coding theory (M836) - next available in October 2018 and following alternate years

• Dissertation: Dissertation in mathematics (M840)

Module study order:

•You must normally pass at least one entry level module before studying an intermediate module.

•You must pass Analytic number theory I (M823) before studying Analytic number theory II (M829).

•You must normally pass four modules before studying the Dissertation in mathematics (M840).

•Some topics for the dissertation have prerequisite modules

Otherwise within each category modules may be studied in any order, and you may register for a module while studying a pre-requisite for that module (i.e. before you know whether you have passed the pre-requisite module or not).

To gain this qualification, you need 180 credits as follows:

150 credits from this list:

Optional modules

• Advanced mathematical methods (M833)

• Analytic number theory I (M823)

• Analytic number theory II (M829)

• Applied complex variables (M828)

• Approximation theory (M832)

• Calculus of variations and advanced calculus (M820)

• Coding theory (M836)

• Fractal geometry (M835)

• Nonlinear ordinary differential equations (M821)

Plus

Compulsory module

Dissertation in mathematics (M840)

The modules quoted in this description are currently available for study. However, as we review the curriculum on a regular basis, the exact selection may change over time.

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Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department.
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Joining the Department as a postgraduate is certainly a good move. The Department maintains strong research in both pure and applied mathematics, as well as the traditional core of a mathematics department. What makes our Department different is the equally strong research in fluid mechanics, scientific computation and statistics.

The quality of research at the postgraduate level is reflected in the scholarly achievements of faculty members, many of whom are recognized as leading authorities in their fields. Research programs often involve collaboration with scholars at an international level, especially in the European, North American and Chinese universities. Renowned academics also take part in the Department's regular colloquia and seminars. The faculty comprises several groups: Pure Mathematics, Applied Mathematics, Probability and Statistics.

Mathematics permeates almost every discipline of science and technology. We believe our comprehensive approach enables inspiring interaction among different faculty members and helps generate new mathematical tools to meet the scientific and technological challenges facing our fast-changing world.

The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. Submission and successful defense of a thesis based on original research are required.### Research Foci

Algebra and Number Theory

The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, Kac-Moody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.

Analysis and Differential Equations

The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.

Geometry and Topology

Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.

Numerical Analysis

The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.

Applied Sciences

The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, mutliphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.

Probability and Statistics

Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.

Financial Mathematics

This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.### Facilities

The Department enjoys a range of up-to-date facilities and equipment for teaching and research purposes. It has two computer laboratories and a Math Support Center equipped with 100 desktop computers for undergraduate and postgraduate students. The Department also provides an electronic homework system and a storage cloud system to enhance teaching and learning.

To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 high-speed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.

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The quality of research at the postgraduate level is reflected in the scholarly achievements of faculty members, many of whom are recognized as leading authorities in their fields. Research programs often involve collaboration with scholars at an international level, especially in the European, North American and Chinese universities. Renowned academics also take part in the Department's regular colloquia and seminars. The faculty comprises several groups: Pure Mathematics, Applied Mathematics, Probability and Statistics.

Mathematics permeates almost every discipline of science and technology. We believe our comprehensive approach enables inspiring interaction among different faculty members and helps generate new mathematical tools to meet the scientific and technological challenges facing our fast-changing world.

The MPhil program seeks to strengthen students' general background in mathematics and mathematical sciences, and to expose students to the environment and scope of mathematical research. Submission and successful defense of a thesis based on original research are required.

The theory of Lie groups, Lie algebras and their representations play an important role in many of the recent development in mathematics and in the interaction of mathematics with physics. Our research includes representation theory of reductive groups, Kac-Moody algebras, quantum groups, and conformal field theory. Number theory has a long and distinguished history, and the concepts and problems relating to the theory have been instrumental in the foundation of a large part of mathematics. Number theory has flourished in recent years, as made evident by the proof of Fermat's Last Theorem. Our research specializes in automorphic forms.

Analysis and Differential Equations

The analysis of real and complex functions plays a fundamental role in mathematics. This is a classical yet still vibrant subject that has a wide range of applications. Differential equations are used to describe many scientific, engineering and economic problems. The theoretical and numerical study of such equations is crucial in understanding and solving problems. Our research areas include complex analysis, exponential asymptotics, functional analysis, nonlinear equations and dynamical systems, and integrable systems.

Geometry and Topology

Geometry and topology provide an essential language describing all kinds of structures in Nature. The subject has been vastly enriched by close interaction with other mathematical fields and with fields of science such as physics, astronomy and mechanics. The result has led to great advances in the subject, as highlighted by the proof of the Poincaré conjecture. Active research areas in the Department include algebraic geometry, differential geometry, low-dimensional topology, equivariant topology, combinatorial topology, and geometrical structures in mathematical physics.

Numerical Analysis

The focus is on the development of advance algorithms and efficient computational schemes. Current research areas include: parallel algorithms, heterogeneous network computing, graph theory, image processing, computational fluid dynamics, singular problems, adaptive grid method, rarefied flow simulations.

Applied Sciences

The applications of mathematics to interdisciplinary science areas include: material science, multiscale modeling, mutliphase flows, evolutionary genetics, environmental science, numerical weather prediction, ocean and coastal modeling, astrophysics and space science.

Probability and Statistics

Statistics, the science of collecting, analyzing, interpreting, and presenting data, is an essential tool in a wide variety of academic disciplines as well as for business, government, medicine and industry. Our research is conducted in four categories. Time Series and Dependent Data: inference from nonstationarity, nonlinearity, long-memory behavior, and continuous time models. Resampling Methodology: block bootstrap, bootstrap for censored data, and Edgeworth and saddle point approximations. Stochastic Processes and Stochastic Analysis: filtering, diffusion and Markov processes, and stochastic approximation and control. Survival Analysis: survival function and errors in variables for general linear models. Probability current research includes limit theory.

Financial Mathematics

This is one of the fastest growing research fields in applied mathematics. International banking and financial firms around the globe are hiring science PhDs who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. The trend has been accelerating in recent years on numerous fronts, driven both by substantial theoretical advances as well as by a practical need in the industry to develop effective methods to price and hedge increasingly complex financial instruments. Current research areas include pricing models for exotic options, the development of pricing algorithms for complex financial derivatives, credit derivatives, risk management, stochastic analysis of interest rates and related models.

To assist computations that require a large amount of processing power in the research area of scientific computation, a High Performance Computing (HPC) laboratory equipped with more than 200 high-speed workstations and servers has been set up. With advanced parallel computing technologies, these powerful computers are capable of delivering 17.2 TFLOPS processing power to solve computationally intensive problems in our innovative research projects. Such equipment helps our faculty and postgraduate students to stay at the forefront of their fields. Research projects in areas such as astrophysics, computational fluid dynamics, financial mathematics, mathematical modeling and simulation in materials science, molecular simulation, numerical ocean modeling, numerical weather prediction and numerical methods for micromagnetics simulations all benefit from our powerful computing facilities.

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The Department of Mathematics offers opportunities for research—leading to the Master of Science and Doctor of Philosophy degrees—in the fields of pure mathematics and applied mathematics.
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The Department of Mathematics offers opportunities for research—leading to the Master of Science and Doctor of Philosophy degrees—in the fields of pure mathematics and applied mathematics. Faculty areas of research include, but are not limited to, real and complex analysis, ordinary and partial differential equations, harmonic analysis, nonlinear analysis, several complex variables, functional analysis, operator theory, C*-algebras, ergodic theory, group theory, analytic and algebraic number theory, Lie groups and Lie algebras, automorphic forms, commutative algebra, algebraic geometry, singularity theory, differential geometry, symplectic geometry, classical synthetic geometry, algebraic topology, set theory, set-theoretic topology, mathematical physics, fluid mechanics, probability, combinatorics, optimization, control theory, dynamical systems, computer algebra, cryptography, and mathematical finance.

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This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines.
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This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. There is a wide range of taught modules on offer, and you will also produce a dissertation on a topic of current research interest taken from your choice of a wide range of subjects offered. ### Course structure and overview

-Six taught modules in October-May.

-A dissertation in June-September.

Modules: Six of available options

In previous years, optional modules available included:

Modules in Pure Mathematics:

-Algebraic Topology IV

-Codes and Cryptography III

-Differential Geometry III

-Galois Theory III

-Geometry III and IV

-Number Theory III and IV

-Riemannian Geometry IV

-Topology III

-Elliptic Functions IV

Modules in Probability and Statistics:

-Mathematical Finance III and IV

-Decision Theory III

-Operations Research III

-Probability III and IV

-Statistical Methods III

-Topics in Statistics III and IV

Modules in Applications of Mathematics:

-Advanced Quantum Theory IV

-Dynamical Systems III

-General Relativity III and IV

-Mathematical Biology III

-Numerical Differential Equations III and IV

-Partial Differential Equations III and IV

-Quantum Information III

-Quantum Mechanics III

-Statistical Mechanics III and IV

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-A dissertation in June-September.

Modules: Six of available options

In previous years, optional modules available included:

Modules in Pure Mathematics:

-Algebraic Topology IV

-Codes and Cryptography III

-Differential Geometry III

-Galois Theory III

-Geometry III and IV

-Number Theory III and IV

-Riemannian Geometry IV

-Topology III

-Elliptic Functions IV

Modules in Probability and Statistics:

-Mathematical Finance III and IV

-Decision Theory III

-Operations Research III

-Probability III and IV

-Statistical Methods III

-Topics in Statistics III and IV

Modules in Applications of Mathematics:

-Advanced Quantum Theory IV

-Dynamical Systems III

-General Relativity III and IV

-Mathematical Biology III

-Numerical Differential Equations III and IV

-Partial Differential Equations III and IV

-Quantum Information III

-Quantum Mechanics III

-Statistical Mechanics III and IV

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This course is for people who need to strengthen their maths knowledge fairly quickly before starting their training to become a secondary mathematics teacher.
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This course is for people who need to strengthen their maths knowledge fairly quickly before starting their training to become a secondary mathematics teacher. ### Course overview

This 24-week fast track course will boost your maths knowledge so that you are able to teach maths up to A Level. To join the Subject Knowledge Enhancement (SKE) course, you should already have received a conditional offer for initial teacher training – or you should at least be considering an application for it.

Typically, you should have already received a conditional offer for initial teacher training (ITT) – or you should at least be considering an application for it. Our course ends in July so that you are ready for ITT in September.

For Home/EU students, there is no tuition fee and you will be paid a bursary while you are studying on the course.

You will cover areas such as geometry, calculus, statistics, mechanics, patterns and equations as well as common errors and misconceptions in mathematics. At the initial interview, we will advise you whether this 24-week fast track course is suitable for you or whether an alternative course would be better for your circumstances.

Once you have successfully completed the SKE course and your initial teacher training, your career prospects will be very good. There is a national shortage of mathematics teachers and there are excellent job prospects, both in the North East and throughout the country.

Reports on our provision by external examiners have been very positive. Comments include: “It is clear that the course remains very successful in preparing candidates appropriately for their subsequent teacher training course”.### Course content

This course enhances your skills and knowledge in mathematics, preparing you for teacher training. You will study the following units:

-Patterns and Equations

-Structure and Pattern

-Development of Geometric Thinking

-Nature of Mathematics

-Investigating Calculus

-Enriching and Strengthening Mathematics

-Elementary Geometry

-Development of Mathematics

-Statistics

-Mechanics

-Using LOGO and 3D Geometry

-Errors and Misconceptions in Mathematics

-Matrices

-Investigating Sequences and Series### Teaching and assessment

We use a wide variety of teaching and learning methods that include lectures, independent work, directed tasks, written assignments and use of ICT. In addition to attending taught sessions, we encourage you to undertake some voluntary work experience in a school. Assessment methods include written work, exams and presentations. We assess all units. ### Facilities & location

This course is based on the banks of the River Wear at The Sir Tom Cowie Campus at St Peter’s. Interactive whiteboards are available in our classrooms and we encourage you to use mathematical software, such as Autograph graph-plotting software, to support your learning.

When it comes to IT provision you can take your pick from over a hundred PCs in the St Peter’s Library, a dedicated computer classroom, and wireless access zones. If you have any problems, just ask the friendly helpdesk team.

The University of Sunderland is a vibrant learning environment with a strong international dimension thanks to the presence of students from around the world.### Employment & careers

This course enhances your maths subject knowledge, allowing you to progress on to a teacher training programme such as the University of Sunderland’s PGCE Mathematics Secondary Education and then achieve Qualified Teacher Status.

There is a shortage of mathematics teachers in England so there are excellent career opportunities both in the North East and nationwide.

The starting salary of a Newly Qualified Teacher is over £22,000, with extra if you work in London. Teachers can expect to see their salaries rise by an average of 30 per cent after their first four years in the job.

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Typically, you should have already received a conditional offer for initial teacher training (ITT) – or you should at least be considering an application for it. Our course ends in July so that you are ready for ITT in September.

For Home/EU students, there is no tuition fee and you will be paid a bursary while you are studying on the course.

You will cover areas such as geometry, calculus, statistics, mechanics, patterns and equations as well as common errors and misconceptions in mathematics. At the initial interview, we will advise you whether this 24-week fast track course is suitable for you or whether an alternative course would be better for your circumstances.

Once you have successfully completed the SKE course and your initial teacher training, your career prospects will be very good. There is a national shortage of mathematics teachers and there are excellent job prospects, both in the North East and throughout the country.

Reports on our provision by external examiners have been very positive. Comments include: “It is clear that the course remains very successful in preparing candidates appropriately for their subsequent teacher training course”.

-Patterns and Equations

-Structure and Pattern

-Development of Geometric Thinking

-Nature of Mathematics

-Investigating Calculus

-Enriching and Strengthening Mathematics

-Elementary Geometry

-Development of Mathematics

-Statistics

-Mechanics

-Using LOGO and 3D Geometry

-Errors and Misconceptions in Mathematics

-Matrices

-Investigating Sequences and Series

When it comes to IT provision you can take your pick from over a hundred PCs in the St Peter’s Library, a dedicated computer classroom, and wireless access zones. If you have any problems, just ask the friendly helpdesk team.

The University of Sunderland is a vibrant learning environment with a strong international dimension thanks to the presence of students from around the world.

There is a shortage of mathematics teachers in England so there are excellent career opportunities both in the North East and nationwide.

The starting salary of a Newly Qualified Teacher is over £22,000, with extra if you work in London. Teachers can expect to see their salaries rise by an average of 30 per cent after their first four years in the job.

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Applied Mathematical Sciences offers a clear and relevant gateway into a successful career in business, education or scientific research.
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Applied Mathematical Sciences offers a clear and relevant gateway into a successful career in business, education or scientific research. The programme arms students with the essential knowledge required by all professional mathematicians working across many disciplines. You will learn to communicate their ideas effectively to peers and others, as well as the importance of research, planning and self-motivation.

Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:### Core courses

:

Modelling and Tools;

Optimization;

Dynamical Systems;

Applied Mathematics (recommended);

Applied Linear Algebra (recommended).### Optional Courses

:

Mathematical Ecology;

Functional Analysis;

Numerical Analysis of ODEs;

Pure Mathematics;

Statistical Methods;

Stochastic Simulation;

Software Engineering Foundations;

Mathematical Biology and Medicine;

Partial Differential Equations;

Numerical Analysis;

Geometry.### Typical project subjects

:

Pattern Formation of Whole Ecosystems;

Climate Change Impact;

Modelling Invasive Tumour Growth;

Simulation of Granular Flow and Growing Sandpiles;

Finite Element Discretisation of ODEs and PDEs;

Domain Decomposition;

Mathematical Modelling of Crime;

The Geometry of Point Particles;

Can we Trust Eigenvalues on a Computer?

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Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:

Modelling and Tools;

Optimization;

Dynamical Systems;

Applied Mathematics (recommended);

Applied Linear Algebra (recommended).

Mathematical Ecology;

Functional Analysis;

Numerical Analysis of ODEs;

Pure Mathematics;

Statistical Methods;

Stochastic Simulation;

Software Engineering Foundations;

Mathematical Biology and Medicine;

Partial Differential Equations;

Numerical Analysis;

Geometry.

Pattern Formation of Whole Ecosystems;

Climate Change Impact;

Modelling Invasive Tumour Growth;

Simulation of Granular Flow and Growing Sandpiles;

Finite Element Discretisation of ODEs and PDEs;

Domain Decomposition;

Mathematical Modelling of Crime;

The Geometry of Point Particles;

Can we Trust Eigenvalues on a Computer?

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Mathematics is the science of structures, including mathematics itself. Discovery of new patterns and relations, and the construction of models with predictive power are the core of mathematics.
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Frequently, we see an interaction between fundamental and applied research. This versatility is reflected in the Master's programme Mathematical Sciences, which a broad range of courses is offered. Both students who want to specialise and students who aim for a wider background in mathematics.

[Tracks]]

You can tailor your programme by selecting one of the following seven tracks:

-Algebraic Geometry and Number Theory

-Applied Analysis

-Complex Systems

-Differential Geometry and Topology

-Logic

-Probability, Statistics, and Stochastic Modelling

-Pure Analysis

-Scientific Computing

-You can also choose to do a Research project in History of Mathematics.

This Master's programme offers a broad scope in a stimulating international environment which is renowned for its excellent research. Students who prefer to research subjects in depth will feel particularly at home at Mathematical Sciences.

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You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics.
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You can study this Mathematical Sciences MSc programme full-time or part-time. It offers students the opportunity to specialise in a broad range of areas across pure and applied mathematics, statistics and probability, and theoretical physics.

The topics we cover include:

- advanced probability theory

- algebra

- asymptotic methods

- geometry

- mathematical biology

- partial differential equations

- quantum field theory

- singularity theory

- stochastic analysis

- standard model/string theory.

By completing the first semester you qualify for the PG certificate. By completing the second, you qualify for the PG Diploma. Then, by completing your dissertation, you qualify for the MSc.### Key Facts

REF 2014

92% of our research impact judged at outstanding and very considerable, 28% improvement in overall research at 4* and 3*.

Facilities

A dedicated student resource suite is available in the Department, with computer and reading rooms and a social area.### Why Department of Mathematical Sciences?

Range and depth of study options

We offer a very wide range of modules, from advanced algebra and geometry, to partial differential equations, probability theory, stochastic analysis, and mathematical physics. With these you can tailor your programme to specialise in one of these areas, or gain a broad understanding of several. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem solving skills, employers require strong communication skills. These are integral to this programme. Graduates go on to research degrees, or become business and finance professionals, or to work in management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.

Accessibility

We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

We provide high quality supervision and teaching, computer labs, and and you will benefit from the friendly and supportive atmosphere in the Department, as evidenced by student feedback available on our university website. A common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.### Career prospects

The excellent University Careers Service is open to all postgraduates. Graduates of the MSc and PhD programmes move on to many different careers. Recent graduates have moved into fast track teacher programmes, jobs in finance (actuarial, banking, insurance), software development, drugs testing and defence work, as well as University postdoctoral or lecturing posts. The MSc programme is of course a natural route into doctoral study in Mathematics and related fields, both at Liverpool and elsewhere. Some of our PhD students move on to postdoctoral positions and to academic teaching jobs and jobs in research institutes, both in the UK and elsewhere.

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The topics we cover include:

- advanced probability theory

- algebra

- asymptotic methods

- geometry

- mathematical biology

- partial differential equations

- quantum field theory

- singularity theory

- stochastic analysis

- standard model/string theory.

By completing the first semester you qualify for the PG certificate. By completing the second, you qualify for the PG Diploma. Then, by completing your dissertation, you qualify for the MSc.

92% of our research impact judged at outstanding and very considerable, 28% improvement in overall research at 4* and 3*.

Facilities

A dedicated student resource suite is available in the Department, with computer and reading rooms and a social area.

We offer a very wide range of modules, from advanced algebra and geometry, to partial differential equations, probability theory, stochastic analysis, and mathematical physics. With these you can tailor your programme to specialise in one of these areas, or gain a broad understanding of several. This allows you to build up the required background for the project and dissertation modules, which offer the opportunity to undertake an in-depth study of a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem solving skills, employers require strong communication skills. These are integral to this programme. Graduates go on to research degrees, or become business and finance professionals, or to work in management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.

Accessibility

We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

We provide high quality supervision and teaching, computer labs, and and you will benefit from the friendly and supportive atmosphere in the Department, as evidenced by student feedback available on our university website. A common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.

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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.
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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.

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 and a well-established system of support and training, with a high level of contact between staff and research students. 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 Mathematics Group at Kent ranked highly in the most recent Research Assessment Exercise. With 100% of the Applied Mathematics Group submitted, all research outputs were judged to be of international quality and 12.5% was rated 4*. For the Pure Mathematics Group, a large proportion of the outputs demonstrated international excellence.

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.

You take eight modules in total: six from the list below; a short project module and a dissertation module. The modules concentrate on a specific topic from: analysis; applied mathematics; geometry; and algebra.### 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.

MA961 - Mathematical Inquiry and Communication (30 credits) - https://www.kent.ac.uk/courses/modules/module/MA961

MA962 - Geometric Integration (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA962

MA963 - Poisson Algebras and Combinatorics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA963

MA964 - Applied Algebraic Topology (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA964

MA965 - Symmetries, Groups and Invariants (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA965

MA966 - Diagram Algebras (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA966

MA967 - Quantum Physics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA967

MA968 - Mathematics and Music (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA968

MA969 - Applied Differential Geometry (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA969

MA970 - Nonlinear Analysis and Optimisation (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA970

Show more... https://www.kent.ac.uk/courses/postgraduate/146/mathematics-and-its-applications#!structure### Assessment

Assessment is by closed book examinations, take-home problem assignments and computer lab assignments (depending on the module). The project and dissertation modules are assessed mainly on the reports or work you produce, but also on workshop activities during the teaching term. ### 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.### 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.### Learn more about Kent

Visit us - https://www.kent.ac.uk/courses/visit/openday/pgevents.html

International Students - https://www.kent.ac.uk/internationalstudent/

Why study at Kent? - https://www.kent.ac.uk/courses/postgraduate/why/

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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.

The Mathematics Group at Kent ranked highly in the most recent Research Assessment Exercise. With 100% of the Applied Mathematics Group submitted, all research outputs were judged to be of international quality and 12.5% was rated 4*. For the Pure Mathematics Group, a large proportion of the outputs demonstrated international excellence.

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.

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.

You take eight modules in total: six from the list below; a short project module and a dissertation module. The modules concentrate on a specific topic from: analysis; applied mathematics; geometry; and algebra.

MA961 - Mathematical Inquiry and Communication (30 credits) - https://www.kent.ac.uk/courses/modules/module/MA961

MA962 - Geometric Integration (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA962

MA963 - Poisson Algebras and Combinatorics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA963

MA964 - Applied Algebraic Topology (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA964

MA965 - Symmetries, Groups and Invariants (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA965

MA966 - Diagram Algebras (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA966

MA967 - Quantum Physics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA967

MA968 - Mathematics and Music (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA968

MA969 - Applied Differential Geometry (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA969

MA970 - Nonlinear Analysis and Optimisation (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA970

Show more... https://www.kent.ac.uk/courses/postgraduate/146/mathematics-and-its-applications#!structure

- 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.

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.

International Students - https://www.kent.ac.uk/internationalstudent/

Why study at Kent? - https://www.kent.ac.uk/courses/postgraduate/why/

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Our MSc Mathematics programme consists of a wide range of modules and a written project.
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Our MSc Mathematics programme consists of a wide range of modules and a written project. Your module choices will be mainly from the two main blocks of pure mathematics and theoretical physics but you are also able to choose certain modules from the Financial Mathematics programme and at other University of London institutions, subject to approval. ### Key benefits

- An intensive course covering a wide range of basic and advanced topics.

- Intimate class environment with small class sizes (typically fewer than twenty students on a module) allowing good student-lecturer interactions.

- A full twelve-month course with a three-month supervised summer project to give a real introduction to research.

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/mathematics-msc.aspx### Course detail

- Description -

The majority of the eight modules are taken from blocks of pure mathematics and theoretical physics, with other options from the MSc Financial Mathematics and other University of London institutions available, subject to approval.

Pure Mathematics:

- Metric & Banach Spaces

- Complex Analysis

- Fourier Analysis

- Non-linear Analysis (new in 2013)

- Operator Theory

- Galois Theory

- Lie Groups & Lie Algebras

- Algebraic Number Theory

- Algebraic Geometry

- Manifolds

- Real Analysis II

- Topology

- Rings & Modules

- Representation Theory of Finite Groups

Theoretical Physics:

- Quantum Field Theory

- String Theory & Branes

- Supersymmetry

- Advanced Quantum Field Theory

- Spacetime geometry and General Relativity

- Advanced General Relativity

- Low-dimensional Quantum Field Theory

- Course purpose -

This programme is suitable for Mathematics graduates who wish to study more advanced mathematics. The programme ideally prepares students for PhD study in a mathematical discipline.

- Course format and assessment -

Eight modules assessed by written examinations; one individual project.### Career prospects

Many of our graduates take up full-time employment in various industries that require good mathematical/computer knowledge or that look for intelligent and creative people. Recent employers of our graduates include Barclays Bank, Kinetic Partners, Lloyds Banking Group and Sapient.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx### About Postgraduate Study at King’s College London:

To study for a postgraduate degree at King’s College London is to study at the city’s most central university and at one of the top 20 universities worldwide (2015/16 QS World Rankings). Graduates will benefit from close connections with the UK’s professional, political, legal, commercial, scientific and cultural life, while the excellent reputation of our MA and MRes programmes ensures our postgraduate alumni are highly sought after by some of the world’s most prestigious employers. We provide graduates with skills that are highly valued in business, government, academia and the professions. ### Scholarships & Funding:

All current PGT offer-holders and new PGT applicants are welcome to apply for the scholarships. For more information and to learn how to apply visit: http://www.kcl.ac.uk/study/pg/funding/sources ### Free language tuition with the Modern Language Centre:

If you are studying for any postgraduate taught degree at King’s you can take a module from a choice of over 25 languages without any additional cost. Visit: http://www.kcl.ac.uk/mlc

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- Intimate class environment with small class sizes (typically fewer than twenty students on a module) allowing good student-lecturer interactions.

- A full twelve-month course with a three-month supervised summer project to give a real introduction to research.

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/mathematics-msc.aspx

The majority of the eight modules are taken from blocks of pure mathematics and theoretical physics, with other options from the MSc Financial Mathematics and other University of London institutions available, subject to approval.

Pure Mathematics:

- Metric & Banach Spaces

- Complex Analysis

- Fourier Analysis

- Non-linear Analysis (new in 2013)

- Operator Theory

- Galois Theory

- Lie Groups & Lie Algebras

- Algebraic Number Theory

- Algebraic Geometry

- Manifolds

- Real Analysis II

- Topology

- Rings & Modules

- Representation Theory of Finite Groups

Theoretical Physics:

- Quantum Field Theory

- String Theory & Branes

- Supersymmetry

- Advanced Quantum Field Theory

- Spacetime geometry and General Relativity

- Advanced General Relativity

- Low-dimensional Quantum Field Theory

- Course purpose -

This programme is suitable for Mathematics graduates who wish to study more advanced mathematics. The programme ideally prepares students for PhD study in a mathematical discipline.

- Course format and assessment -

Eight modules assessed by written examinations; one individual project.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx

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This intensive introduction to advanced pure and applied mathematics draws on our strengths in algebra, geometry, topology, number theory, fluid dynamics and solar physics.
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Our Statistical Services Unit works with industry, commerce and the public sector. The services they provide include consultancy, training courses and computer software development.

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