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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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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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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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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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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

◾Mathematics at the University of Glasgow is ranked 3rd in Scotland (Complete University Guide 2017).

◾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.### 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

◾Further topics in group theory

◾Lie groups, lie algebras & their representations

◾Magnetohydrodynamics

◾Operator algebras

◾Solitons

◾Special relativity & classical field theory.

SMSTC courses (20 credits)

◾Advanced Functional Analysis

◾Advanced Mathematical Methods

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.

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

◾Further topics in group theory

◾Lie groups, lie algebras & their representations

◾Magnetohydrodynamics

◾Operator algebras

◾Solitons

◾Special relativity & classical field theory.

SMSTC courses (20 credits)

◾Advanced Functional Analysis

◾Advanced Mathematical Methods

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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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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The Mathematical and Computational Sciences at Western are represented by four separate departments. Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences.
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The Mathematical and Computational Sciences at Western are represented by four separate departments: Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences. The Department of Mathematics has established research groups in several areas of contemporary mathematics including algebra, analysis and analytic geometry, homotopy theory, and noncommutative geometry.

Visit the website: http://www.admin.findamasters.com/editcourse.asp?theaction=add### Fields of Research

• Algebra/Number Theory

• Analysis

• Geometry/Topology### How to apply

For information on how to apply, please see: http://grad.uwo.ca/prospective_students/applying/index.html ### Financing your studies

As one of Canada's leading research institutions, we place great importance on helping you finance your education. It is crucial that you devote your full energy to the successful completion of your studies, so we want to ensure that stable funding is available to you.

For information please see: http://grad.uwo.ca/current_students/student_finances/index.html

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Visit the website: http://www.admin.findamasters.com/editcourse.asp?theaction=add

• Analysis

• Geometry/Topology

For information please see: http://grad.uwo.ca/current_students/student_finances/index.html

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Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem.
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Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem.

The programme closely follows the structure of our Applied Mathematical Sciences MSc and will equip you with the skill to perform efficient accurate computer simulations in a wide variety of applied mathematics, physics, chemical and industrial problems.

The MSc, has at its core, fundamental courses in pure mathematics and students will be able to take options from both pure and applied mathematics.

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;

Functional Analysis;

Partial Differential Equations;

Pure Mathematics (recommended).### Optional Courses

Mathematical Ecology;

Optimization;

Numerical Analysis of ODEs;

Applied Mathematics;

Dynamical Systems;

Stochastic Simulation;

Applied Linear Algebra;

Partial Differential Equations;

Numerical Analysis;

Bayesian Inference and Computational Methods;

Geometry.### Typical project subjects

Domain Decomposition;

Mathematical Modelling of Crime;

The Geometry of Point Particles;

Can we Trust Eigenvalues on a Computer?;

Braess Paradox;

The Ising Model: Exact and Numerical Results;

Banach Alegbras.

The final part of the MSc is an extended project in computational mathematics, giving the opportunity to investigate a topic in some depth guided by leading research academics from our 5-rated mathematics and statistics groups.

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The programme closely follows the structure of our Applied Mathematical Sciences MSc and will equip you with the skill to perform efficient accurate computer simulations in a wide variety of applied mathematics, physics, chemical and industrial problems.

The MSc, has at its core, fundamental courses in pure mathematics and students will be able to take options from both pure and applied mathematics.

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:

Functional Analysis;

Partial Differential Equations;

Pure Mathematics (recommended).

Optimization;

Numerical Analysis of ODEs;

Applied Mathematics;

Dynamical Systems;

Stochastic Simulation;

Applied Linear Algebra;

Partial Differential Equations;

Numerical Analysis;

Bayesian Inference and Computational Methods;

Geometry.

Mathematical Modelling of Crime;

The Geometry of Point Particles;

Can we Trust Eigenvalues on a Computer?;

Braess Paradox;

The Ising Model: Exact and Numerical Results;

Banach Alegbras.

The final part of the MSc is an extended project in computational mathematics, giving the opportunity to investigate a topic in some depth guided by leading research academics from our 5-rated mathematics and statistics groups.

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From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age.
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From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our Masters in Mathematics offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age. ### PROGRAMME OVERVIEW

This programme reflects and benefits from the strong research activities of the Department of Mathematics.

The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:

-Mathematics of Life and Social Sciences

-Dynamical Systems and Partial Differential Equations

-Fields, Strings and Geometry

-Fluids, Meteorology and Symmetry

During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.### PROGRAMME STRUCTURE

This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation. The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.

-Maths of Weather

-Graphs and Networks

-Manifolds and Topology

-Quantum Mechanics

-Numerical Solutions of PDEs

-Functional Analysis and Partial Differential Equations

-Nonlinear Wave Equations

-Representation Theory

-Advanced Techniques in Mathematics

-Lie Algebras

-Nonlinear Patterns

-Geometric Mechanics

-Relativity

-Ecological and Epidemiological Modelling

-Mathematical Biology and Physiology

-Topology

-Non-Commutative Algebra

-Dissertation### CAREERS

Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.

There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.

As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.### EDUCATIONAL AIMS OF THE PROGRAMME

-To provide graduates with a strong background in advanced mathematical theory and its applications to the solution of real problems

-To develop students understanding of core areas in advanced mathematics including standard tools for the solution of real life applied mathematical problems

-To develop the skill of formulating a mathematical problem from a purely verbal description

-To develop the skill of writing a sophisticated mathematical report and, additionally, in presenting the results in the form of an oral presentation

-To lay a foundation for carrying out mathematical research leading to a research degree and/or a career as a professional mathematician in an academic or non-academic setting### PROGRAMME LEARNING OUTCOMES

Knowledge and understanding

-Knowledge of the core theory and methods of advanced pure and applied mathematics and how to apply that theory to real life problems

-An in-depth study of a specific problem arising in a research context

Intellectual / cognitive skills

-Ability to demonstrate knowledge of key techniques in advanced mathematics and to apply those techniques in problem solving

-Ability to formulate a mathematical description of a problem that may be described only verbally

-An understanding of possible shortcomings of mathematical descriptions of reality

-An ability to use software such as MATLAB and IT facilities more generally including research databases such as MathSciNet and Web of Knowledge

Professional practical skills

-Fluency in advanced mathematical theory

-The ability to interpret the results of the application of that theory

-An awareness of any weaknesses in the assumptions being made and of possible shortcomings with model predictions

-The skill of writing an extended and sophisticated mathematical report and of verbally summarising its content to specialist and/or non-specialist audiences

Key / transferable skills

-Ability to reason logically and creatively

-Effective oral presentation skills

-Written report writing skills

-Skills in independent learning

-Time management

-Use of information and technology### GLOBAL OPPORTUNITIES

We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.

In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.

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The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:

-Mathematics of Life and Social Sciences

-Dynamical Systems and Partial Differential Equations

-Fields, Strings and Geometry

-Fluids, Meteorology and Symmetry

During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.

-Maths of Weather

-Graphs and Networks

-Manifolds and Topology

-Quantum Mechanics

-Numerical Solutions of PDEs

-Functional Analysis and Partial Differential Equations

-Nonlinear Wave Equations

-Representation Theory

-Advanced Techniques in Mathematics

-Lie Algebras

-Nonlinear Patterns

-Geometric Mechanics

-Relativity

-Ecological and Epidemiological Modelling

-Mathematical Biology and Physiology

-Topology

-Non-Commutative Algebra

-Dissertation

There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.

As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.

-To develop students understanding of core areas in advanced mathematics including standard tools for the solution of real life applied mathematical problems

-To develop the skill of formulating a mathematical problem from a purely verbal description

-To develop the skill of writing a sophisticated mathematical report and, additionally, in presenting the results in the form of an oral presentation

-To lay a foundation for carrying out mathematical research leading to a research degree and/or a career as a professional mathematician in an academic or non-academic setting

-Knowledge of the core theory and methods of advanced pure and applied mathematics and how to apply that theory to real life problems

-An in-depth study of a specific problem arising in a research context

Intellectual / cognitive skills

-Ability to demonstrate knowledge of key techniques in advanced mathematics and to apply those techniques in problem solving

-Ability to formulate a mathematical description of a problem that may be described only verbally

-An understanding of possible shortcomings of mathematical descriptions of reality

-An ability to use software such as MATLAB and IT facilities more generally including research databases such as MathSciNet and Web of Knowledge

Professional practical skills

-Fluency in advanced mathematical theory

-The ability to interpret the results of the application of that theory

-An awareness of any weaknesses in the assumptions being made and of possible shortcomings with model predictions

-The skill of writing an extended and sophisticated mathematical report and of verbally summarising its content to specialist and/or non-specialist audiences

Key / transferable skills

-Ability to reason logically and creatively

-Effective oral presentation skills

-Written report writing skills

-Skills in independent learning

-Time management

-Use of information and technology

In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.

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The academic staff in the Applied Computing Department (ACD) are all engaged in research and publications. Considering its modest size, ACD has successfully attracted research funding from various sources in the UK and the EU, including industry, research councils, HEA and EU framework projects such as FP6.
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For the academic year 2012-2013, 2 DPhil and 6 MSc students (1 in Mathematics) have graduated, four of whom graduated with Distinction. The 2 DPhil students have made it for the March graduation and we expect to have 3 or 4 more completing their DPhil research programmes for the next graduation. One of our new MPhil/DPhil students in Computing joined the Department last October, and 3 other MPhil/DPhil students have joined us since. Over the last few years, the number of research students in ACD has grown steadily to (currently) 29 PhD and 2 Master’s research students.

We have had over 20 refereed conference and journal papers published during the last 12 months, and two of the papers have been awarded best paper awards.

ACD supports diverse research topics addressing varied applied computing technologies such as:

- Image processing and pattern recognition with applications in biometric-based person identification, image super-resolution, digital watermarking and steganography, content-based image / video indexing and retrieval, biomedical image analysis.

- Multi-factor authentication and security algorithms.

- Wireless networks technologies (Multi-frequency Software-Defined / Cognitive Radios, convergence and integration of different wireless technologies and standards such as WiFi and WiMax, IPv4 and IPv6, wireless mesh technologies, intrusion detection and prevention, efficiency and stability of ad hoc networks).

- Hybrid navigation and localisation integrations for mobile handsets, including using Cellular and WiFi in conjunction with GPS and Glonass for seamless positioning indoors, Multiplexed receive chain of GPS/Glonass with on-board handset Bluetooth/WiFi, GNSS signals multiplexing for real time simulation.

- Cloud computing, including the readiness of mobile operating systems for cloud services and focusing on techniques for fast computing handovers, efficient virtualisation and optimised security algorithms.

- Data mining techniques, including database systems, the application of data mining techniques in image and biological data, human-computer interaction and visual languages.

- Research and development of Apps for mobile devices and smart TVs, particularly for application in the areas of education and healthcare.

- Differential geometry – Einstein metrics, quasi-Einstein metrics, Ricci solitons, numerical methods in differential geometry.

As well as researching the chosen subject, our students engage in delivering seminars weekly, attending conferences and workshops, attending online webinars and discussion forums, attending training and focused group studies, supervising tutorial and laboratory sessions for undergraduate students, peer reviews and final year project supervision, among a host of technical and networking activities to enhance their skills and techniques.

Find out more about our Department of Applied Computing on http://www.buckingham.ac.uk/appliedcomputing.

Apply here http://www.buckingham.ac.uk/sciences/msc/computingresearch.

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The Algebra and Topology section is an active research group consisting of renowned experts covering a remarkably broad range of topics.
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The section offers a Master's specialisation in Algebra in Topology, which is a 2-year programme aimed at students with an interest in pure mathematics and its applications.

The Master's programme has a strong focus on current research developments. It introduces students to a broad range of techniques and concepts that play a central role in modern mathematics. In addition to providing a strong theoretical basis, the programme offers excellent opportunities for a further specialisation focusing on applications of pure mathematics or on interactions with other fields.

The programme offers courses in Algebra, Topology, Geometry, Number Theory, and Logic and Computation. There are strong interactions with other Master's specialisations at Radboud University, notably the ones in Mathematical Physics and in Mathematical Foundations of Computer Science.

In addition, the programme offers a variety of seminars from beginning Master's level to research level. Moreover, students have the possibility to incorporate courses from related programmes (e.g. Mathematical Physics and Mathematical Foundations of Computer Science into their programme, as well as individual reading courses. Each student concludes his programme by studying a special topic and writing a Master's thesis about it.

Excellent students having completed this Master's programme or a similar programme elsewhere can in principle continue and enrol in the PhD Programme, but admission for this is limited and highly selective.

See the website http://www.ru.nl/masters/algebratopology

Entering the Master’s programme in Mathematics requires a Bachelor’s degree in Mathematics that is the equivalent to a Dutch university diploma (this does not include a Bachelor’s from a university of applied science, in Dutch hbo; in German Fachhochschule). That means we expect you to have a solid background in the core areas groups, rings, fields and topology. We expect students to have passed core mathematics courses during their Bachelor’s in:

The Examination Board will determine if an international student has the required mathematical knowledge to be admitted. The Examination Board will also indicate if the student is required to follow specific courses from the Bachelor's programme to eliminate possible deficiencies.

- Basic notions in Mathematics

- Linear Algebra

- Algebra

- Analysis

- Topology

- Geometry

- Differential Equations

2. A proficiency in English

In order to take part in this programme, you need to have fluency in both written and spoken English. Non-native speakers of English without a Dutch Bachelor's degree or VWO diploma need one of the following:

- TOEFL score of ≥575 (paper based) or ≥90 (internet based)

- An IELTS score of ≥6.5

- Cambridge Certificate of Advanced English (CAE) or Certificate of Proficiency in English (CPE) with a mark of C or higher

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

See the website http://www.ru.nl/masters/algebratopology

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High-level training in statistics and the modelling of random processes for applications in science, business or health care.
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High-level training in statistics and the modelling of random processes for applications in science, business or health care.

For many complex systems in nature and society, stochastics can be used to efficiently describe the randomness present in all these systems, thereby giving the data greater explanatory and predictive power. Examples include statistical mechanics, financial markets, mobile phone networks, and operations research problems. The Master’s specialisation in Applied Stochastics will train you to become a mathematician that can help both scientists and businessmen make better decisions, conclusions and predictions. You’ll be able to bring clarity to the accumulating information overload they receive.

The members of the Applied Stochastics group have ample experience with the pure mathematical side of stochastics. This area provides powerful techniques in functional analysis, partial differential equations, geometry of metric spaces and number theory, for example. The group also often gives advice to both their academic colleagues, and organisations outside of academia. They will therefore not only be able to teach you the theoretical basis you need to solve real world stochastics problems, but also to help you develop the communications skills and professional expertise to cooperate with people from outside of mathematics.

See the website http://www.ru.nl/masters/mathematics/stochastics### Why study Applied Stochastics at Radboud University?

- This specialisation focuses both on theoretical and applied topics. It’s your choice whether you want to specialise in pure theoretical research or perform an internship in a company setting.

- Mathematicians at Radboud University are expanding their knowledge of random graphs and networks, which can be applied in the ever-growing fields of distribution systems, mobile phone networks and social networks.

- In a unique and interesting collaboration with Radboudumc, stochastics students can help researchers at the hospital with very challenging statistical questions.

- Because the Netherlands is known for its expertise in the field of stochastics, it offers a great atmosphere to study this field. And with the existence of the Mastermath programme, you can follow the best mathematics courses in the country, regardless of the university that offers them.

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

- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating.### Career prospects

### Master's programme in Mathematics

Mathematicians are needed in all industries, including the banking, technology and service industries, to name a few. 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 and is the reason 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 Applied Stochastics Department, focuses on combinatorics, (quantum) probability and mathematical statistics. Below, a small sample of the research our members pursue.

Eric Cator’s research has two main themes, probability and statistics.

1. In probability, he works on interacting particles systems, random polymers and last passage percolation. He has also recently begun working on epidemic models on finite graphs.

2. In statistics, he works on problems arising in mathematical statistics, for example in deconvolution problems, the CAR assumption and more recently on the local minimax property of least squares estimators.

Cator also works on more applied problems, usually in collaboration with people from outside statistics, for example on case reserving for insurance companies or airplane maintenance. He has a history of changing subjects: “I like to work on any problem that takes my fancy, so this description might be outdated very quickly!”

Hans Maassen researches quantum probability or non-commutative probability, which concerns a generalisation of probability theory that is broad enough to contain quantum mechanics. He takes part in the Geometry and Quantum Theory (GQT) research cluster of connected universities in the Netherlands. In collaboration with Burkhard Kümmerer he is also developing the theory of quantum Markov chains, their asymptotic completeness and ergodic theory, with applications to quantum optics. Their focal point is shifting towards quantum information and control theory, an area which is rapidly becoming relevant to experimental physicists.

Ross Kang conducts research in probabilistic and extremal combinatorics, with emphasis on graphs (which abstractly represent networks). He works in random graph theory (the study of stochastic models of networks) and often uses the probabilistic method. This involves applying probabilistic tools to shed light on extremes of large-scale behaviour in graphs and other combinatorial structures. He has focused a lot on graph colouring, an old and popular subject made famous by the Four Colour Theorem (erstwhile Conjecture).

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

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For many complex systems in nature and society, stochastics can be used to efficiently describe the randomness present in all these systems, thereby giving the data greater explanatory and predictive power. Examples include statistical mechanics, financial markets, mobile phone networks, and operations research problems. The Master’s specialisation in Applied Stochastics will train you to become a mathematician that can help both scientists and businessmen make better decisions, conclusions and predictions. You’ll be able to bring clarity to the accumulating information overload they receive.

The members of the Applied Stochastics group have ample experience with the pure mathematical side of stochastics. This area provides powerful techniques in functional analysis, partial differential equations, geometry of metric spaces and number theory, for example. The group also often gives advice to both their academic colleagues, and organisations outside of academia. They will therefore not only be able to teach you the theoretical basis you need to solve real world stochastics problems, but also to help you develop the communications skills and professional expertise to cooperate with people from outside of mathematics.

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

- Mathematicians at Radboud University are expanding their knowledge of random graphs and networks, which can be applied in the ever-growing fields of distribution systems, mobile phone networks and social networks.

- In a unique and interesting collaboration with Radboudumc, stochastics students can help researchers at the hospital with very challenging statistical questions.

- Because the Netherlands is known for its expertise in the field of stochastics, it offers a great atmosphere to study this field. And with the existence of the Mastermath programme, you can follow the best mathematics courses in the country, regardless of the university that offers them.

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

- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating.

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

Eric Cator’s research has two main themes, probability and statistics.

1. In probability, he works on interacting particles systems, random polymers and last passage percolation. He has also recently begun working on epidemic models on finite graphs.

2. In statistics, he works on problems arising in mathematical statistics, for example in deconvolution problems, the CAR assumption and more recently on the local minimax property of least squares estimators.

Cator also works on more applied problems, usually in collaboration with people from outside statistics, for example on case reserving for insurance companies or airplane maintenance. He has a history of changing subjects: “I like to work on any problem that takes my fancy, so this description might be outdated very quickly!”

Hans Maassen researches quantum probability or non-commutative probability, which concerns a generalisation of probability theory that is broad enough to contain quantum mechanics. He takes part in the Geometry and Quantum Theory (GQT) research cluster of connected universities in the Netherlands. In collaboration with Burkhard Kümmerer he is also developing the theory of quantum Markov chains, their asymptotic completeness and ergodic theory, with applications to quantum optics. Their focal point is shifting towards quantum information and control theory, an area which is rapidly becoming relevant to experimental physicists.

Ross Kang conducts research in probabilistic and extremal combinatorics, with emphasis on graphs (which abstractly represent networks). He works in random graph theory (the study of stochastic models of networks) and often uses the probabilistic method. This involves applying probabilistic tools to shed light on extremes of large-scale behaviour in graphs and other combinatorial structures. He has focused a lot on graph colouring, an old and popular subject made famous by the Four Colour Theorem (erstwhile Conjecture).

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

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How does a bank check whether your digital signature is a valid one? Do planets move in stable orbits or will they eventually collide? How can a 3D-sphere within the 3D-figures be characterized?.
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How does a bank check whether your digital signature is a valid one? Do planets move in stable orbits or will they eventually collide? How can a 3D-sphere within the 3D-figures be characterized?

The mathematics behind these questions is dealt with in the Master's degree programme in Mathematics. The objective of the Master's degree in Mathematics is to teach you the mathematical knowledge, skills and attitude needed to pursue a professional (research) career.

You will gain specialized mathematical knowledge in selected areas such as algebra and geometry, dynamical systems and analysis, and statistics probability theory. Furthermore, you will learn how to solve a problem by using abstraction and modelling and to find scientific literature on the subject. You will be able to determine whether the problem can be solved by using existing mathematical theory or whether new theory should be developed. Finally, you will learn how to present mathematical results in written and oral form, for both specialized and general audiences.

The Master's programme in Mathematics offers four specialisations:

* Algebra and Geometry

* Dynamical Systems and Analysis

* Statistics and Probability

* Science, Business and Policy### Why in Groningen?

- For a career in science or a company

- Acquire skills highly appreciated by employers

- Informal community, small classes### Job perspectives

A Master's degree in Mathematics opens up many job opportunities. During the Master's programme, you will learn to think in a logical, systematic and problem-oriented way. These qualities are highly appreciated by employers. If you want to work in a company you can find employment at, for instance, banks, insurance companies, the consultancy branch and research and development departments of companies like Philips, TNO, Gasunie, Ericsson and LogicaCMG.

You can start a scientific career as a PhD student at a university. This means working for four years on a research project and writing a thesis. After successfully defending this thesis, you will be awarded a PhD degree. Afterwards you can continue your career at a university or start a career in a company.### Job examples

- Work for multinationals such as TNO and Philips

- Start an academic career

- Analyst at bank or insurance company

- Consultant

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The mathematics behind these questions is dealt with in the Master's degree programme in Mathematics. The objective of the Master's degree in Mathematics is to teach you the mathematical knowledge, skills and attitude needed to pursue a professional (research) career.

You will gain specialized mathematical knowledge in selected areas such as algebra and geometry, dynamical systems and analysis, and statistics probability theory. Furthermore, you will learn how to solve a problem by using abstraction and modelling and to find scientific literature on the subject. You will be able to determine whether the problem can be solved by using existing mathematical theory or whether new theory should be developed. Finally, you will learn how to present mathematical results in written and oral form, for both specialized and general audiences.

The Master's programme in Mathematics offers four specialisations:

* Algebra and Geometry

* Dynamical Systems and Analysis

* Statistics and Probability

* Science, Business and Policy

- Acquire skills highly appreciated by employers

- Informal community, small classes

You can start a scientific career as a PhD student at a university. This means working for four years on a research project and writing a thesis. After successfully defending this thesis, you will be awarded a PhD degree. Afterwards you can continue your career at a university or start a career in a company.

- Start an academic career

- Analyst at bank or insurance company

- Consultant

Read less

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