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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:

- A TOEFL score of >550 (paper based) or >213 (computer based) or >80 (internet based)

- An IELTS score of >6.0

- 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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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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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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A minimum GPA of 3.0 in all undergraduate coursework in mathematics. A letter of intent written by the applicant expressing professional goals as applied to the program.
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• A minimum GPA of 3.0 in all undergraduate coursework in mathematics.

• A letter of intent written by the applicant expressing professional goals as applied to the program.

• Submission of three letters of recommendation, using the required recommendation form. Two letters must be from mathematics faculty with whom the applicant has taken courses.

• Resume or curriculum vitae.

E-mail: [email protected]

Phone: 315-267-2165

Visit http://www.potsdam.edu/graduate to view the full application checklist and online application

The Master of Arts program in Mathematics is designed to develop the student’s ability to work independently and to obtain basic knowledge in algebra, real and complex variables, and topology so that mathematics literature can be read with understanding and enjoyment. The successful completion of this program should prepare a student to enter a second-year doctoral program in mathematics, to begin a career as an industrial mathematician or as a faculty member at a junior or community college. Program start dates: Fall or Spring (in certain cases).

Required Program Courses

Minimum of 30 credit hours

MATH 661, Topology I ...................................................3 credits

MATH 671, Abstract Algebra I ..........................................3 credits

MATH 672, Abstract Algebra II .........................................3 credits

MATH 681, Complex Variables I .......................................3 credits

MATH 691, Real Variables I .............................................3 credits

MATH 698, Seminar .....................................................3 credits

One of the following:

MATH 662, Topology II ...............................................3 credits

MATH 682, Complex Variables II ...................................3 credits

MATH 692, Real Variables II ........................................3 credits

Mathematics Electives ..................................................9 credits### Success Stories

SUNY Potsdam Mathematics graduates are employed by com-panies such as Aetna, AT&T, IBM, General Electric, Kodak, the National Security Agency and Hewlett Packard. Others have received assistantships and fellowships at reputable universities, and many have earned Ph.D. degrees in mathematics or statistics. ### Uniqueness of the Program

The MA Mathematics program develops rigorous mathematical thinking and offers a spectrum of well-taught courses in pure and theoretical mathematics. ### Testimonials

"I was accepted to all but three Ph.D. programs I applied to. I feel very fortunate to be in this position, [with] so many great offers from excellent schools. I would recommend a stats program to any BA/MA student interested in furthering their education through a degree that’s not math as they’ll be highly qualified and prepared. That stance has only been further confirmed as I talk to faculty in different statistics departments." — Justin J. Raimondi, Class of 2014

"As a somewhat sheltered student through high school, I found that the mathematics faculty at SUNY Potsdam nurtured me carefully, providing the support I needed to develop confidence in the content area, and to deepen my love of mathematics. After graduating from the BA/MA program, I have taught successfully at the high school and college levels for nearly 30 years." —Donald C. Straight, Class of 1988

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• A letter of intent written by the applicant expressing professional goals as applied to the program.

• Submission of three letters of recommendation, using the required recommendation form. Two letters must be from mathematics faculty with whom the applicant has taken courses.

• Resume or curriculum vitae.

E-mail: [email protected]

Phone: 315-267-2165

Visit http://www.potsdam.edu/graduate to view the full application checklist and online application

The Master of Arts program in Mathematics is designed to develop the student’s ability to work independently and to obtain basic knowledge in algebra, real and complex variables, and topology so that mathematics literature can be read with understanding and enjoyment. The successful completion of this program should prepare a student to enter a second-year doctoral program in mathematics, to begin a career as an industrial mathematician or as a faculty member at a junior or community college. Program start dates: Fall or Spring (in certain cases).

Required Program Courses

Minimum of 30 credit hours

MATH 661, Topology I ...................................................3 credits

MATH 671, Abstract Algebra I ..........................................3 credits

MATH 672, Abstract Algebra II .........................................3 credits

MATH 681, Complex Variables I .......................................3 credits

MATH 691, Real Variables I .............................................3 credits

MATH 698, Seminar .....................................................3 credits

One of the following:

MATH 662, Topology II ...............................................3 credits

MATH 682, Complex Variables II ...................................3 credits

MATH 692, Real Variables II ........................................3 credits

Mathematics Electives ..................................................9 credits

"As a somewhat sheltered student through high school, I found that the mathematics faculty at SUNY Potsdam nurtured me carefully, providing the support I needed to develop confidence in the content area, and to deepen my love of mathematics. After graduating from the BA/MA program, I have taught successfully at the high school and college levels for nearly 30 years." —Donald C. Straight, Class of 1988

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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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Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes. Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017.
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Take advantage of one of our 100 Master’s Scholarships to study Stochastic Processes: Theory and Application at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

The MRes in Stochastic Processes: Theory and Application is delivered through optional modules for the taught element followed by a large research project that contributes to the field in an explicit way, rather than merely applying existing knowledge.

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

The Department’s research groups include:

Algebra and Topology Group

Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group

Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group

Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multi-fractal and multi-scale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group

Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing.### Key Features

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields. ### Course Content

As a student on the MRes Stochastic Processes programme you will study a range of topics for the taught element including:

Stochastic Calculus based on Brownian Motion

Levy processes and more general jump processes

The advanced Black-Scholes theory

Theory and numerics of parabolic differential equations

Java programming

The Stochastic Processes: Theory and Application course consists of a taught part (60 credits) and a research project (120 credits). Students will have a personal supervisor for their research project from the start of their studies.

Research projects could be of a theoretical mathematical nature, or they could be more applied, for example in financial mathematics or actuarial studies. Some of the research projects will be of an interdisciplinary character in collaboration with some of Swansea's world class engineers. For such projects it is likely that EPSRC funding would be available.### Facilities

The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use. It is a popular venue for students to work independently on the regular example sheets set by their lecturers, and to discuss Mathematics together.

Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.### Careers

The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistical analysis, marketing and sales.

Some of our students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths graduates will find plenty of career opportunities.### Research

The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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The MRes in Stochastic Processes: Theory and Application is delivered through optional modules for the taught element followed by a large research project that contributes to the field in an explicit way, rather than merely applying existing knowledge.

The Department of Mathematics hosts one of the strongest research groups in probability theory, especially in stochastic processes, in the UK. The senior members of this group are world leaders in their fields.

The Department’s research groups include:

Algebra and Topology Group

Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group

Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group

Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multi-fractal and multi-scale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group

Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing.

Stochastic Calculus based on Brownian Motion

Levy processes and more general jump processes

The advanced Black-Scholes theory

Theory and numerics of parabolic differential equations

Java programming

The Stochastic Processes: Theory and Application course consists of a taught part (60 credits) and a research project (120 credits). Students will have a personal supervisor for their research project from the start of their studies.

Research projects could be of a theoretical mathematical nature, or they could be more applied, for example in financial mathematics or actuarial studies. Some of the research projects will be of an interdisciplinary character in collaboration with some of Swansea's world class engineers. For such projects it is likely that EPSRC funding would be available.

Our main university library, Information Services and Systems (ISS), contains a notably extensive collection of Mathematics books.

Some of our students have been employed by AXA, BA, Deutsche Bank, Shell Research, Health Authorities and Local Government. Teaching is another area where maths graduates will find plenty of career opportunities.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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Take advantage of one of our 100 Master’s Scholarships to study Mathematics at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017.
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Take advantage of one of our 100 Master’s Scholarships to study Mathematics at Swansea University, the Times Good University Guide’s Welsh University of the Year 2017. Postgraduate loans are also available to English and Welsh domiciled students. For more information on fees and funding please visit our website.

As an MSc by Research in Mathematics student you will be guided by internationally leading researchers and will carry out a large individual research project.

You will be fully integrated into one of our established research groups and participate in research activities such as seminars, workshops, laboratories, and field work.### Key Features

Swansea is a research-led University and the Mathematics Department makes a significant contribution, meaning that as a postgraduate Mathematics student you will benefit from the knowledge and skills of internationally renowned academics.

In the Department of Mathematics at Swansea you will find friendly teaching staff that are fully committed to providing you with a supportive teaching and learning environment. This includes outstanding student support.

All postgraduate Mathematics programmes at Swansea will equip you with skills relevant for a rewarding career in a range of diverse fields. You will also further develop your communication, presentation and analytical skills.

The Mathematics Department’s research groups include:

Algebra and Topology Group

Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group

Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group

Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multifractal and multiscale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group

Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing### Employability

The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistical analysis, marketing and sales. ### Facilities

The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use, and is a popular venue for students to work independently on the regular exercise sheets set by their lecturers, and to discuss mathematics together.

The main university library, the Learning and Information Centre (LIC), contains a notably extensive collection of mathematics books.

As part of our expansion, we are building the Computational Foundry on our Bay Campus for computer and mathematical sciences. This development is exciting news for Swansea Mathematics who are part of the vibrant and growing community of world-class research leaders drawn from computer and mathematical sciences.### Research

The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Mathematics Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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As an MSc by Research in Mathematics student you will be guided by internationally leading researchers and will carry out a large individual research project.

You will be fully integrated into one of our established research groups and participate in research activities such as seminars, workshops, laboratories, and field work.

In the Department of Mathematics at Swansea you will find friendly teaching staff that are fully committed to providing you with a supportive teaching and learning environment. This includes outstanding student support.

All postgraduate Mathematics programmes at Swansea will equip you with skills relevant for a rewarding career in a range of diverse fields. You will also further develop your communication, presentation and analytical skills.

The Mathematics Department’s research groups include:

Algebra and Topology Group

Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.

Analysis and Nonlinear Partial Differential Equations Group

Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.

Stochastic Analysis Group

Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multifractal and multiscale systems, Infinite dimensional stochastic analysis and others.

Mathematical Methods in Biology and Life Sciences Group

Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing

The main university library, the Learning and Information Centre (LIC), contains a notably extensive collection of mathematics books.

As part of our expansion, we are building the Computational Foundry on our Bay Campus for computer and mathematical sciences. This development is exciting news for Swansea Mathematics who are part of the vibrant and growing community of world-class research leaders drawn from computer and mathematical sciences.

All academic staff in Mathematics are active researchers and the department has a thriving research culture.

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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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The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate.
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Mathematical research of course stands on its own, as is notably the case with the large group in algebraic topology led by Spinoza laureate Ieke Moerdijk. In addition, within IMAPP, researchers link with high-energy physics, including Higgs physics and quantum gravity. Outside IMAPP but within the Faculty of Science, there are close ties with the Institute for Computing and Information Sciences (ICIS) (think of logic and category theory) and outside the Faculty of Science (but within Radboud University) researchers at both the Donders Institute for Neurosciences and the University Medical Center collaborate with the applied stochastics group.

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

- Applied Stochastics

- Mathematical Physics

- Mathematical Foundations of Computer Science

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.

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

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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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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.

If your mathematical background is insufficient for direct entry to the MSc in Mathematics and its Applications, you may apply for this course. The first year of this Master's programme gives you a strong background in mathematics, equivalent to the Graduate Diploma in Mathematics, with second year studies following the MSc in Mathematics and its Applications.

Visit the website https://www.kent.ac.uk/courses/postgraduate/148/international-masters-in-mathematics-and-its-applications### 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.### 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. You strengthen your grounding in the subject and gain a sound grasp of the wider relevance and application of mathematics.

There are opportunities for outreach and engagement with the public on mathematics.### 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.

MA552 - Analysis (15 credits)

MA553 - Linear Algebra (15 credits)

MA588 - Mathematical Techniques and Differential Equations (15 credits)

MA591 - Nonlinear Systems and Mathematical Biology (15 credits)

MA593 - Topics in Modern Applied Mathematics (30 credits)

MA549 - Discrete Mathematics (15 credits)

MA572 - Complex Analysis (15 credits)

MA563 - Calculus of Variations (15 credits)

MA587 - Numerical Solution of Differential Equations (15 credits)

MA577 - Elements of Abstract Analysis (15 credits)

MA576 - Groups and Representations (15 credits)

MA574 - Polynomials in Several Variables (15 credits)

MA961 - Mathematical Inquiry and Communication (30 credits)

MA962 - Geometric Integration (15 credits)

MA964 - Applied Algebraic Topology (15 credits)

MA965 - Symmetries, Groups and Invariants (15 credits)

MA968 - Mathematics and Music (15 credits)

MA969 - Applied Differential Geometry (15 credits)

MA970 - Nonlinear Analysis and Optimisation (15 credits)

MA971 - Introduction to Functional Analysis (15 credits)

MA972 - Algebraic Curves in Nature (15 credits)

MA973 - Basic Differential Algebra (15 credits)

CB600 - Games and Networks (15 credits)

MA562 - Nonlinear Waves and Solitons (15 credits)

MA960 - Dissertation (60 credits)### Assessment

Closed book examinations, take-home problem assignments and computer lab assignments (depending on the module). ### 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.### Study support

Postgraduate resources

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

Support

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

Dynamic publishing culture

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

Global Skills Award

All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme (http://www.kent.ac.uk/graduateschool/skills/programmes/gsa.html). The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.### 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.

Find out how to apply here - https://www.kent.ac.uk/courses/postgraduate/apply/

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If your mathematical background is insufficient for direct entry to the MSc in Mathematics and its Applications, you may apply for this course. The first year of this Master's programme gives you a strong background in mathematics, equivalent to the Graduate Diploma in Mathematics, with second year studies following the MSc in Mathematics and its Applications.

Visit the website https://www.kent.ac.uk/courses/postgraduate/148/international-masters-in-mathematics-and-its-applications

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.

There are opportunities for outreach and engagement with the public on mathematics.

MA552 - Analysis (15 credits)

MA553 - Linear Algebra (15 credits)

MA588 - Mathematical Techniques and Differential Equations (15 credits)

MA591 - Nonlinear Systems and Mathematical Biology (15 credits)

MA593 - Topics in Modern Applied Mathematics (30 credits)

MA549 - Discrete Mathematics (15 credits)

MA572 - Complex Analysis (15 credits)

MA563 - Calculus of Variations (15 credits)

MA587 - Numerical Solution of Differential Equations (15 credits)

MA577 - Elements of Abstract Analysis (15 credits)

MA576 - Groups and Representations (15 credits)

MA574 - Polynomials in Several Variables (15 credits)

MA961 - Mathematical Inquiry and Communication (30 credits)

MA962 - Geometric Integration (15 credits)

MA964 - Applied Algebraic Topology (15 credits)

MA965 - Symmetries, Groups and Invariants (15 credits)

MA968 - Mathematics and Music (15 credits)

MA969 - Applied Differential Geometry (15 credits)

MA970 - Nonlinear Analysis and Optimisation (15 credits)

MA971 - Introduction to Functional Analysis (15 credits)

MA972 - Algebraic Curves in Nature (15 credits)

MA973 - Basic Differential Algebra (15 credits)

CB600 - Games and Networks (15 credits)

MA562 - Nonlinear Waves and Solitons (15 credits)

MA960 - Dissertation (60 credits)

- 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.

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

Support

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

Dynamic publishing culture

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

Global Skills Award

All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme (http://www.kent.ac.uk/graduateschool/skills/programmes/gsa.html). The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.

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.

Find out how to apply here - https://www.kent.ac.uk/courses/postgraduate/apply/

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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 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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Gain an understanding of advanced mathematics, concentrating on pure, applied and numerical mathematics. This grounding allows you to choose the mathematical orientation that best fits your tastes and aspirations.
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Gain an understanding of advanced mathematics, concentrating on pure, applied and numerical mathematics. This grounding allows you to choose the mathematical orientation that best fits your tastes and aspirations.

Mathematics at Sussex plays an important role in the current development of areas as diverse as:

-Analysis and partial differential equations

-Geometry and topology

-Mathematical physics

-Mathematics applied to biology

-Numerical analysis and scientific computing

-Probability and statistics

This course is for you if you’re a mathematician in industry or a mathematical educator looking for training, or if you’re preparing to do research.### How will I study?

In the autumn and spring terms, you choose from a range of core modules and options.

In the summer term, you work on your MSc dissertation. You can choose from a wide range of dissertation topics. You’ll be supervised by research-active faculty members.

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals.

Chancellor's International Scholarship (2017)

-25 scholarships of a 50% tuition fee waiver

-Application deadline: 1 May 2017

HESPAL Scholarship (Higher Education Scholarships Scheme for the Palestinian Territories) (2017)

-Two full fee waivers in conjuction with maintenance support from the British Council

-Application deadline: 1 January 2017

USA Friends Scholarships (2017)

-A scholarship of an amount equivalent to $10,000 for nationals or residents of the USA on a one year taught Masters degree course

-Application deadline: 3 April 2017### Careers

Our graduates go on to careers in:

-Academia

-Scientific research

-Teaching

-Management

-Actuarial roles

-Financial management and analysis

-Programming

-Scientific journalism

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Mathematics at Sussex plays an important role in the current development of areas as diverse as:

-Analysis and partial differential equations

-Geometry and topology

-Mathematical physics

-Mathematics applied to biology

-Numerical analysis and scientific computing

-Probability and statistics

This course is for you if you’re a mathematician in industry or a mathematical educator looking for training, or if you’re preparing to do research.

In the summer term, you work on your MSc dissertation. You can choose from a wide range of dissertation topics. You’ll be supervised by research-active faculty members.

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals.

Chancellor's International Scholarship (2017)

-25 scholarships of a 50% tuition fee waiver

-Application deadline: 1 May 2017

HESPAL Scholarship (Higher Education Scholarships Scheme for the Palestinian Territories) (2017)

-Two full fee waivers in conjuction with maintenance support from the British Council

-Application deadline: 1 January 2017

USA Friends Scholarships (2017)

-A scholarship of an amount equivalent to $10,000 for nationals or residents of the USA on a one year taught Masters degree course

-Application deadline: 3 April 2017

-Academia

-Scientific research

-Teaching

-Management

-Actuarial roles

-Financial management and analysis

-Programming

-Scientific journalism

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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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Last Minute courses for 2016

Our dedicated 2016 Courses list includes hundreds of Masters degrees worldwide, all with a 2016 start-date.