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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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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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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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This is a two-year full-time taught course. It is aimed at students who have a primary degree with a significant Mathematical content (such as Mathematical Studies graduates), but who do not hold an Honours Degree in Mathematics.
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PAC Code

MHR50/MHR551

The following information should be forwarded to PAC, 1 Courthouse Square, Galway or uploaded to your online application form:

Certified copies of all official transcripts of results for all non-Maynooth University qualifications listed MUST accompany the application. Failure to do so will delay your application being processed. Non-Maynooth University students are asked to provide two academic references and a copy of birth certificate or valid passport.

Find information on Scholarships here https://www.maynoothuniversity.ie/study-maynooth/postgraduate-studies/fees-funding-scholarships

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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Stochastic Processes.
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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Stochastic Processes: Theory and Application at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

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.

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.

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.

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.

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.

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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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).
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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

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.

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

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.

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.

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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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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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.
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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.

This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation.

**Example module listing**

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

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.

- 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

**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

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 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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The MSc in Mathematics and Foundations of Computer Science, run jointly by the. Mathematical Institute. and the. Department of Computer Science.
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The MSc in Mathematics and Foundations of Computer Science, run jointly by the Mathematical Institute and the Department of Computer Science, focuses on the interface between pure mathematics and theoretical computer science.

The mathematical side concentrates on areas where computers are used, or which are relevant to computer science, namely algebra, general topology, number theory, combinatorics and logic. Examples from the computing side include computational complexity, concurrency, and quantum computing. Students take a minimum of five options and write a dissertation.

The course is suitable for those who wish to pursue research in pure mathematics (especially algebra, number theory, combinatorics, general topology and their computational aspects), mathematical logic, or theoretical computer science. It is also suitable for students wishing to enter industry with an understanding of the mathematical and logical design and concurrency.

The course will consist of examined lecture courses and a written dissertation. The lecture courses will be divided into two sections:

- Section A: Mathematical Foundations
- Section B: Applicable Theories

Each section shall be divided into schedule I (basic) and schedule II (advanced). Students will be required to satisfy the examiners in at least two courses taken from section B and in at least two courses taken from schedule II. The majority of these courses should be given in the first two terms.

During Trinity term and over the summer students should complete a dissertation on an agreed topic. The dissertation must bear regard to course material from section A or section B, and it must demonstrate relevance to some area of science, engineering, industry or commerce.

It is intended that a major feature of this course is that candidates should show a broad knowledge and understanding over a wide range of material. Consequently, each lecture course taken will receive an assessment upon its completion by means of a test based on written work. Students will be required to pass five courses, that include two courses from section B and two at the schedule II level - these need not be distinct - and the dissertation.

The course runs from the beginning of October through to the end of September, including the dissertation.

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This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics and Mathematical Logic.
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This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics and Mathematical Logic. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics.

The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from May until September.

During the taught component of the course, you will normally take five units together with a written project. You may choose exclusively pure topics, exclusively logic topics, or, a mixture of both. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.

After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor.

You can also take the programme part-time, over a period of two years. There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.### Aims

The aims of the programme are to provide training in a range of topics related to pure mathematics and mathematical logic, to encourage a sophisticated and critical approach to mathematics, and to prepare students who have the ability and desire to follow careers as professional mathematicians and logicians in industry or research. ### Coursework and assessment

The taught component is assessed by coursework, project work and by written examination. The written exams take place at the end of January (for the first semester course units) and the end of May (for the second semester course units). The dissertation component is assessed by the quality and competence of the written dissertation.

The Postgraduate Diploma and Postgraduate Certificate exist as exit awards for students who do not pass at MSc level.### Course unit details

The taught courses cover material related to the research interests of the academic staff. Topics covered in lectured course units normally include: set theory, group theory, dynamical systems and ergodic theory, measure theory, functional analysis, algebraic topology, Godel's theorems, hyperbolic geometry, Lie algebras, analytic number theory, Galois theory, predicate logic, computation and complexity, and other topics relevant to current mathematics.

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The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from May until September.

During the taught component of the course, you will normally take five units together with a written project. You may choose exclusively pure topics, exclusively logic topics, or, a mixture of both. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.

After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor.

You can also take the programme part-time, over a period of two years. There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.

The Postgraduate Diploma and Postgraduate Certificate exist as exit awards for students who do not pass at MSc level.

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