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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 ALGANT Master program provides a study and research track in pure mathematics, with a strong focus on algebra, geometry and number theory. …
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The ALGANT Master program provides a study and research track in pure mathematics, with a strong focus on algebra, geometry and number theory. This track may be completed throughout Europe and the world, thanks to a partnership between leading research universities. The ALGANT course introduces students to the latest developments within these subjects, and provides the best possible preparation for their forthcoming doctoral studies.

The ALGANT program consists mainly of advanced courses within the field of mathematics and of a research project or internship leading to a Master thesis. Courses are offered in: algebraic geometry, algebraic and geometric topology, algebraic and analytic number theory, coding theory, combinatorics, complex function theory, cryptology, elliptic curves, manifolds. Students are encouraged to participate actively in seminars.

The university partners offer compatible basic preparation in the first year (level 1), which then leads to a complementary offer for more specialized courses in the second year (level 2).

**Year 1 (courses in French)**

**Semester 1**

- Modules and quadratic spaces (9 ECTS)
- Group theory (6 ECTS)
- Complex analysis (9 ECTS)
- Functional analysis (6 ECTS)

**Semester 2**

- Geometry (6 ECTS)
- Number theory (6 ECTS)
- Spectral theory and distributions (6 ECTS)
- Probability and statistics (6 ECTS)
- Cryptology (6 ECTS)
- Algebra and formal computations (6 ECTS)

**Year 2 (courses in English)**

**Semester 1**

- Number theory (9 ECTS)
- Algorithmic number theory (6 ECTS)
- Geometry (9 ECTS)
- Elliptic curves (6 ECTS)
- Algebraic geometry (9 ECTS)
- Analytic number theory: advanced course 1 (6 ECTS)

**Semester 2**

- Cohomology of groups: advanced course 2 (6 ECTS)
- The key role of certain inequalities at the interface between complex geometry (6 ECTS)

- Courses given by academic experts within the field of mathematics.
- Individually tailored study tracks.
- Top-quality scientific environment and facilities provided by leading global research institutes, e.g. Institut de Mathématiques de Bordeaux.
- Supported by the International Master program of the Bordeaux Initiative of Excellence.

Students who successfully complete the ALGANT program will be well equipped to pursue a career in research by preparing a Ph.D.

Graduates may also directly apply for positions as highly trained mathematicians, especially in the areas of cryptography, information security and numerical communications.

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In this Master's specialisation, mathematicians working in areas pertinent to (theoretical) computer science, like algebra and logic, and theoretical computer scientists, working in areas as formal methods and theorem proving, have joined forces to establish a specialisation in the Mathematical Foundations of Computer Science.
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In this Master's specialisation, mathematicians working in areas pertinent to (theoretical) computer science, like algebra and logic, and theoretical computer scientists, working in areas as formal methods and theorem proving, have joined forces to establish a specialisation in the Mathematical Foundations of Computer Science. The programme is unique in the Netherlands and will be built on the excellence of both research institutes and the successful collaborations therein.

The emphasis of the Master's is on a combination of a genuine theoretical and up-to-date foundation in the pertinent mathematical subjects combined with an equally genuine and up-to-date training in key aspects of theoretical computer science. For this reason, the mathematics courses in this curriculum concentrate on Algebra, Complexity Theory, Logic, Number Theory, and Combinatorics. The computer science courses concentrate on Formal Methods, Type Theory, Category Theory, Coalgebra and Theorem Proving.

Within both institutes, ICIS and WINST, there is a concentration of researchers working on mathematical logic and theoretical computer science with a collaboration that is unique in the Netherlands. The research topics range from work on algebra, logic and computability, to models of distributed, parallel and quantum computation, as well as mathematical abstractions to reason about programmes and programming languages.

See the website http://www.ru.nl/masters/mathematics/foundations### Admission requirements for international students

1. A completed Bachelor's degree in Mathematics or Computer Science

In order to get admission to this Master’s you will need a completed Bachelor's in mathematics or computer science that have a strong mathematical background and theoretical interests. We will select students based on their motivation and their background. Mathematical maturity is essential and basic knowledge of logic and discrete mathematics is expected.

2. A proficiency in English

In order to take part in the programme, you need to have fluency in English, both written and spoken. 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)

- 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### Career prospects

There is a serious shortage of well-trained information specialists. Often students are offered a job before they have actually finished their study. About 20% of our graduates choose to go on to do a PhD but most find jobs as systems builders, ICT specialists or ICT managers in the private sector or within government. ### Our approach to this field

In this Master's specialisation, mathematicians working in areas pertinent to (theoretical) computer science, like algebra and logic, and theoretical computer scientists, working in areas as formal methods and theorem proving, have joined forces to establish a specialisation in the Mathematical Foundations of Computer Science. The programme is unique in the Netherlands and will be built on the excellence of both research institutes and the successful collaborations therein.

The emphasis of the Master's is on a combination of a genuine theoretical and up-to-date foundation in the pertinent mathematical subjects combined with an equally genuine and up-to-date training in key aspects of theoretical computer science. For this reason, the mathematics courses in this curriculum concentrate on Algebra, General Topology, Logic, Number Theory, and Combinatorics. The computer science courses concentrate on Formal Methods, Type Theory, Category Theory, Coalgebra and Theorem Proving.### Our research in this field

Within both institutes, ICIS and WINST, there is a concentration of researchers working on mathematical logic and theoretical computer science with a collaboration that is unique in the Netherlands. The research topics range from work on algebra, logic and computability, to models of distributed, parallel and quantum computation, as well as mathematical abstractions to reason about programmes and programming languages.

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

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The emphasis of the Master's is on a combination of a genuine theoretical and up-to-date foundation in the pertinent mathematical subjects combined with an equally genuine and up-to-date training in key aspects of theoretical computer science. For this reason, the mathematics courses in this curriculum concentrate on Algebra, Complexity Theory, Logic, Number Theory, and Combinatorics. The computer science courses concentrate on Formal Methods, Type Theory, Category Theory, Coalgebra and Theorem Proving.

Within both institutes, ICIS and WINST, there is a concentration of researchers working on mathematical logic and theoretical computer science with a collaboration that is unique in the Netherlands. The research topics range from work on algebra, logic and computability, to models of distributed, parallel and quantum computation, as well as mathematical abstractions to reason about programmes and programming languages.

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

In order to get admission to this Master’s you will need a completed Bachelor's in mathematics or computer science that have a strong mathematical background and theoretical interests. We will select students based on their motivation and their background. Mathematical maturity is essential and basic knowledge of logic and discrete mathematics is expected.

2. A proficiency in English

In order to take part in the programme, you need to have fluency in English, both written and spoken. 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)

- 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

The emphasis of the Master's is on a combination of a genuine theoretical and up-to-date foundation in the pertinent mathematical subjects combined with an equally genuine and up-to-date training in key aspects of theoretical computer science. For this reason, the mathematics courses in this curriculum concentrate on Algebra, General Topology, Logic, Number Theory, and Combinatorics. The computer science courses concentrate on Formal Methods, Type Theory, Category Theory, Coalgebra and Theorem Proving.

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

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This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory.
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This highly focused MSc explores some of the mathematics behind modern secure information and communications systems, specialising in mathematics relevant for public key cryptography, coding theory and information theory. During the course critical awareness of problems in information transmission, data compression and cryptography is raised, and the mathematical techniques which are commonly used to solve these problems are explored.

The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography and our academic staff include several leading researchers in these areas. Students on the programme have the opportunity to carry out their dissertation projects in cutting-edge research areas and to be supervised by experts.

The transferable skills gained during the MSc will open up a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsofcryptographyandcommunications(msc).aspx### Why choose this course?

- You will be provided with a solid mathematical foundation and a knowledge and understanding of the subjects of cryptography and communications preparing you for research or professional employment in this area.

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course former students have a good foundation for the next step of their career both inside and outside academia.### Department research and industry highlights

The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry. ### Course content and structure

You will study eight courses as well as complete a main project under the supervision of a member of staff.

Core courses:

Advanced Cipher Systems

Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed as well as methods for obtaining confidentiality and authentication.

Channels

In this unit, you will investigate the problems of data compression and information transmission in both noiseless and noisy environments.

Theory of Error-Correcting Codes

The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Public Key Cryptography

This course introduces some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves. Several important public key cryptosystems are studied, such as RSA, Rabin, ElGamal Encryption, Schnorr signatures; and modern notions of security and attack models for public key cryptosystems are discussed.

Main project

The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:

Applications of Field Theory

You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory

‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms

In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics

In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics

The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory

You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory

Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:

- a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications

- the appropriate background in information theory and coding theory enabling them to understand and be able to apply the theory of communication through noisy channels

- the appropriate background in algebra and number theory to develop an understanding of modern public key cryptosystems

- a critical awareness of problems in information transmission and data compression, and the mathematical techniques which are commonly used to solve these problems

- a critical awareness of problems in cryptography and the mathematical techniques which are commonly used to provide solutions to these problems

- a range of transferable skills including familiarity with a computer algebra package, experience with independent research and managing the writing of a dissertation.### Assessment

Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 75% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 25%. ### Employability & career opportunities

Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security manager at London Underground. ### How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography and our academic staff include several leading researchers in these areas. Students on the programme have the opportunity to carry out their dissertation projects in cutting-edge research areas and to be supervised by experts.

The transferable skills gained during the MSc will open up a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsofcryptographyandcommunications(msc).aspx

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course former students have a good foundation for the next step of their career both inside and outside academia.

Core courses:

Advanced Cipher Systems

Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed as well as methods for obtaining confidentiality and authentication.

Channels

In this unit, you will investigate the problems of data compression and information transmission in both noiseless and noisy environments.

Theory of Error-Correcting Codes

The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Public Key Cryptography

This course introduces some of the mathematical ideas essential for an understanding of public key cryptography, such as discrete logarithms, lattices and elliptic curves. Several important public key cryptosystems are studied, such as RSA, Rabin, ElGamal Encryption, Schnorr signatures; and modern notions of security and attack models for public key cryptosystems are discussed.

Main project

The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:

Applications of Field Theory

You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory

‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms

In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics

In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics

The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory

You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory

Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:

- a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications

- the appropriate background in information theory and coding theory enabling them to understand and be able to apply the theory of communication through noisy channels

- the appropriate background in algebra and number theory to develop an understanding of modern public key cryptosystems

- a critical awareness of problems in information transmission and data compression, and the mathematical techniques which are commonly used to solve these problems

- a critical awareness of problems in cryptography and the mathematical techniques which are commonly used to provide solutions to these problems

- a range of transferable skills including familiarity with a computer algebra package, experience with independent research and managing the writing of a dissertation.

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We invite MPhil proposals in any of our research areas. In Pure Mathematics our two main fields are functional analysis and geometric algebra.
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We invite MPhil proposals in any of our research areas. In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.

As a research postgraduate in the School of Mathematics and Statistics you will be working under the supervision of an expert in your chosen field. To help you identify a topic and potential supervisor, we encourage you to find out more about our staff specialisms.### Research areas

Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries

Our Applied Mathematics staff have research interests in:

-Fluid dynamics, including numerical modelling of quantum fluids (superfluid liquid Helium and Bose-Einstein condensates)

-Classical and astrophysical fluids (the Earth's core, planetary dynamos, accretion discs and galaxies)

-Cosmology, including the very early universe and quantum gravity### Research seminars and events

We run weekly research seminars in algebra and geometries, analysis, and applied mathematics, as well as postgraduate seminars led by students.

Specialist courses are offered through the MAGIC distance learning consortium, sponsored in part by the Engineering and Physical Sciences Research Council (EPSRC).### Partnerships and networks

We are part of:

-The North British Functional Analysis Seminar

-The North British Geometric Group Theory Seminar

-Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society

With Durham University, we are part of the Joint Quantum Centre broadly dedicated to various aspects of quantum science.### Facilities

You will have access to online research facilities via your own desktop PC in a shared postgraduate work space. There is also a teaching cluster (of about 150 PCs) within the School.

As well as the library resources provided by the main Robinson Library, you will have access to the School's mathematics and statistics library and reading room.

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As a research postgraduate in the School of Mathematics and Statistics you will be working under the supervision of an expert in your chosen field. To help you identify a topic and potential supervisor, we encourage you to find out more about our staff specialisms.

Our Applied Mathematics staff have research interests in:

-Fluid dynamics, including numerical modelling of quantum fluids (superfluid liquid Helium and Bose-Einstein condensates)

-Classical and astrophysical fluids (the Earth's core, planetary dynamos, accretion discs and galaxies)

-Cosmology, including the very early universe and quantum gravity

Specialist courses are offered through the MAGIC distance learning consortium, sponsored in part by the Engineering and Physical Sciences Research Council (EPSRC).

-The North British Functional Analysis Seminar

-The North British Geometric Group Theory Seminar

-Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society

With Durham University, we are part of the Joint Quantum Centre broadly dedicated to various aspects of quantum science.

As well as the library resources provided by the main Robinson Library, you will have access to the School's mathematics and statistics library and reading room.

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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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The master’s programme Mathematics focuses on analysis and number theory. From applied to fundamental research, and from algebra to data science, our master’s programme spans these fields entirely.
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The master’s programme Mathematics focuses on analysis and number theory. From applied to fundamental research, and from algebra to data science, our master’s programme spans these fields entirely.

The two-year master's programme Mathematics has two components: an analysis-oriented component with topics such as dynamical systems, differential equations, probability theory and stochastics, percolation and mathematics in the life sciences, and an algebra/geometry-oriented component with topics such as algebraic number theory, algebraic geometry, algebraic topology and cryptology. The goal of each programme is to train the student as an independent researcher, and to develop the necessary skills and proficiency to advance your career.

Read more about our Mathematics programme.

- Your study programme can be fine-tuned to your own mathematical interests, both pure and applied.
- You will be educated by renowned researchers like Spinoza prize winner Aad van der Vaart and Hendrik Lenstra and receive a top level education in Mathematics.
- The institute has an extensive international network which allows you to broaden your horizon and provide you with ample opportunities to join interdisciplinary seminars and pursue interdisciplinary research projects.

Find more reasons to choose Mathematics at Leiden University.

The master’s programme in Mathematics in Leiden focuses on analysis, probability and statistics, number theory and (arithmetic) geometry. If you are looking for an opportunity to specialize in one of these areas, Leiden is an excellent possibility. Students who have obtained a Master of Science degree in Mathematics possess a thorough theoretical basis, know how to work in a multinational environment, and are able to operate well on the international market.

Read more about the entry requirements for Mathematics.

- Algebra, Geometry and Number Theory (MSc)
- Mathematics and Education (MSc)
- Mathematics and Science Communication and Society (MSc)
- Applied Mathematics (MSc)
- Mathematics and Business Studies (MSc)

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This course covers a wide range of topics from both applied and applicable mathematics and is aimed at students who want to study the field in greater depth, in areas which are relevant to real life applications.
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This course covers a wide range of topics from both applied and applicable mathematics and is aimed at students who want to study the field in greater depth, in areas which are relevant to real life applications.

You will explore the mathematical techniques that are commonly used to solve problems in the real world, in particular in communication theory and in physics. As part of the course you will carry out an independent research investigation under the supervision of a member of staff. Popular dissertation topics chosen by students include projects in the areas of communication theory, mathematical physics, and financial mathematics.

The transferable skills gained on this course will open you up to a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsforapplications.aspx### Why choose this course?

- You will be provided with a solid mathematical foundation and knowledge and understanding of the subjects of cryptography and communications, preparing you for research or professional employment in this area.

- The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography. The academics who teach on this course include several leading researchers in these areas.

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course students have a good foundation for the next step of their career both inside and outside academia.### Department research and industry highlights

The members of the Mathematics Department cover a range of research areas. There are particularly strong groups in information security, number theory, quantum theory, group theory and combinatorics. The Information Security Group has particularly strong links to industry. ### Course content and structure

You will study eight courses and complete a main project under the supervision of a member of staff.

Core courses:

Theory of Error-Correcting Codes

The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Advanced Cipher Systems

Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed, as well as methods for obtaining confidentiality and authentication.

Main project

The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:

Applications of Field Theory

You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory

‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms

In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics

In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics

The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory

You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory

Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:

- knowledge and understanding of: the principles of communication through noisy channels using coding theory; the principles of cryptography as a tool for securing data; and the role and limitations of mathematics in the solution of problems arising in the real world

- a high level of ability in subject-specific skills, such as algebra and number theory

- developed the capacity to synthesise information from a number of sources with critical awareness

- critically analysed the strengths and weaknesses of solutions to problems in applications of mathematics

- the ability to clearly formulate problems and express technical content and conclusions in written form

- personal skills of time management, self-motivation, flexibility and adaptability.### Assessment

Assessment is carried out by a variety of methods including coursework, examinations and a dissertation. The examinations in May/June count for 75% of the final average and the dissertation, which has to be submitted in September, counts for the remaining 25%. ### Employability & career opportunities

Our students have gone on to successful careers in a variety of industries, such as information security, IT consultancy, banking and finance, higher education and telecommunication. In recent years our graduates have entered into roles including Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security Manager at London Underground. ### How to apply

Applications for entry to all our full-time postgraduate degrees can be made online https://www.royalholloway.ac.uk/studyhere/postgraduate/applying/howtoapply.aspx .

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You will explore the mathematical techniques that are commonly used to solve problems in the real world, in particular in communication theory and in physics. As part of the course you will carry out an independent research investigation under the supervision of a member of staff. Popular dissertation topics chosen by students include projects in the areas of communication theory, mathematical physics, and financial mathematics.

The transferable skills gained on this course will open you up to a range of career options as well as provide a solid foundation for advanced research at PhD level.

See the website https://www.royalholloway.ac.uk/mathematics/coursefinder/mscmathematicsforapplications.aspx

- The Mathematics Department at Royal Holloway is well known for its expertise in information security and cryptography. The academics who teach on this course include several leading researchers in these areas.

- The mathematical foundations needed for applications in communication theory and cryptography are covered including Algebra, Combinatorics Complexity Theory/Algorithms and Number Theory.

- You will have the opportunity to carry out your dissertation project in a cutting-edge research area; our dissertation supervisors are experts in their fields who publish regularly in internationally competitive journals and there are several joint projects with industrial partners and Royal Holloway staff.

- After completing the course students have a good foundation for the next step of their career both inside and outside academia.

Core courses:

Theory of Error-Correcting Codes

The aim of this unit is to provide you with an introduction to the theory of error-correcting codes employing the methods of elementary enumeration, linear algebra and finite fields.

Advanced Cipher Systems

Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed, as well as methods for obtaining confidentiality and authentication.

Main project

The main project (dissertation) accounts for 25% of the assessment of the course and you will conduct this under the supervision of a member of academic staff.

Additional courses:

Applications of Field Theory

You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

Quantum Information Theory

‘Anybody who is not shocked by quantum theory has not understood it' (Niels Bohr). The aim of this unit is to provide you with a sufficient understanding of quantum theory in the spirit of the above quote. Many applications of the novel field of quantum information theory can be studied using undergraduate mathematics.

Network Algorithms

In this unit you will be introduced to the formal idea of an algorithm, when it is a good algorithm and techniques for constructing algorithms and checking that they work; explore connectivity and colourings of graphs, from an algorithmic perspective; and study how algebraic methods such as path algebras and cycle spaces may be used to solve network problems.

Advanced Financial Mathematics

In this unit you will investigate the validity of various linear and non-linear time series occurring in finance and extend the use of stochastic calculus to interest rate movements and credit rating;

Combinatorics

The aim of this unit is to introduce some standard techniques and concepts of combinatorics, including: methods of counting including the principle of inclusion and exclusion; generating functions; probabilistic methods; and permutations, Ramsey theory.

Computational Number Theory

You will be provided with an introduction to many major methods currently used for testing/proving primality and for the factorisation of composite integers. The course will develop the mathematical theory that underlies these methods, as well as describing the methods themselves.

Complexity Theory

Several classes of computational complexity are introduced. You will discuss how to recognise when different problems have different computational hardness, and be able to deduce cryptographic properties of related algorithms and protocols.

On completion of the course graduates will have:

- knowledge and understanding of: the principles of communication through noisy channels using coding theory; the principles of cryptography as a tool for securing data; and the role and limitations of mathematics in the solution of problems arising in the real world

- a high level of ability in subject-specific skills, such as algebra and number theory

- developed the capacity to synthesise information from a number of sources with critical awareness

- critically analysed the strengths and weaknesses of solutions to problems in applications of mathematics

- the ability to clearly formulate problems and express technical content and conclusions in written form

- personal skills of time management, self-motivation, flexibility and adaptability.

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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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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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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: graduate@potsdam.edu

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: graduate@potsdam.edu

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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Mathematics is the language that underpins the rest of science. Our Department of Mathematical Sciences has an international reputation in many areas like such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.
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Mathematics is the language that underpins the rest of science. Our Department of Mathematical Sciences has an international reputation in many areas like such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology.

Graduate Diplomas last for six to nine months (full-time) and include the modules and assessed work of a Masters, without a dissertation. Our Graduate Diploma in Mathematics gives you training in basic mathematics techniques if your first degree contained only a modest amount of mathematics, so that you can proceed to a Masters in mathematics.

At Essex, Mathematics has truly broad reach; we are working on projects ranging from the economic impact of the behaviour of dairy cows, to understanding crowd behaviour through modelling a zombie apocalypse, to circular Sudoku and other puzzles. Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

You therefore gain an exceptional range of knowledge and skills that are currently in demand in mathematically oriented employment; in business, commerce, industry, government service, education and in the wider economy.### Our expert staff

Our Department of Mathematical Sciences is a small but influential department, so our students and staff know each other personally. You never need an appointment to see your tutors and supervisors, just knock on our office doors – we are one of the few places to have an open-door policy, and no issue is too big or small.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.### Specialist facilities

-Unique to Essex is our renowned Maths Support Centre, which offers help to students, staff and local businesses on a range of mathematical problems. Throughout term-time, we can chat through mathematical problems either on a one-to-one or small group basis

-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple

-We host regular events and seminars throughout the year

-Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students### Your future

Our graduates are highly sought after by a range of employers and find employment in financial services, scientific computation, decision making support and government, risk assessment, statistics, education and other sectors.

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.### Example structure

-Applied Statistics (optional)

-Bayesian Computational Statistics (optional)

-Combinatorial Optimisation (optional)

-Complex Variables and Applications (optional)

-Contingencies I

-Contingencies II

-Cryptography and Codes

-Finance and Financial Reporting (optional)

-Financial Derivatives (optional)

-Graph Theory (optional)

-Introduction to Numerical Methods (optional)

-Linear Algebra (optional)

-Mathematical Biology (optional)

-Mathematical Methods (optional)

-Mathematics of Portfolios (optional)

-Modelling Experimental Data (optional)

-Nonlinear Programming (optional)

-Ordinary Differential Equations (optional)

-Partial Differential Equations (optional)

-Project: Mathematics (optional)

-Quantum Mechanics (optional)

-Real Analysis (optional)

-Statistical Methods (optional)

-Statistics II (optional)

-Stochastic Processes (optional)

-Survival Analysis (optional)

-The Laws of Physics (optional)

-Vector Calculus (optional)

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Graduate Diplomas last for six to nine months (full-time) and include the modules and assessed work of a Masters, without a dissertation. Our Graduate Diploma in Mathematics gives you training in basic mathematics techniques if your first degree contained only a modest amount of mathematics, so that you can proceed to a Masters in mathematics.

At Essex, Mathematics has truly broad reach; we are working on projects ranging from the economic impact of the behaviour of dairy cows, to understanding crowd behaviour through modelling a zombie apocalypse, to circular Sudoku and other puzzles. Our interdisciplinary research recognises that mathematics, including what can be very abstract mathematics, is an essential part of research in many other disciplines.

You therefore gain an exceptional range of knowledge and skills that are currently in demand in mathematically oriented employment; in business, commerce, industry, government service, education and in the wider economy.

Our staff have published several well-regarded text books and are world leaders in their individual specialisms, with their papers appearing in learned journals like Communications in Algebra, Studia Logica, International Journal of Algebra and Computation, SIAM Journal in Optimization, IEEE Evolutionary Computation, Computers and Operations Research, Ecology, Journal of Mathematical Biology, and Journal of Statistical Applications in Genetics and Molecular Biology.

-We have our own computer labs for the exclusive use of students in the Department of Mathematical Sciences – in addition to your core maths modules, you gain computing knowledge of software including Matlab and Maple

-We host regular events and seminars throughout the year

-Our students run a lively Mathematics Society, an active and social group where you can explore your interest in your subject with other students

We also offer supervision for PhD, MPhil and MSc by Dissertation. We have an international reputation in many areas such as semi-group theory, optimisation, probability, applied statistics, bioinformatics and mathematical biology, and our staff are strongly committed to research and to the promotion of graduate activities.

We additionally work with our Employability and Careers Centre to help you find out about further work experience, internships, placements, and voluntary opportunities.

-Bayesian Computational Statistics (optional)

-Combinatorial Optimisation (optional)

-Complex Variables and Applications (optional)

-Contingencies I

-Contingencies II

-Cryptography and Codes

-Finance and Financial Reporting (optional)

-Financial Derivatives (optional)

-Graph Theory (optional)

-Introduction to Numerical Methods (optional)

-Linear Algebra (optional)

-Mathematical Biology (optional)

-Mathematical Methods (optional)

-Mathematics of Portfolios (optional)

-Modelling Experimental Data (optional)

-Nonlinear Programming (optional)

-Ordinary Differential Equations (optional)

-Partial Differential Equations (optional)

-Project: Mathematics (optional)

-Quantum Mechanics (optional)

-Real Analysis (optional)

-Statistical Methods (optional)

-Statistics II (optional)

-Stochastic Processes (optional)

-Survival Analysis (optional)

-The Laws of Physics (optional)

-Vector Calculus (optional)

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Candidates who have a good undergraduate (BSc) degree or equivalent but whose mathematical background is insufficient for direct entry to the MSc programme may apply for a place on the conversion year for the MSc in Mathematical Finance.
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Candidates who have a good undergraduate (BSc) degree or equivalent but whose mathematical background is insufficient for direct entry to the MSc programme may apply for a place on the conversion year for the MSc in Mathematical Finance.

A place on the conversion year is normally offered together with a conditional offer for the MSc in Mathematical Finance in the following year, subject to successfully completing the conversion year. The normal progression requirement for progression from the conversion year to the MSc in Mathematical Finance is a final weighted average at 2:1 level (60% or above) for the modules taken in the conversion year.### Programme structure

The conversion year consists of a selection of modules to the value of 120 credits being part of the undergraduate degree in Mathematics and Finance at the University of York, with emphasis on the mathematical aspects of the course. Module choice is subject to prerequisites, timetabling constraints, availability of modules, and is subject to approval by the programme director.

The available modules may vary from year to year but are likely to include:

Term 1 (Autumn)

-Calculus (30 credits) (continues into Spring and Summer Terms)

-Algebra (20 credits) (continues into Spring and Summer Terms)

-Introduction to Probability and Statistics (20 credits)

-Statistics I (10 credits)

-Applied Probability (10 credits)

-Differential Equations (10 credits)

-Mathematical Finance I MAT00015H (10 credits)

Terms 2 and 3 (Spring and Summer Terms)

-Calculus (30 credits) (starts in Autumn, continues through Spring and completes in Summer Term)

-Algebra (20 credits) (starts in Autumn, continues through Spring and completes in Summer Term)

-Introduction to Applied Mathematics (20 credits) (starts in Spring Term, continues into Summer Term)

-Real Analysis (20 credits) (starts in Spring Term, continues into Summer Term)

-Linear Algebra (20 credits) (starts in Spring Term, continues into Summer Term)

-Vector Calculus (20 credits) (starts in Spring Term, continues into Summer Term)

-Statistics II (20 credits) (starts in Spring Term, continues into Summer Term)

-Numerical Analysis (10 credits) (Spring Term only)

-Mathematical Finance II (10 credits) (Spring Term only)

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A place on the conversion year is normally offered together with a conditional offer for the MSc in Mathematical Finance in the following year, subject to successfully completing the conversion year. The normal progression requirement for progression from the conversion year to the MSc in Mathematical Finance is a final weighted average at 2:1 level (60% or above) for the modules taken in the conversion year.

The available modules may vary from year to year but are likely to include:

Term 1 (Autumn)

-Calculus (30 credits) (continues into Spring and Summer Terms)

-Algebra (20 credits) (continues into Spring and Summer Terms)

-Introduction to Probability and Statistics (20 credits)

-Statistics I (10 credits)

-Applied Probability (10 credits)

-Differential Equations (10 credits)

-Mathematical Finance I MAT00015H (10 credits)

Terms 2 and 3 (Spring and Summer Terms)

-Calculus (30 credits) (starts in Autumn, continues through Spring and completes in Summer Term)

-Algebra (20 credits) (starts in Autumn, continues through Spring and completes in Summer Term)

-Introduction to Applied Mathematics (20 credits) (starts in Spring Term, continues into Summer Term)

-Real Analysis (20 credits) (starts in Spring Term, continues into Summer Term)

-Linear Algebra (20 credits) (starts in Spring Term, continues into Summer Term)

-Vector Calculus (20 credits) (starts in Spring Term, continues into Summer Term)

-Statistics II (20 credits) (starts in Spring Term, continues into Summer Term)

-Numerical Analysis (10 credits) (Spring Term only)

-Mathematical Finance II (10 credits) (Spring Term only)

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

The topics we cover include:

- advanced probability theory

- algebra

- asymptotic methods

- geometry

- mathematical biology

- partial differential equations

- quantum field theory

- singularity theory

- stochastic analysis

- standard model/string theory.

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

REF 2014

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

Facilities

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

Range and depth of study options

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

Exceptional employability

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

Teaching quality

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

Accessibility

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

Supportive atmosphere

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

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

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The topics we cover include:

- advanced probability theory

- algebra

- asymptotic methods

- geometry

- mathematical biology

- partial differential equations

- quantum field theory

- singularity theory

- stochastic analysis

- standard model/string theory.

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

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

Facilities

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

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

Exceptional employability

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

Teaching quality

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

Accessibility

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

Supportive atmosphere

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

Read less

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