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Masters Degrees (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. … Read more

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). 

Program structure

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)

Strengths of this Master program

  • 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.

After this Master program?

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

Key features of the course

•Ideal for mathematically inclined scientists and engineers as well as mathematicians
•Extends your knowledge and refines your abilities to process information accurately, and critically analyse and communicate complex ideas
•Develops an enhanced skill set that will put you at an advantage in careers as diverse as mathematics, education, computer science, economics, engineering and finance.
•The most popular MSc in mathematics in the UK.
This qualification is eligible for a Postgraduate Loan available from Student Finance England. For more information, see Fees and funding

Course details

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

Modules

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

Entry:

• Calculus of variations and advanced calculus (M820)
• Analytic number theory I (M823)

Intermediate:

• Nonlinear ordinary differential equations (M821)
• Applied complex variables (M828) - next available in October 2017 and following alternate years
• Analytic number theory II (M829) - next available in October 2018 and following alternate years
• Approximation theory (M832) - next available in October 2018 and following alternate years
• Advanced mathematical methods (M833) - next available in October 2017 and following alternate years
• Fractal geometry (M835) - next available in October 2017 and following alternate years
• Coding theory (M836) - next available in October 2018 and following alternate years
• Dissertation: Dissertation in mathematics (M840)

Module study order:

•You must normally pass at least one entry level module before studying an intermediate module.
•You must pass Analytic number theory I (M823) before studying Analytic number theory II (M829).
•You must normally pass four modules before studying the Dissertation in mathematics (M840).
•Some topics for the dissertation have prerequisite modules

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

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

150 credits from this list:

Optional modules

• Advanced mathematical methods (M833)
• Analytic number theory I (M823)
• Analytic number theory II (M829)
• Applied complex variables (M828)
• Approximation theory (M832)
• Calculus of variations and advanced calculus (M820)
• Coding theory (M836)
• Fractal geometry (M835)
• Nonlinear ordinary differential equations (M821)

Plus

Compulsory module

Dissertation in mathematics (M840)

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

Credit transfer

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

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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. Read more

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.

What does this master’s programme entail?

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.

Why study Mathematics at Leiden University?

  • 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.

Mathematics: the right master’s programme for you?

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.

Specialisations



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Excited by the role of mathematics in securing the modern electronics and communications that we all rely on? This intensive MSc programme explores the mathematics behind secure information and communications systems, in a department that is world renowned for research in the field. Read more

Excited by the role of mathematics in securing the modern electronics and communications that we all rely on? This intensive MSc programme explores the mathematics behind secure information and communications systems, in a department that is world renowned for research in the field.

You will learn to apply advanced mathematical ideas to cryptography, coding theory and information theory, by studying the relevant functions of algebra, number theory and combinatorial complexity theory and algorithms. In the process you will develop a critical appreciation of the challenges that mathematicians face in facilitating secure information transmission, data compression and encryption. You will learn to use advanced cypher systems, correcting codes and modern public key crypto-systems. As part of your studies you will have the opportunity to complete a supervised dissertation in an area of your choice, under the guidance of experts in the field who regularly publish in internationally competitive journals and work closely with partners in industry.

We are a lively, collaborative and supportive community of mathematicians and information security specialists, and thanks to our relatively compact scale we will take the time to get to know you as an individual. You will be assigned a personal advisor to guide you through your studies.

Mathematicians who can push the boundaries and stay ahead when it comes to cryptography and information security are in demand, and the skills you gain will open up a range of career options and provide a solid foundation if you wish to progress to a PhD. These include transferable skills such as familiarity with a computer-based algebra package, experience of carrying out independent research and managing the writing of a dissertation.

  • Learn from internationally renowned mathematicians, cryptographers and communications specialists.
  • Complete a cutting-edge research project under the supervision of cryptography and communications experts.
  • Enjoy the flexibility to tailor your degree to your interests and specialisms.
  • Join a mathematics department that ranks second in the UK for research impact and fourth for world leading or internationally excellent research output (Research Excellence Framework 2014).
  • Feel at home in a friendly department where you will be known as an individual.

Course structure

Core modules

  • Main Project
  • Advanced Cipher Systems
  • Channels
  • Theory of Error-Correcting Codes
  • Public Key Cryptography

Optional modules

In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.

  • Applications of Field Theory
  • Quantum Information and Coding
  • Principles of Algorithm Design
  • Advanced Financial Mathematics
  • Combinatorics
  • Computational Number Theory
  • Complexity Theory
  • Inference
  • Topology
  • Applied Probability

Teaching & assessment

You will initially choose 8 courses from the list of available options, of which you specify 6 courses during the second term that will count towards your final award. You will also complete a core research project under the supervision of one of our academic staff.There is a strong focus on small group teaching throughout the programme.

Assessment is carried out through a variety of methods, including coursework, examinations and the main project. End-of-year examinations in May or June will count for 66.7% of your final award, while the dissertation will make up the remaining 33.3% and has to be submitted by September.

Your future career

By the end of this programme you will have an advanced knowledge and understanding of all the key mathematical principles and applications that underpin modern cryptography and communications. You will have advanced skills in coding, algebra and number theory, and be able to synthesise and interpret information from multiple sources with insight and critical awareness. You will have learnt to formulate problems clearly, to undertake independent research and to express your technical work and conclusions clearly in writing. You will also have valuable transferable skills such as advanced numeracy and IT skills, time management, adaptability and self-motivation.

Graduates from this programme have gone on to carry out cutting-edge research in the fields of communication theory and cryptography, as well as to successful careers in industries such as: information security, IT consultancy, banking and finance, higher education and telecommunications. Our mathematics postgraduates have taken up roles such as: 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.

The campus Careers team will be on hand to offer advice and guidance on your chosen career. The University of London Careers Advisory Service runs regular, tailored sessions for mathematics students, on finding summer internships or vacation employment and getting into employment.

  • Open doors to a range of exciting opportunities in academic research or professional employment.
  • Our strong ties with industry mean we understand the needs of employers and we have a strong track record of helping graduates into successful, high-level careers.
  • 90% of our graduates are in work or undertaking further study within six months of leaving (Unistats 2015).


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

Current faculty projects and research interests:

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

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

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

• Algebraic Number Theory, especially rings of algebraic integers

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

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

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

• Coding theory, especially relation of designs to codes

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

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

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

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

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

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

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

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

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

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

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

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

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

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

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

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

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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. Read more

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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To gain this qualification, you need 180 credits as follows. Stage 1. 60 credits from List A. List A. optional modules. Advanced routing - CCNP 1 (T824). Read more

Modules

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

Stage 1

60 credits from List A:

List A: optional modules

• Advanced routing - CCNP 1 (T824)
• Capacities for managing development (T878)
• Conflict and development (T879)
• Development: context and practice (T877)
• Environmental monitoring and protection (T868)
• Finite element analysis: basic principles and applications (T804)
• Institutional development (TU872)
• Making environmental decisions (T891)
• Managing for sustainability (T867)
• Managing systemic change: inquiry, action and interaction (TU812)
• Managing technological innovation (T848)
• Manufacture materials design (T805)
• Multilayer switching - CCNP 3 (T826)
• Network security (T828)
• Optimising networks - CCNP 4 (T827)
• Problem solving and improvement: quality and other approaches (T889)
• Strategic capabilities for technological innovation (T849)
• Thinking strategically: systems tools for managing change (TU811)

Plus 30 credits from List B:

List B: optional modules

• Advanced mathematical methods (M833)
• Advanced routing - CCNP 1 (T824)
• Analytic number theory I (M823)
• Analytic number theory II (M829)
• Applied complex variables (M828)
• Approximation theory (M832)
• Calculus of variations and advanced calculus (M820)
• Capacities for managing development (T878)
• Coding theory (M836)
• Conflict and development (T879)
• Data management (M816)
• Developing research skills in science (S825)
• Development: context and practice (T877)
• Digital forensics (M812)
• Environmental monitoring and protection (T868)
• Finite element analysis: basic principles and applications (T804)
• Fractal geometry (M835)
• Information security (M811)
• Institutional development (TU872)
• Making environmental decisions (T891)
• Managing for sustainability (T867)
• Managing systemic change: inquiry, action and interaction (TU812)
• Managing technological innovation (T848)
• Manufacture materials design (T805)
• Multilayer switching - CCNP 3 (T826)
• Network security (T828)
• Nonlinear ordinary differential equations (M821)
• Optimising networks - CCNP 4 (T827)
• Problem solving and improvement: quality and other approaches (T889)
• Project management (M815)
• Researching mathematics learning (ME825)*
• Software development (M813)
• Software engineering (M814)
• Space science (S818) NEW1
• Strategic capabilities for technological innovation (T849)
• Thinking strategically: systems tools for managing change (TU811)

* 60-credit module of which only 30 credits count towards this qualification

Plus 30 credits from:

Compulsory module

Team engineering (T885)

Stage 2

60 credits from:

Compulsory module

Research project (T802)

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

Credit transfer

Credit transfer is not permitted for the MSc except for any awarded as part of the Postgraduate Diploma in Engineering.
For further advice and guidance, please email us.

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Mathematics. is a core scientific subject and an essential basis for a range of other sciences. Read more

Mathematics is a core scientific subject and an essential basis for a range of other sciences. This programme brings together the latest developments in a range of mathematical disciplines to provide you with a thorough grounding in the subject, together with a substantial project that can be used to develop a specialisation.

Internationally leading research supports this programme, with particular research strengths including magnetic fields, interface of algebraic number theory and abstract algebra, climate system dynamics and display-structure on crystalline cohomology.

The programme prepares you for a career in numerous industries or for progression to a PhD for those interested in pursuing a research pathway.

Programme structure

The programme comprises three compulsory taught modules and 90 credits of option modules. The taught component of the programme is completed in June with the project extending over the summer period for submission in September.

Compulsory Modules

The compulsory modules can include;

  • Research in Mathematical Sciences;
  • Advanced Mathematics Project

Optional Modules

Some examples of the optional modules are as follows;

  • Logic and Philosophy of Mathematics;
  • Methods for Stochastics and Finance;
  • Mathematical Theory of Option Pricing;
  • Dynamical Systems and Chaos;
  • Fluid Dynamics of Atmospheres and Oceans;
  • Modelling the Weather and Climate;
  • The Climate System;
  • Algebraic Number Theory;
  • Algebraic Curves;
  • Waves, Instabilities and Turbulence;
  • Magnetic Fields and Fluid Flows;
  • Statistical Modelling in Space and Time
  • Mathematical Modelling in Biology and Medicine.

The modules we outline here provide examples of what you can expect to learn on this degree course based on recent academic teaching. The precise modules available to you in future years may vary depending on staff availability and research interests, new topics of study, timetabling and student demand.



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About the course. This intensive introduction to advanced pure and applied mathematics draws on our strengths in algebra, geometry, topology, number theory, fluid dynamics and solar physics. Read more

About the course

This intensive introduction to advanced pure and applied mathematics draws on our strengths in algebra, geometry, topology, number theory, fluid dynamics and solar physics.

You’ll attend lectures but you’ll also get hands-on research experience, writing a dissertation supervised by an active researcher.

Your career

Our graduates go into finance, manufacturing and pharmaceuticals. They work for government agencies and research institutes with major organisations such as First Direct, GlaxoSmithKline, Marks and Spencer, the Government Statistical Service and Medical Research Council units. Our courses can also prepare you for PhD-level research.

About us

Our academics are in demand. They are members of international societies and organisations, and they speak at conferences around the world. They bring new ideas into the classroom so you can see how research is improving on existing approaches. Our solar scientists were the first to record musical sounds created by vibrations in the sun’s atmosphere.

Our Statistical Services Unit works with industry, commerce and the public sector. The services they provide include consultancy, training courses and computer software development.

Different ways to study

You can study full-time over a year or part-time over two to three years via online distance learning. The MSc Mathematics is only available as a full-time course.

Modules

Possible module choices include:

  • Algebra
  • Analysis
  • Geometry
  • Algebraic Topology
  • Number Theory
  • Topics in Advanced Fluid Dynamics
  • Analytical Dynamics and Classical Field Theory
  • Mathematical Modelling of Natural Systems
  • Stochastic Processes and Finance
  • Waves and Magnetohydrodynamics

Teaching and assessment

There are lectures and seminars. You’re assessed by exams, coursework and a dissertation.



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Overview. The MSc Pure Mathematics offers a modern research-oriented taught course, providing students with a broader and deeper understanding of several core areas of pure mathematics that are of strong current interest and with a solid foundation for a career in research in pure mathematics. Read more

Overview

The MSc Pure Mathematics offers a modern research-oriented taught course, providing students with a broader and deeper understanding of several core areas of pure mathematics that are of strong current interest and with a solid foundation for a career in research in pure mathematics. The programme covers a wide range of topics in algebra, analysis and number theory.

The course is informed by the research interests of the members of the Division of Pure Mathematics

Key facts:

- The School of Mathematical Sciences is one of the largest and strongest mathematics departments in the UK, with over 60 full-time academic staff

- In the latest independent Research Assessment Exercise, the school ranked eighth in the UK in terms of research power across the three subject areas within the School of Mathematical Sciences (pure mathematics, applied mathematics, statistics and operational research)

Modules

Advanced Linear Analysis

Algebraic Geometry

Algebraic Number Theory

Combinatorial Group Theory

Complex Analysis

Further Topics in Analysis

Further Topics in Rings and Modules

Pure Mathematics Dissertation

English language requirements for international students

IELTS: 6.0 (with no less than 5.5 in any element)

Further information



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The MSc in Mathematics and Foundations of Computer Science, run jointly by the. Mathematical Institute. and the. Department of Computer Science. Read more

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

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

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

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

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

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

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

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

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



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This programme offers you the chance to study a range of theories in depth. It engages with modern literary theory, psychoanalytical theory, political theory and theories of visual and aesthetic experience. Read more
This programme offers you the chance to study a range of theories in depth. It engages with modern literary theory, psychoanalytical theory, political theory and theories of visual and aesthetic experience.

You reflect on these areas of thinking in themselves and as they relate to particular literary texts, to post-enlightenment philosophy and to other relevant areas of culture and experience. It is for those interested in writing, reading, language, art, the self, literature and discovering more about the relations between literature and philosophy.

The MA in Critical Theory offers a choice of two core courses that survey a wide range of modern theoretical approaches, and a range of taught options covering postcolonial theory, theories of art, modern approaches to comparative literature, deconstruction and a chance to work in depth on a single key theoretical text and the writings it refers to.

Visit the website https://www.kent.ac.uk/courses/postgraduate/216/critical-theory

About the School of English

The School of English has a strong international reputation and global perspective, apparent both in the background of its staff and in the diversity of our teaching and research interests.

Our expertise ranges from the medieval to the postmodern, including British, American and Irish literature, postcolonial writing, 18th-century studies, Shakespeare, early modern literature and culture, Victorian studies, modern poetry, critical theory and cultural history. The international standing of the School ensures that we have a lively, confident research culture, sustained by a vibrant, ambitious intellectual community. We also count a number of distinguished creative writers among our staff, and we actively explore crossovers between critical and creative writing in all our areas of teaching and research.

The Research Excellence Framework 2014 has produced very strong results for the School of English at Kent. With 74% of our work graded as world-leading or internationally excellent, the School is ranked 10th out of 89 English departments in terms of Research Intensity (Times Higher Education). The School also received an outstanding assessment of the quality of its research environment and public impact work.

Course structure

You take two modules in the autumn term and two in the spring term; one core module (FR866: Literature and Theory) and three optional modules. You are also expected to attend the Faculty and School Research Methods Programmes.

You then write a theory-based dissertation between the start of the Summer Term and the end of August.

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.

FR866 - Literature and Theory (30 credits)
FR807 - Postmodern French Detective Fiction (30 credits)
EN889 - Literary Theory (30 credits)
EN897 - Advanced Critical Reading (30 credits)
FR872 - Theories of Art in Modern French Thought (30 credits)
CP808 - Writing the Self: Autobiography in the Modern Period (30 credits)
CP810 - Comparative Literature in Theory and Practice (30 credits)
EN852 - Colonial and Postcolonial Discourses (30 credits)
EN857 - Body and Place in the Postcolonial Text (30 credits)
TH831 - Spirituality and Therapy (30 credits)
TH833 - Contemporary Critical Approaches to the Study of Religion (30 credits)
EN876 - Dickens and the Condition of England (30 credits)
EN888 - Extremes of Feeling: Literature and Empire in the Eighteenth Century (30 credits)
EN818 - American Modernism 1900-1930 (Teaching Period I) (30 credits)
EN832 - Hacks, Dunces and Scribblers: Authorship and the Marketplace in the Eig (30 credits)
EN835 - Dickens, The Victorians and the Body (30 credits)
EN842 - Reading the Contemporary (30 credits)
EN850 - Centres and Edges: Modernist and PostcolonialQuest Literature (30 credits)
MT864 - Reading the Medieval Town: Canterbury, an International City (30 credits)

Assessment

The course is assessed by coursework for each module and by the dissertation which accounts for a third of the final grade.

Programme aims

This programme aims to:

- extend and deepen through coursework and research your understanding of modern literary and critical theory

- study the reading-practices, analytic tools and vocabularies of modern critical thought

- develop your independent critical thinking and judgement

- introduce you to the research methods that facilitate advanced theoretical study of literature

- provide a basis in knowledge and skills if you intend to teach critical theory, especially in higher education

- develop your understanding and critical awareness of the expressive and analytical resources of language

- offer scope for the study of critical theory within an interdisciplinary context, notably that provided by philosophy

- develop your ability to argue a point of view with clarity and cogency, both orally and in written form

- examine this writing in the wider context of literature, culture and philosophy

- provide teaching which is informed by current research and scholarship and which requires you to engage with aspects of work at the frontiers of knowledge

- develop your research skills to the point where you are ready to undertake a research degree, should you so wish.

Careers

Many career paths can benefit from the writing and analytical skills that you develop as a postgraduate student in the School of English. Our students have gone on to work in academia, journalism, broadcasting and media, publishing, writing and teaching; as well as more general areas such as banking, marketing analysis and project management.

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

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

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

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

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

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

Why study Applied Stochastics at Radboud University?

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

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

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

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

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

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

Career prospects

Master's programme in Mathematics

Mathematicians are needed in all industries, including the banking, technology and service industries, to name a few. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.

Job positions

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

PhD positions

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

Our research in this field

The research of members of the Applied Stochastics Department, focuses on combinatorics, (quantum) probability and mathematical statistics. Below, a small sample of the research our members pursue.

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

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

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

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

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

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

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



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

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

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

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

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

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

Aims

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

Coursework and assessment

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

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

Course unit details

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



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“There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world.” –. Nikolai Ivanovich Lobachevsky. Read more

“There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world.” – Nikolai Ivanovich Lobachevsky

If you're looking to take your undergraduate mathematics experience to new levels and develop advanced research skills, this intensive programme covers the wide spectrum of discrete mathematics, applied mathematics and statistics, and addresses some of the key quantifiable challenges and opportunities in the world around us. An interdisciplinary subject by nature, we will help you to apply mathematical concepts and methods to the ever-changing worlds of science, engineering, business, digital technology and industry, and particularly to communication theory, mathematical physics and financial mathematics, where some of our key research interests lie.

The skills you gain will open up a range of career options and provide a solid foundation if you wish to progress to a PhD. You will be guided by renowned specialists in the field who publish in internationally competitive journals and work closely with partners in industry.

Join our friendly and inspiring department and you will benefit from a thoroughly supportive learning environment, with generous staff office hours and a dedicated personal advisor to help you with any queries and guide you through your degree. Our graduates are in demand for their skills in research, numeracy, data handling and analysis, logical thinking and creative problem solving.

  • Apply your mathematics to real-world situations and gain the skills to work at a high level in industry, business or research.
  • Learn from internationally renowned mathematicians. We rank second in the UK for our research impact and fourth for world leading or internationally excellent research output (Research Excellence Framework 2014).
  • Feel at home in a friendly department where you will be known as an individual.

Course structure

Core modules

  • Main Project: You will carry out a detailed study into a topic of your choosing in mathematics, analysing information from a range of sources. You will submit a written report of between 8,000 and 16,000 words in length.

Optional modules

In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.

  • Theory of Error-Correcting Codes
  • Channels
  • Advanced Cipher Systems
  • Public Key Cryptography
  • Applications of Field Theory
  • Quantum Information and Coding
  • Principles of Algorithm Design
  • Advanced Financial Mathematics
  • Combinatorics
  • Computational Number Theory
  • Applied Probability
  • Inference
  • Topology

Teaching & assessment

You will initially choose eight modules from the list of available options, of which you specify modules during the second term that will count towards your final award. You will also complete a core research project under the supervision of one of our academic staff. There is a strong focus on small group teaching throughout the programme.

Assessment is carried out through a variety of methods, including coursework, examinations and the main project. End-of-year examinations in May or June will count for 66.7% of your final award, while the dissertation will make up the remaining 33.3%.

Your future career

By the end of this programme you will have completed a major research project and acquired an advanced knowledge and understanding of: the role and limitations of mathematics in solving problems that arise in real-world scenarios. You will also have impressive skills in selected areas of mathematics and their applications, and the ability to synthesise and interpret information from multiple sources with insight and critical awareness. We will teach you to formulate problems clearly and express your technical work and conclusions clearly in writing, and you will develop valuable transferable skills such as time management, adaptability and self-motivation.

Our graduates have gone on to carry out cutting-edge research in the fields of communication theory and cryptography, as well as successful careers in industries such as: information security, IT consultancy, banking and finance, higher education and telecommunication. They have taken up roles such as: 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.

You will have a dedicated personal adviser to guide you through your studies and advise you on postgraduate opportunities, and the campus Careers team will be on hand to offer advice and guidance on your chosen career. The University of London Careers Advisory Service offers regular, tailored sessions for Mathematics students, on finding summer internships or vacation employment and getting into employment.

  • Open doors to a range of exciting opportunities in advanced research, science and industry.
  • 90% of our graduates are in work or undertaking further study within six months of leaving (Unistats 2015).
  • Our strong ties with industry mean we understand the needs of employers.
  • Take advantage of our summer work placement scheme and fine-tune your CV before you enter your final year.
  • Benefit from a personal advisor who will guide you through your studies and future options.


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