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Masters Degrees (Algebraic Topology)

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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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This is a one-year full-time course, though it could be taken part-time over two or more years. It provides a broad introduction to Mathematics at the graduate level. Read more

Overview

This is a one-year full-time course, though it could be taken part-time over two or more years. It provides a broad introduction to Mathematics at the graduate level.

Course Structure

Modules include Galois Theory, Differential Geometry, Probability, Functional Analysis, Numerical analysis, Research Projects, Representation Theory and Algebraic Topology.

Career Options

The course provides an excellent foundation for those who intend to go on to pursue the PhD. Many MSc graduates take up employment in areas such as Industry, Commerce, Banking and Finance, Insurance, Software Development, Process Engineering or Education.

How To Apply

Online application only http://www.pac.ie/maynoothuniversity

PAC Code
MHR52 Full-time
MHR53 Part-time

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

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

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

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

Overview

This is a two-year full-time taught course. It is aimed at students who have a primary degree with a significant Mathematical content (such as Mathematical Studies graduates), but who do not hold an Honours Degree in Mathematics. The MA course is equivalent to taking a Higher Diploma in Mathematics followed by the MSc by examination. A mark of 50% is required to proceed to second year. Candidates who fail to reach the mark of 50% may be awarded a Higher Diploma in Mathematics, subject to a threshold of 40%.

Course Structure

Modules include Numerical Analysis, Point Set Topology, Research projects, Complex Analysis, Rings and Fields, Functional Analysis, Riemann Surfaces, Algebraic Topology, Partial Differential Equations and Introduction To Programming For Mathematicians.

Career Options

The Course provides a broad introduction to Mathematics at the graduate level, and provides an excellent foundation for those who intend to go on to pursue the PhD.

How To Apply

Online application only http://www.pac.ie/maynoothuniversity

PAC Code
MHR50/MHR551

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

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

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

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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. Read more
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.

This programme allows you to further enhance your knowledge, creativity and computational skills in core mathematical subjects and their applications giving you a competitive advantage in a wide range of mathematically based careers. The modules, which are designed and taught by internationally known researchers, are accessible, relevant, interesting and challenging.

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.

National ratings

In the Research Excellence Framework (REF) 2014, research by the School of Mathematics, Statistics and Actuarial Science was ranked 25th in the UK for research power and 100% or our research was judged to be of international quality.

An impressive 92% of our research-active staff submitted to the REF and the School’s environment was judged to be conducive to supporting the development of world-leading research.

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

You take eight modules in total: six from the list below; a short project module and a dissertation module. The modules concentrate on a specific topic from: analysis; applied mathematics; geometry; and algebra.

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.

MA961 - Mathematical Inquiry and Communication (30 credits) - https://www.kent.ac.uk/courses/modules/module/MA961
MA962 - Geometric Integration (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA962
MA963 - Poisson Algebras and Combinatorics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA963
MA964 - Applied Algebraic Topology (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA964
MA965 - Symmetries, Groups and Invariants (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA965
MA966 - Diagram Algebras (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA966
MA967 - Quantum Physics (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA967
MA968 - Mathematics and Music (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA968
MA969 - Applied Differential Geometry (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA969
MA970 - Nonlinear Analysis and Optimisation (15 credits) - https://www.kent.ac.uk/courses/modules/module/MA970
Show more... https://www.kent.ac.uk/courses/postgraduate/146/mathematics-and-its-applications#!structure

Assessment

Assessment is by closed book examinations, take-home problem assignments and computer lab assignments (depending on the module). The project and dissertation modules are assessed mainly on the reports or work you produce, but also on workshop activities during the teaching term.

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.

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.

Learn more about Kent

Visit us - https://www.kent.ac.uk/courses/visit/openday/pgevents.html

International Students - https://www.kent.ac.uk/internationalstudent/

Why study at Kent? - https://www.kent.ac.uk/courses/postgraduate/why/

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This intensive introduction to advanced pure and applied mathematics draws on our strengths in algebra, geometry, topology, number theory, fluid dynamics and solar physics. 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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Mathematics in Nijmegen. From Applied Stochastics to Infinity-Categories. The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate. Read more

Mathematics in Nijmegen: From Applied Stochastics to Infinity-Categories

The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate. Its wide scope, which ranges from medical statistics to the mathematical foundations of computer science, physics and even mathematics itself, reflects the diversity of research at the Institute for Mathematics, Astrophysics and Particle Physics (IMAPP).

Mathematical research of course stands on its own, as is notably the case with the large group in algebraic topology led by Spinoza laureate Ieke Moerdijk. In addition, within IMAPP, researchers link with high-energy physics, including Higgs physics and quantum gravity. Outside IMAPP but within the Faculty of Science, there are close ties with the Institute for Computing and Information Sciences (ICIS) (think of logic and category theory) and outside the Faculty of Science (but within Radboud University) researchers at both the Donders Institute for Neurosciences and the University Medical Center collaborate with the applied stochastics group.

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

Specialisations within the Master's Programme in Mathematics

- Algebra & Topology

- Applied Stochastics

- Mathematical Physics

- Mathematical Foundations of Computer Science

Career prospects

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

Job positions

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

- PhD positions

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

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

Radboud University Master's Open Day 10 March 2018



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This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. Read more

This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. There is a wide range of taught modules on offer, and you will also produce a dissertation on a topic of current research interest taken from your choice of a wide range of subjects offered.

Course structure and overview

  • Six taught modules in October-May
  • A dissertation in June-September.

Modules: Six of available options

In previous years, optional modules available included:

Modules in Pure Mathematics:

  •  Algebraic Topology IV
  •  Analysis III and IV
  •  Codes and Cryptography III
  •  Differential Geometry III
  •  Galois Theory III
  •  Representation Theory III and IV
  •  Riemannian Geometry IV
  •  Topology III
  •  Topics in Algebra and Geometry IV

Modules in Probability and Statistics:

  •  Bayesian Statistics III and IV 
  •  Mathematical Finance III and IV
  •  Decision Theory III
  •  Operations Research III
  •  Statistical Methods III
  • Stochastic Processes III and IV

Modules in Applications of Mathematics:

  •  Advanced Quantum Theory IV
  •  Continuum Mechanics III and IV
  •  Dynamical Systems III
  •  General Relativity IV
  •  Mathematical Biology III 
  •  Partial Differential Equations III and IV
  •  Quantum Information III
  •  Quantum Mechanics III
  •  Solitons III and IV

Course Learning and Teaching

This is a full-year degree course, starting early October and finishing in the middle of the subsequent September. The aim of the course is to give the students a wide mathematical background allowing them to either proceed to PhD or to apply the gained knowledge in industry.

The course consists of three modules: the first two are the Michaelmas and Epiphany lecture courses covering variety of topics in pure and applied mathematics and statistics. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics.

The main group of lectures is given in the first two terms of the academic year (Michaelmas and Epiphany), there are also two revision lectures in the third term (Easter). This part of the course is assessed by examinations. Students choose 6 modules, each module has 2 lectures per week and one fortnightly problems class. There are 10 teaching weeks in the Michaelmas term and 9 teaching weeks in Epiphany term. In addition lecturers also set a number of homework assignments which give the student a chance to test their understanding of the material.

The dissertation must be submitted by mid-September, the end of the twelve month course period 



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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. Read more
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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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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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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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. Read more

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 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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Working at a frontier of mathematics that intersects with cutting edge research in physics. Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. Read more

Working at a frontier of mathematics that intersects with cutting edge research in physics.

Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.

Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.

At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.

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

Why study Mathematical Physics at Radboud University?

- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.

- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).

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

- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.

- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.

- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.

Career prospects

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

Job positions

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

PhD positions

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

Our research in this field

The research of members of the Mathematical Physics Department, emphasise operator algebras and noncommutative geometry, Lie theory and representation theory, integrable systems, and quantum field theory. Below, a small sample of the research our members pursue.

Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.

Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:

1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.

2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

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

Radboud University Master's Open Day 10 March 2018



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EXPLORE THE INTERSECTION OF FUNDAMENTAL AND APPLIED RESEARCH. In our Master’s programme in. Mathematical Sciences. , you’ll engage in the core activities of mathematics while discovering new patterns and relationships and learning to construct models with predictive power. Read more

EXPLORE THE INTERSECTION OF FUNDAMENTAL AND APPLIED RESEARCH

In our Master’s programme in Mathematical Sciences, you’ll engage in the core activities of mathematics while discovering new patterns and relationships and learning to construct models with predictive power. You’ll also study the science of structures within the different branches of the physical sciences. Our institute of Mathematical Sciences offers you a versatile, internationalised learning environment at the intersection of fundamental and applied research

PERSONALIZING YOUR MASTER'S

You can tailor your programme by selecting one of the following 8 tracks:

  • Algebraic Geometry and Number Theory
  • Applied Analysis
  • Complex Systems
  • Differential Geometry and Topology
  • Logic
  • Probability, Statistics, and Stochastic Modelling
  • Pure Analysis
  • Scientific Computing

You can also choose to do a Research project in History of Mathematics. Choosing a track will allow you to pursue your Master's degree through either a theoretical or more applied focus.

Honours programmes

You have the opportunity to combine the Mathematical Sciences Master's programme with other Master's programmes within the Graduate School of Natural Sciences, such as Theoretical Physics. If you have an interest in geometry and plan to do a PhD in this field, you can apply for the selective honours programma of the Utrecht Geometry Centre.

PROGRAMME OBJECTIVE

Our Mathematical Sciences MSc degree programme will prepare you for a challenging career in academic research or as a professional mathematician.



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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. Read more
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.

You would be joining a vibrant research community of almost 100 postgraduate and postdoctoral researchers and academic staff. You have the opportunity to engage with a very wide range of research topics within a well-established system of support and training, with a high level of contact between staff and research students.

A very active research seminar programme further enhances the Mathematics research experience.

Visit the website https://www.kent.ac.uk/courses/postgraduate/149/mathematics

About the School of Mathematics, Statistics and Actuarial Science (SMSAS):

The School has a strong reputation for world-class research as indicated by our results in the latest Research Assessment Exercise (RAE). 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 RAE. 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.

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.

- Researcher Development Programme

Kent's Graduate School co-ordinates the Researcher Development Programme (http://www.kent.ac.uk/graduateschool/skills/programmes/tstindex.html) for research students, which includes workshops focused on research, specialist and transferable skills. The programme is mapped to the national Researcher Development Framework and covers a diverse range of topics, including subjectspecific research skills, research management, personal effectiveness, communication skills, networking and teamworking, and career management skills.

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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