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Masters Degrees (Pure Mathematics)

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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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Postgraduate combined research and teaching degree programme Pure Mathematics MRes. This programme involves both taught classes in Pure Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. . Read more

Postgraduate combined research and teaching degree programme Pure Mathematics MRes:

This programme involves both taught classes in Pure Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. 

The MRes can be used as the first phase of our fast track PhD programme, in which the MRes thesis is extended over a further period of two years into a PhD thesis.

Course details

This programme involves both taught classes in Pure Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. The minimum period of registration is 12 months. 

The MRes is an ideal preparation for entry into the PhD programme at Birmingham or at any other UK university. Indeed, the MRes programme can be used as the first phase of our fast track PhD programme. This is an excellent option for well-qualified mathematics students who do not have all the necessary mathematical background to start immediately on a PhD in their area of choice. In the fast track programme the MRes thesis is extended over a further period of two years into a PhD thesis. 

Each MRes student is assigned a project supervisor who will act as director and mentor in the preparation of the MRes thesis. This gives each student the opportunity to work one-to-one with mathematicians who are international experts in their fields. 

In addition to the assessed elements of the course, students are expected to play a full part in the research life of the School. The School has an active seminar programme, and organises international conferences in all areas of mathematics.

Related links

Learning and teaching

These courses are approximately one-third course work and two-thirds dissertation. The dissertation is completed under the direction of a project supervisor which gives our students the opportunity to work one-to-one with a leading expert in their field. 

A regular programme of seminars and conferences takes place within the School in a wide range of subjects. Currently thriving at Birmingham are the following research groups:

  • Applied Mathematics: applied analysis, mathematical biology, fluid mechanics, hydrogen energy, fuel cells and their applications, numerical analysis and scientific computation
  • Pure Mathematics: algebra, analysis, combinatorics and logic
  • Theoretical and Computational Optimization: mathematical theory and methods applicable to managerial decision-making
  • Statistics: time series analysis, multivariate statistics, kernel and wavelet based nonparametric smoothing methods, econometrics and medical statistics

Employability

This programme gives comprehensive training in mathematics and areas appropriate to professional development and research foundations. The MRes is an ideal preparation for entry into the PhD programme at Birmingham. In fact, the MRes programme can be used as the first phase of our ?Fast-track? PhD programme.

University Careers Network

Preparation for your career should be one of the first things you think about as you start university. Whether you have a clear idea of where your future aspirations lie or want to consider the broad range of opportunities available once you have a Birmingham degree, our Careers Network can help you achieve your goal.

Our unique careers guidance service is tailored to your academic subject area, offering a specialised team (in each of the five academic colleges) who can give you expert advice. Our team source exclusive work experience opportunities to help you stand out amongst the competition, with mentoring, global internships and placements available to you. Once you have a career in your sights, one-to-one support with CVs and job applications will help give you the edge.

If you make the most of the wide range of services you will be able to develop your career from the moment you arrive.



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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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Pure Mathematics at Doctoral level offers the opportunity investigate the purely abstract, theoretical areas of mathematical discovery at the highest level. Read more
Pure Mathematics at Doctoral level offers the opportunity investigate the purely abstract, theoretical areas of mathematical discovery at the highest level.

The School of Mathematics and Physics offers the opportunity to work alongside specialists within the field in a vibrant community,
sharing ideas and experiences.

Postgraduate research in pure mathematics covers the areas of lie algebras and group theory. Training is provided through individual supervision of research and by advanced seminars. As a research student, you can benefit from a comprehensive programme of training designed to develop your research skills and methodologies.

A team of academics will offer advice and support on publishing your work in international journals and presenting at global conferences. You may also have an opportunity to engage in international collaborations during your study.

Research Areas, Projects & Topics

Research Areas:
-Algebra
-Group Theory

For information about the School’s research activity please visit: http://www.lincoln.ac.uk/home/smp/research/

How You Study

You can benefit from specialist computational facilities, training programmes to enhance your research skills and support from dedicated academic supervisors. You will be supported and encouraged to submit papers to international scientific journals, present your findings at conferences and share knowledge with colleagues across the University.

Due to the nature of postgraduate research programmes, the vast majority of your time will be spent in independent study and research. You will have meetings with your academic supervisor, however the regularity of these will vary depending on your own individual requirements, subject area, staff availability and the stage of your programme.

How You Are Assessed

A PhD is usually awarded based on the quality of your thesis and your ability in an oral examination (viva voce) to present and successfully defend your chosen research topic.

Career and Personal Development

Pure Mathematics students have the opportunity to develop the problem solving skills that may lead to careers in academia, research or industry. 

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The School of Mathematics and Physics offers the opportunity to work alongside academics in a vibrant community, sharing ideas and experiences. Read more
The School of Mathematics and Physics offers the opportunity to work alongside academics in a vibrant community, sharing ideas and experiences.

Postgraduate research in pure mathematics covers the areas of lie algebras and group theory. Training is provided through individual supervision of research and by advanced seminars. As a research student, you can benefit from a comprehensive programme of training designed to develop your research skills and methodologies.

A team of academics will offer advice and support in publishing your work in international journals and presenting at global conferences. You may also have the opportunity to engage in international collaborations during your study.

Research Areas, Projects & Topics

Main Research Areas:
-Algebra
-Group Theory

For information about the School’s research activity please visit: http://www.lincoln.ac.uk/home/smp/research/

How You Study

You can benefit from training programmes designed to enhance your research skills and support from dedicated academic supervisors. All our research students are encouraged to submit papers to international scientific journals, present their findings at conferences in the UK and overseas, and share knowledge with colleagues across the University.

Due to the nature of postgraduate research programmes, the vast majority of your time will be spent in independent study and research. You will have meetings with your academic supervisor, however the regularity of these will vary depending on your own individual requirements, subject area, staff availability and the stage of your programme.

How You Are Assessed

The MSc by Research involves writing a Master's thesis under the supervision of a member of academic staff on a topic to be agreed with your supervisor. The MSc by Research is usually awarded based on the quality of your thesis and your ability in an oral examination (viva voce) to present and successfully defend your chosen research topic.

Career and Personal Development

Pure Mathematics students have the opportunity to develop the problem solving skills that may lead to careers in academia, research or industry.

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This course, commonly referred to as Part III, is a one-year taught Master's course in mathematics. Read more
This course, commonly referred to as Part III, is a one-year taught Master's course in mathematics. It is an excellent preparation for mathematical research and it is also a valuable course in mathematics and in its applications for those who want further training before taking posts in industry, teaching, or research establishments.

Students admitted from outside Cambridge to Part III study towards the Master of Advanced Study (MASt). Students continuing from the Cambridge Tripos for a fourth year, study towards the Master of Mathematics (MMath). The requirements and course structure for Part III are the same for all students irrespective of whether they are studying for the MASt or MMath degree.

There are over 200 Part III (MASt and MMath) students each year; almost all are in their fourth or fifth year of university studies. There are normally about 80 courses, covering an extensive range of pure mathematics, probability, statistics and the mathematics of operational research, applied mathematics and theoretical physics. They are designed to cover those advanced parts of the subjects that are not normally covered in a first degree course, but which are an indispensable preliminary to independent study and research. Students have a wide choice of the combination of courses that they offer, though naturally they tend to select groups of cognate courses. Normally classes are provided as back-up to lecture courses.

See the website http://www.graduate.study.cam.ac.uk/courses/directory/mapmaspmm

Course detail

The structure of Part III is such that students prepare between six and nine lecture courses for examination. These lecture courses may be selected from the wide range offered by both Mathematics Departments. As an alternative to one lecture course, an essay may be submitted. Examinations usually begin in late May, and are scheduled in morning and afternoon sessions, over a period of about two weeks. Two or three hours are allocated per paper, depending on the subject. Details of the courses for the current academic year are available on the Faculty of Mathematics website. Details for subsequent years are expected to be broadly similar, although not identical.

Most courses in the Part III are self-contained. Students may freely mix courses offered by the two Mathematics Departments. Courses are worth either two or three credit units depending on whether they last for 16 or 24 lectures respectively. Candidates for Part III may offer a maximum of 19 credit units for examination. In the past it has been recommended that candidates offer between 17 and 19 units. An essay (should a candidate choose to submit one) counts for 3 credit units. Part III is graded Distinction, Merit, Pass or Fail. A Merit or above is the equivalent of a First Class in other Parts of the Mathematical Tripos.

Learning Outcomes

After completing Part III, students will be expected to have:

- Studied advanced material in the mathematical sciences to a level not normally covered in a first degree;
- Further developed the capacity for independent study of mathematics and problem solving at a higher level;
- Undertaken (in most cases) an extended essay normally chosen from a list covering a wide range of topics.

Students are also expected to have acquired general transferable skills relevant to mathematics as outlined in the Faculty Transferable Skills Statement http://www.maths.cam.ac.uk/undergrad/course/transferable_skills.pdf .

Format

Courses are delivered predominantly by either 16 or 24 hours of formal lectures, supported by additional examples classes. As an alternative to one lecture course, an essay may be submitted. There is also the possibility of taking a reading course for examination. There are normally additional non-examinable courses taught each year.

Essay supervision and support for lectures by means of examples classes is approximately 30 hours per year.

Formal examinable lectures and non-examinable lectures total approximately 184 hours per year, of which on average 112 hours are for examinable courses.

Some statistics courses may involve practical data analysis sessions.

There is an opportunity to participate in the Part III seminar series, either by giving a talk or through attendance. This is encouraged but does not contribute to the formal assessment.

Twice a year students have an individual meeting with a member of academic staff to discuss their progress in Part III. Students offering an essay as part of their degree may meet their essay supervisor up to three times during the academic year.

Assessment

Candidates may substitute an essay for one lecture course. The essay counts for 3 credit units.

Lecture courses are assessed by formal examination. Courses are worth either two or three credit units depending on whether they are 16 or 24 hours in length respectively. A 16 hour course is assessed by a 2 hour examination and a 24 hour course, a 3 hour examination. Candidates for Part III may offer a maximum of 19 credit units for examination. In the past it has been recommended that candidates offer between 17 and 19 units.

Continuing

MASt students wishing to apply for the PhD must apply via the Graduate Admissions Office for readmission by the relevant deadline. Applicants will be considered on a case by case basis and offer of a place will usually include an academic condition on their Part III result.

How to apply: http://www.graduate.study.cam.ac.uk/applying

Funding Opportunities

There are no specific funding opportunities advertised for this course. For information on more general funding opportunities, please follow the link below.

General Funding Opportunities http://www.graduate.study.cam.ac.uk/finance/funding

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This course is offered full and part-time. The full-time course lasts one calendar year, October to September; the part-time course lasts two years. Read more
This course is offered full and part-time. The full-time course lasts one calendar year, October to September; the part-time course lasts two years.

The course includes a wide range of lecture modules in analysis, geometry and topology, algebra, number theory and combinatorics.

You also undertake a written project under the direction of a supervisor who is an expert in that field.

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The Master of Science in Mathematics (120 ECTS) is a research-based master’s programme in which you can specialize in the following fields of mathematics. Read more

The Master of Science in Mathematics (120 ECTS) is a research-based master’s programme in which you can specialize in the following fields of mathematics: Pure Mathematics: Algebra, Analysis and Geometry; and Applied Mathematics: Statistics, Financial Mathematics, Computational Mathematics, Plasma-Astrophysics. 

What is the Master of Mathematics all about?

Besides a solid, all-round education in mathematics, the programme offers you the possibility to focus on either pure or applied mathematics. This allows you to acquire both breadth of knowledge and depth in your own areas of interest. Pure and applied mathematics courses are firmly grounded in the core research activities of the Department of Mathematics. Gradually, you will gain experience and autonomy in learning how to cope with new concepts, higher levels of abstraction, new techniques, new applications, and new results. This culminates in the Master’s thesis, where you become actively involved in the research performed in the various mathematical research groups of the Departments of Mathematics, Physics, Astronomy and Computer Sciences.

 This is an initial Master's programme and can be followed on a full-time or part-time basis.

Structure

The programme of the Master of Science in Mathematics consists of 120 ECTS. You choose one of the two profiles – Pure Mathematics or Applied Mathematics (54 ECTS) – and one of the two options – Research Option or Professional Option (30 ECTS). The profile allows you to specialize either in pure mathematics (algebra, geometry, analysis), or in applied mathematics (statistics, computational mathematics, fluid dynamics).

There is one common course: ‘Mathematics of the 21st Century’ (6 ECTS). To complete the programme, you carry out a research project that results in a master’s thesis (30 ECTS).

Department

All staff members of the Department of Mathematics are actively involved in the two-year Master of Science in Mathematics programme. The academic staff at the Department of Mathematics consists of leading experts in their fields. Researchers in pure mathematics focus on algebraic geometry, group theory, differential geometry, functional analysis, and complex analysis. Researchers in mathematical statistics deal with extreme values, robust statistics, non-parametric statistics, and financial mathematics. Research in the applied mathematics group is in computational fluid dynamics and plasma-astrophysics.

Career perspectives

Mathematicians find employment in industry and in the banking, insurance, and IT sectors. Many graduates from the research option pursue a career in research and start a PhD in mathematics, mathematical physics, astrophysics, engineering, or related fields.



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Subject Knowledge Enhancement Courses (SKEs) are about improving subject knowledge in preparation for a Teacher Training course. You will be taught by experienced teachers of mathematics, and will spend 2 of the 12 weeks in a school where you will have the opportunity to apply your subject knowledge. Read more
Subject Knowledge Enhancement Courses (SKEs) are about improving subject knowledge in preparation for a Teacher Training course. You will be taught by experienced teachers of mathematics, and will spend 2 of the 12 weeks in a school where you will have the opportunity to apply your subject knowledge. You will benefit from extensive use of interactive methods which will help you learn mathematics and form links with colleagues which will be invaluabe throughout the PGCE programme. This course is available to PGCE offer holders at London Metropolitan University or at other universities whose offer stipulates completion of subject knowledge enhancement.

More about this course

The course will cover higher level GCSE level and early A level Pure Mathematics and Statistics. There will be mathematical modules on: Algebra of Polynomial Functions and Equations, Trigonometry and Continuous Functions, Calculus, Data Handling and Statistics, Euclidean Geometry. An introduction to educational issues will include reading, films, and an introduction to current issues in education policy.

We will use mathematics materials which are commonly used in classrooms to promote interactive engagement in mathematics including group work and extensive use of ICT. The course will include an introduction to relevant themes in teaching and learning which will also develop reading and writing skills necessary for the PGCE. There will be a two week school placement where you will have an opportunity to observe and participate in classroom mathematics.

The course will be assessed by a continuous assessment portfolio and a final examination. The portfolio will include mathematical tasks, written assignments, a profile of the school placement and work designed to practice specific areas of the curriculum. The final examination will include a GCSE Higher Mathematics paper (calculator and non-calculator papers) and a paper of relevant questions of A-level standard.

Professional accreditation

The course is funded by the National College for Teaching and Leadership (NCTL), and London Met is approved to provide SKE with NCTL funding for either maths or French.

Modular structure

The twelve-week course will be based at the University for four days each week Tuesday to Friday, with the exception of a two week placement in schools which will be arranged for you. You will be following a course which focusses on the content of higher GCSE level and early A level Pure Mathematics and Statistics.

There will be mathematical modules on: Algebra of Polynomial Functions and Equations, Trigonometry and Continuous Functions, Calculus, Data Handling and Euclidean Statistics, and Geometry. An introduction to educational issues will include reading, films, and an introduction to current issues in education policy. There will be a 2 week placement in a mathematics department in a secondary school.

You will learn mathematics in a variety of ways including mathematics software, group work and by following targets tailored to your own needs. Learning mathematics in these ways will give you first-hand experience of the pedagogies which you will use in the PGCE course. The school placement will give you the chance to see mathematics teaching in a school and you will, by completing specially designed evaluation tasks, develop reading and writing skills necessary for the PGCE. Throughout the course there will be regular tutorials to monitor your progress and provide help and guidance to make the London Met maths enhancement course a successful first step in your teaching career.

[[After the course[[
You will be able to move onto the PGCE programme upon successful completion of the SKE course.

Funding

Our Subject Knowledge Enhancement courses (SKEs) are 12 weeks long. Your fees are paid by the National College of Teaching and Leadership (NCTL). In addition, you will receive a bursary of £2,400 or £800 per month. More information on Enhancement Courses is available from the DfE.

Moving to one campus

Between 2016 and 2020 we're investing £125 million in the London Metropolitan University campus, moving all of our activity to our current Holloway campus in Islington, north London. This will mean the teaching location of some courses will change over time.

Whether you will be affected will depend on the duration of your course, when you start and your mode of study. The earliest moves affecting new students will be in September 2017. This may mean you begin your course at one location, but over the duration of the course you are relocated to one of our other campuses. Our intention is that no full-time student will change campus more than once during a course of typical duration.

All students will benefit from our move to one campus, which will allow us to develop state-of-the-art facilities, flexible teaching areas and stunning social spaces.

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

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

Research areas

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

Our Applied Mathematics staff have research interests in:
-Fluid dynamics, including numerical modelling of quantum fluids (superfluid liquid Helium and Bose-Einstein condensates)
-Classical and astrophysical fluids (the Earth's core, planetary dynamos, accretion discs and galaxies)
-Cosmology, including the very early universe and quantum gravity

Research seminars and events

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

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

Partnerships and networks

We are part of:
-The North British Functional Analysis Seminar
-The North British Geometric Group Theory Seminar
-Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society

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

Facilities

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

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

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Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem. Read more
Accurate and efficient scientific computations lie at the heart of most cross-discipline collaborations. It is key that such computations are performed in a stable, efficient manner and that the numerics converge to the true solutions, dynamics of the physics, chemistry or biology in the problem.

The programme closely follows the structure of our Applied Mathematical Sciences MSc and will equip you with the skill to perform efficient accurate computer simulations in a wide variety of applied mathematics, physics, chemical and industrial problems.

The MSc, has at its core, fundamental courses in pure mathematics and students will be able to take options from both pure and applied mathematics.

Students will take a total of 8 courses, 4 in each of the 1st and 2nd Semesters followed by a 3-month Project in the summer. A typical distribution for this programme is as follows:

Core courses

Modelling and Tools;
Functional Analysis;
Partial Differential Equations;
Pure Mathematics (recommended).

Optional Courses

Mathematical Ecology;
Optimization;
Numerical Analysis of ODEs;
Applied Mathematics;
Dynamical Systems;
Stochastic Simulation;
Applied Linear Algebra;
Partial Differential Equations;
Numerical Analysis;
Bayesian Inference and Computational Methods;
Geometry.

Typical project subjects

Domain Decomposition;
Mathematical Modelling of Crime;
The Geometry of Point Particles;
Can we Trust Eigenvalues on a Computer?;
Braess Paradox;
The Ising Model: Exact and Numerical Results;
Banach Alegbras.

The final part of the MSc is an extended project in computational mathematics, giving the opportunity to investigate a topic in some depth guided by leading research academics from our 5-rated mathematics and statistics groups.

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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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Master's specialisation in Algebra and Topology. The Algebra and Topology section is an active research group consisting of renowned experts covering a remarkably broad range of topics. Read more

Master's specialisation in Algebra and Topology

The Algebra and Topology section is an active research group consisting of renowned experts covering a remarkably broad range of topics. The group consists of two full professors (I. Moerdijk, Spinoza Laureate 2012, and B. Moonen), four permanent members, and a large number of post-docs and PhD students. More information about the research activities of the group can be found at http://www.math.ru.nl/topology.

The section offers a Master's specialisation in Algebra in Topology, which is a 2-year programme aimed at students with an interest in pure mathematics and its applications.

The Master's programme has a strong focus on current research developments. It introduces students to a broad range of techniques and concepts that play a central role in modern mathematics. In addition to providing a strong theoretical basis, the programme offers excellent opportunities for a further specialisation focusing on applications of pure mathematics or on interactions with other fields.

The programme offers courses in Algebra, Topology, Geometry, Number Theory, and Logic and Computation. There are strong interactions with other Master's specialisations at Radboud University, notably the ones in Mathematical Physics and in Mathematical Foundations of Computer Science.

In addition, the programme offers a variety of seminars from beginning Master's level to research level. Moreover, students have the possibility to incorporate courses from related programmes (e.g. Mathematical Physics and Mathematical Foundations of Computer Science into their programme, as well as individual reading courses. Each student concludes his programme by studying a special topic and writing a Master's thesis about it.

Excellent students having completed this Master's programme or a similar programme elsewhere can in principle continue and enrol in the PhD Programme, but admission for this is limited and highly selective.

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

Admission requirements for international students

1. A completed Bachelor's degree in Mathematics or related area

Entering the Master’s programme in Mathematics requires a Bachelor’s degree in Mathematics that is the equivalent to a Dutch university diploma (this does not include a Bachelor’s from a university of applied science, in Dutch hbo; in German Fachhochschule). That means we expect you to have a solid background in the core areas groups, rings, fields and topology. We expect students to have passed core mathematics courses during their Bachelor’s in:

The Examination Board will determine if an international student has the required mathematical knowledge to be admitted. The Examination Board will also indicate if the student is required to follow specific courses from the Bachelor's programme to eliminate possible deficiencies.

- Basic notions in Mathematics

- Linear Algebra

- Algebra

- Analysis

- Topology

- Geometry

- Differential Equations

2. A proficiency in English

In order to take part in this programme, you need to have fluency in both written and spoken English. Non-native speakers of English without a Dutch Bachelor's degree or VWO diploma need one of the following:

- TOEFL score of ≥575 (paper based) or ≥90 (internet based)

- An IELTS score of ≥6.5

- Cambridge Certificate of Advanced English (CAE) or Certificate of Proficiency in English (CPE) with a mark of C or higher

Career prospects

Mathematicians are needed in all industries, including the banking, technology and service industries, amongst many others. 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 specialised 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 not seem initially relevant. This makes your job opportunities very broad 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/algebratopology

Radboud University Master's Open Day 10 March 2018



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Do you have an aptitude and passion for mathematics and statistics, a keen interest in finance and insurance and want to work for a major financial organisation in finance, insurance or the money market? This course will provide you with a deep understanding of the world of finance, and give you the ability to speak its 'language'. Read more
Do you have an aptitude and passion for mathematics and statistics, a keen interest in finance and insurance and want to work for a major financial organisation in finance, insurance or the money market? This course will provide you with a deep understanding of the world of finance, and give you the ability to speak its 'language'. This course combines theory with hands-on practical skills via an industry placement or research project – ensuring you graduate with the right skills increasingly being sought by banks and other financial institutions.

The Master of Financial Mathematics offers advanced training in the core areas of stochastic, financial and insurance modelling, statistical analysis and computational methodology, as well as in a wide range of elective topics from economics, econometrics, finance, mathematics and probability.

Graduates of this course are likely to enter specialist careers in research departments within banks, insurance and consultancy firms or derivatives of valuation and portfolio management within investment houses.

The School of Mathematical Sciences sits within the leading Faculty of Science at Monash University. This vibrant, dynamic and successful School is undergoing a period of growth with the appointment of several new senior academic staff including Professor Gregoire Loeper, Course Director for the Masters of Financial Mathematics. With mathematics as the fundamental underpinning of so many subject areas, sectors and disciplines, the School is also building ever stronger collaborations with relevant industries, including the financial sector.

Visit the website http://www.study.monash/courses/find-a-course/2016/financial-mathematics-s6001?domestic=true

Course Structure

The course is structured in three Parts. Part A. Orientation studies, Part B. Specialist studies, Part C. Applied professional practice. All students complete Part B. Depending upon prior qualifications, you may receive credit for Part A or Part C or a combination of the two.

Part A. Orientation studies
These studies provide an orientation to the field of Financial Mathematics. You will choose studies that complement your current knowledge relevant to financial mathematics, including principles of econometrics, mathematical methods and stochastic processes.

Part B. Specialist studies
These studies will provide you with advanced knowledge and skills relevant to thoughtful, innovative and evidence-based practice in financial modelling and analysis. You will acquire core knowledge of and skills in financial econometrics, and advanced mathematical modelling and computational methods in finance. You will complement these with study in areas of your choice, including interest rate modelling, Markov processes, statistical learning in finance, and global financial markets.

Part C. Applied professional practice
These studies will provide you with the opportunity to apply your knowledge skills developed in Part A and B to "real life" problems, through completing an industry project or an industry internship. Students admitted to the course who have a recognised honours degree or graduate diploma or graduate certificate in a cognate discipline including mathematics or statistics, will receive credit for this part however, should they wish to complete a 24 point research project as part of Part B they should consult with the course convenor.

For more information visit the faculty website - http://www.study.monash/media/links/faculty-websites/science

About Mathematical Sciences

The School of Mathematical Sciences at Monash University is leading the way towards finding effective solutions to some of society's most pressing problems. Maths is the language of science and forms the basis of most of modern science and engineering. Our enthusiastic mathematicians love finding the true magic and beauty in maths and subsequently pass this passion on to their students.

Teaching

Studying maths equips you with a range of valuable, unique skills. Some of the exciting areas mathematicians at Monash are working on include mathematical modelling to predict behaviour, analysis using pure maths, and stochastic processes involving risk, randomness and change.

Mathematics and statistics are also the two cornerstones for decision making and various quantitative activities in commerce, industry, education and defence. From direct and daily experience, most companies and organisations have realised that success depends critically on the level of analytical, quantitative and statistical skills of their workforce and they therefore seek employees with a sound mathematical training.

By studying mathematics at Monash, you will also develop general skills in problem-solving, critical thinking, modelling, learning, analysis, research and creativity, which can be used wherever your career may take you.

Research

The School of Mathematical Sciences focuses on these main areas of research:

- Applied and Computational Mathematics
- Pure Mathematics
- Stochastic Processes

Find out how to apply here - http://www.study.monash/courses/find-a-course/2016/financial-mathematics-s6001?domestic=true#making-the-application

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