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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.
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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)

- The University of Nottingham is ranked in the top 1% of all universities worldwide.

Algebraic Geometry

Algebraic Number Theory

Combinatorial Group Theory

Complex Analysis

Further Topics in Analysis

Further Topics in Rings and Modules

Pure Mathematics Dissertation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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.

-Algebra

-Group Theory

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

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.

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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.
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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.

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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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.

-Algebra

-Group Theory

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

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.

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

The School of Mathematics is one of seven schools in the College of Engineering and Physical Sciences. The school is situated in the Watson Building on the main Edgbaston campus of the University of Birmingham. There are about 50 academic staff, 15 research staff, 10 support staff, 60 postgraduate students and 600 undergraduate students.

At the School of Mathematics we take the personal development and careers planning of our students very seriously. Jointly with the University of Birmingham's Careers Network we have developed a structured programme to support maths students with their career planning from when they arrive to when they graduate and beyond.### Funding and Scholarships

There are many ways to finance your postgraduate study at the University of Birmingham. To see what funding and scholarships are available, please visit: http://www.birmingham.ac.uk/postgraduate/funding ### Open Days

Explore postgraduate study at Birmingham at our on-campus open days.

Register to attend at: http://www.birmingham.ac.uk/postgraduate/visit### Virtual Open Days

If you can’t make it to one of our on-campus open days, our virtual open days run regularly throughout the year. For more information, please visit: http://www.pg.bham.ac.uk

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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.

At the School of Mathematics we take the personal development and careers planning of our students very seriously. Jointly with the University of Birmingham's Careers Network we have developed a structured programme to support maths students with their career planning from when they arrive to when they graduate and beyond.

Register to attend at: http://www.birmingham.ac.uk/postgraduate/visit

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This course, commonly referred to as Part III, is a one-year taught Master's course in mathematics.
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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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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

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.

- 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 .

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.

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.

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

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.
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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.

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 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.
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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: Pure Mathematics: Algebra, Analysis and Geometry; and Applied Mathematics: Statistics, Financial Mathematics, Computational Mathematics, Plasma-Astrophysics.

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.

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).

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.

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

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

Read more about our Mathematics programme.

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

Find more reasons to choose Mathematics at Leiden University.

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

Read more about the entry requirements for Mathematics.

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

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Our MSc Mathematics programme consists of a wide range of modules and a written project.
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Our MSc Mathematics programme consists of a wide range of modules and a written project. Your module choices will be mainly from the two main blocks of pure mathematics and theoretical physics but you are also able to choose certain modules from the Financial Mathematics programme and at other University of London institutions, subject to approval. ### Key benefits

- An intensive course covering a wide range of basic and advanced topics.

- Intimate class environment with small class sizes (typically fewer than twenty students on a module) allowing good student-lecturer interactions.

- A full twelve-month course with a three-month supervised summer project to give a real introduction to research.

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/mathematics-msc.aspx### Course detail

- Description -

The majority of the eight modules are taken from blocks of pure mathematics and theoretical physics, with other options from the MSc Financial Mathematics and other University of London institutions available, subject to approval.

Pure Mathematics:

- Metric & Banach Spaces

- Complex Analysis

- Fourier Analysis

- Non-linear Analysis (new in 2013)

- Operator Theory

- Galois Theory

- Lie Groups & Lie Algebras

- Algebraic Number Theory

- Algebraic Geometry

- Manifolds

- Real Analysis II

- Topology

- Rings & Modules

- Representation Theory of Finite Groups

Theoretical Physics:

- Quantum Field Theory

- String Theory & Branes

- Supersymmetry

- Advanced Quantum Field Theory

- Spacetime geometry and General Relativity

- Advanced General Relativity

- Low-dimensional Quantum Field Theory

- Course purpose -

This programme is suitable for Mathematics graduates who wish to study more advanced mathematics. The programme ideally prepares students for PhD study in a mathematical discipline.

- Course format and assessment -

Eight modules assessed by written examinations; one individual project.### Career prospects

Many of our graduates take up full-time employment in various industries that require good mathematical/computer knowledge or that look for intelligent and creative people. Recent employers of our graduates include Barclays Bank, Kinetic Partners, Lloyds Banking Group and Sapient.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx### About Postgraduate Study at King’s College London:

To study for a postgraduate degree at King’s College London is to study at the city’s most central university and at one of the top 20 universities worldwide (2015/16 QS World Rankings). Graduates will benefit from close connections with the UK’s professional, political, legal, commercial, scientific and cultural life, while the excellent reputation of our MA and MRes programmes ensures our postgraduate alumni are highly sought after by some of the world’s most prestigious employers. We provide graduates with skills that are highly valued in business, government, academia and the professions. ### Scholarships & Funding:

All current PGT offer-holders and new PGT applicants are welcome to apply for the scholarships. For more information and to learn how to apply visit: http://www.kcl.ac.uk/study/pg/funding/sources ### Free language tuition with the Modern Language Centre:

If you are studying for any postgraduate taught degree at King’s you can take a module from a choice of over 25 languages without any additional cost. Visit: http://www.kcl.ac.uk/mlc

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- Intimate class environment with small class sizes (typically fewer than twenty students on a module) allowing good student-lecturer interactions.

- A full twelve-month course with a three-month supervised summer project to give a real introduction to research.

Visit the website: http://www.kcl.ac.uk/study/postgraduate/taught-courses/mathematics-msc.aspx

The majority of the eight modules are taken from blocks of pure mathematics and theoretical physics, with other options from the MSc Financial Mathematics and other University of London institutions available, subject to approval.

Pure Mathematics:

- Metric & Banach Spaces

- Complex Analysis

- Fourier Analysis

- Non-linear Analysis (new in 2013)

- Operator Theory

- Galois Theory

- Lie Groups & Lie Algebras

- Algebraic Number Theory

- Algebraic Geometry

- Manifolds

- Real Analysis II

- Topology

- Rings & Modules

- Representation Theory of Finite Groups

Theoretical Physics:

- Quantum Field Theory

- String Theory & Branes

- Supersymmetry

- Advanced Quantum Field Theory

- Spacetime geometry and General Relativity

- Advanced General Relativity

- Low-dimensional Quantum Field Theory

- Course purpose -

This programme is suitable for Mathematics graduates who wish to study more advanced mathematics. The programme ideally prepares students for PhD study in a mathematical discipline.

- Course format and assessment -

Eight modules assessed by written examinations; one individual project.

How to apply: http://www.kcl.ac.uk/study/postgraduate/apply/taught-courses.aspx

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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications.
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The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines. ### Why this programme

◾Mathematics at the University of Glasgow is ranked 3rd in Scotland (Complete University Guide 2017).

◾The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.

◾You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.

◾You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.

◾Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.### Programme structure

Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)

◾Algebraic & geometric topology

◾Continuum mechanics & elasticity

◾Differential geometry

◾Fluid mechanics

◾Functional analysis

◾Further complex analysis

◾Galois theory

◾Mathematical biology

◾Mathematical physics

◾Numerical methods

◾Number theory

◾Partial differential equations

◾Topics in algebra.

Level-M courses (20 credits)

◾Advanced algebraic & geometric topology

◾Advanced differential geometry & topology

◾Advanced functional analysis

◾Advanced methods in differential equations

◾Advanced numerical methods

◾Biological & physiological fluid mechanics

◾Commutative algebra & algebraic geometry

◾Elasticity

◾Further topics in group theory

◾Lie groups, lie algebras & their representations

◾Magnetohydrodynamics

◾Operator algebras

◾Solitons

◾Special relativity & classical field theory.

SMSTC courses (20 credits)

◾Advanced Functional Analysis

◾Advanced Mathematical Methods

The project titles are offered each year by academic staff and so change annually.### Career prospects

Career opportunities are diverse and varied and include academia, teaching, industry and finance.

Graduates of this programme have gone on to positions such as:

Maths Tutor at a university.

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◾The School has a strong international reputation in pure and applied mathematics research and our PGT programmes in Mathematics offer a large range of courses ranging from pure algebra and analysis to courses on mathematical biology and fluids.

◾You will be taught by experts across a wide range of pure and applied mathematics and you will develop a mature understanding of fundamental theories and analytical skills applicable to many situations.

◾You will participate in an extensive and varied seminar programme, are taught by internationally renowned lecturers and experience a wide variety of projects.

◾Our students graduate with a varied skill set, including core professional skills, and a portfolio of substantive applied and practical work.

If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).

You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.

Level-H courses (10 or 20 credits)

◾Algebraic & geometric topology

◾Continuum mechanics & elasticity

◾Differential geometry

◾Fluid mechanics

◾Functional analysis

◾Further complex analysis

◾Galois theory

◾Mathematical biology

◾Mathematical physics

◾Numerical methods

◾Number theory

◾Partial differential equations

◾Topics in algebra.

Level-M courses (20 credits)

◾Advanced algebraic & geometric topology

◾Advanced differential geometry & topology

◾Advanced functional analysis

◾Advanced methods in differential equations

◾Advanced numerical methods

◾Biological & physiological fluid mechanics

◾Commutative algebra & algebraic geometry

◾Elasticity

◾Further topics in group theory

◾Lie groups, lie algebras & their representations

◾Magnetohydrodynamics

◾Operator algebras

◾Solitons

◾Special relativity & classical field theory.

SMSTC courses (20 credits)

◾Advanced Functional Analysis

◾Advanced Mathematical Methods

The project titles are offered each year by academic staff and so change annually.

Graduates of this programme have gone on to positions such as:

Maths Tutor at a university.

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

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

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

Our Applied Mathematics staff have research interests in:

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

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

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

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

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

We are part of:

-The North British Functional Analysis Seminar

-The North British Geometric Group Theory Seminar

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

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

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

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

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

Our Applied Mathematics staff have research interests in:

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

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

-Cosmology, including the very early universe and quantum gravity

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

-The North British Functional Analysis Seminar

-The North British Geometric Group Theory Seminar

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

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

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

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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.
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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.

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 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:

Functional Analysis;

Partial Differential Equations;

Pure Mathematics (recommended).

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.

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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A minimum GPA of 3.0 in all undergraduate coursework in mathematics. A letter of intent written by the applicant expressing professional goals as applied to the program.
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• A minimum GPA of 3.0 in all undergraduate coursework in mathematics.

• A letter of intent written by the applicant expressing professional goals as applied to the program.

• Submission of three letters of recommendation, using the required recommendation form. Two letters must be from mathematics faculty with whom the applicant has taken courses.

• Resume or curriculum vitae.

E-mail: [email protected]

Phone: 315-267-2165

Visit http://www.potsdam.edu/graduate to view the full application checklist and online application

The Master of Arts program in Mathematics is designed to develop the student’s ability to work independently and to obtain basic knowledge in algebra, real and complex variables, and topology so that mathematics literature can be read with understanding and enjoyment. The successful completion of this program should prepare a student to enter a second-year doctoral program in mathematics, to begin a career as an industrial mathematician or as a faculty member at a junior or community college. Program start dates: Fall or Spring (in certain cases).

Required Program Courses

Minimum of 30 credit hours

MATH 661, Topology I ...................................................3 credits

MATH 671, Abstract Algebra I ..........................................3 credits

MATH 672, Abstract Algebra II .........................................3 credits

MATH 681, Complex Variables I .......................................3 credits

MATH 691, Real Variables I .............................................3 credits

MATH 698, Seminar .....................................................3 credits

One of the following:

MATH 662, Topology II ...............................................3 credits

MATH 682, Complex Variables II ...................................3 credits

MATH 692, Real Variables II ........................................3 credits

Mathematics Electives ..................................................9 credits### Success Stories

SUNY Potsdam Mathematics graduates are employed by com-panies such as Aetna, AT&T, IBM, General Electric, Kodak, the National Security Agency and Hewlett Packard. Others have received assistantships and fellowships at reputable universities, and many have earned Ph.D. degrees in mathematics or statistics. ### Uniqueness of the Program

The MA Mathematics program develops rigorous mathematical thinking and offers a spectrum of well-taught courses in pure and theoretical mathematics. ### Testimonials

"I was accepted to all but three Ph.D. programs I applied to. I feel very fortunate to be in this position, [with] so many great offers from excellent schools. I would recommend a stats program to any BA/MA student interested in furthering their education through a degree that’s not math as they’ll be highly qualified and prepared. That stance has only been further confirmed as I talk to faculty in different statistics departments." — Justin J. Raimondi, Class of 2014

"As a somewhat sheltered student through high school, I found that the mathematics faculty at SUNY Potsdam nurtured me carefully, providing the support I needed to develop confidence in the content area, and to deepen my love of mathematics. After graduating from the BA/MA program, I have taught successfully at the high school and college levels for nearly 30 years." —Donald C. Straight, Class of 1988

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• A letter of intent written by the applicant expressing professional goals as applied to the program.

• Submission of three letters of recommendation, using the required recommendation form. Two letters must be from mathematics faculty with whom the applicant has taken courses.

• Resume or curriculum vitae.

E-mail: [email protected]

Phone: 315-267-2165

Visit http://www.potsdam.edu/graduate to view the full application checklist and online application

The Master of Arts program in Mathematics is designed to develop the student’s ability to work independently and to obtain basic knowledge in algebra, real and complex variables, and topology so that mathematics literature can be read with understanding and enjoyment. The successful completion of this program should prepare a student to enter a second-year doctoral program in mathematics, to begin a career as an industrial mathematician or as a faculty member at a junior or community college. Program start dates: Fall or Spring (in certain cases).

Required Program Courses

Minimum of 30 credit hours

MATH 661, Topology I ...................................................3 credits

MATH 671, Abstract Algebra I ..........................................3 credits

MATH 672, Abstract Algebra II .........................................3 credits

MATH 681, Complex Variables I .......................................3 credits

MATH 691, Real Variables I .............................................3 credits

MATH 698, Seminar .....................................................3 credits

One of the following:

MATH 662, Topology II ...............................................3 credits

MATH 682, Complex Variables II ...................................3 credits

MATH 692, Real Variables II ........................................3 credits

Mathematics Electives ..................................................9 credits

"As a somewhat sheltered student through high school, I found that the mathematics faculty at SUNY Potsdam nurtured me carefully, providing the support I needed to develop confidence in the content area, and to deepen my love of mathematics. After graduating from the BA/MA program, I have taught successfully at the high school and college levels for nearly 30 years." —Donald C. Straight, Class of 1988

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The Algebra and Topology section is an active research group consisting of renowned experts covering a remarkably broad range of topics.
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The section offers a Master's specialisation in Algebra in Topology, which is a 2-year programme aimed at students with an interest in pure mathematics and its applications.

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

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

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

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

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

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

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

- Basic notions in Mathematics

- Linear Algebra

- Algebra

- Analysis

- Topology

- Geometry

- Differential Equations

2. A proficiency in English

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

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

- An IELTS score of ≥6.5

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

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

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