Masters Degrees (Quantum)

The Quantum Technologies MSc will take students to the cutting-edge of research in the emerging area of quantum technologies, giving them not only an advanced training in the relevant physics but also the chance to acquire key skills in the engineering and information sciences.

Degree information

Students learn the language and techniques of advanced quantum mechanics, quantum information and quantum computation, as well as state-of-the-art implementation with condensed matter and quantum optical systems.

Students undertake modules to the value of 180 credits.

The programme consists of five core modules (75 credits), three optional modules (45 credits) and a research project with a dissertation/report (60 credits).

Core modules
-Advanced Quantum Theory
-Atom and Photon Physics
-Quantum Communication and Computation
-Research Case Studies for Quantum Technologies
-Transferable Skills in Research Case Studies for Quantum Technologies

Optional modules - students choose three of the following optional modules:
-Advanced Photonic Devices
-Introduction to Cryptography
-Nanoelectronic Devices
-Nanoscale Processing for Advanced Devices
-Optical Transmission and Networks
-Order and Excitations in Condensed Matter
-Physics and Optics of Nano-Structures
-Research Computing with C++
-Research Software Engineering with Python

Dissertation/report
All students undertake an independent research project (experimental or theoretical) related to quantum technologies, which culminates in a presentation and a dissertation of 10,000 words.

Teaching and learning
The programme is delivered through a combination of lectures and seminars, with self-study on two modules devoted to the critical assessment of current research topics and the corresponding research skills. Assessment is through a combination of problem sheets, written examinations, case study reports and presentations, as well as the MSc project dissertation.

Careers

The programme prepares graduates for careers in the emerging quantum technology industries which play an increasingly important role in: secure communication; sensing and metrology; the simulation of other quantum systems; and ultimately in general-purpose quantum computation. Graduates will also be well prepared for research at the highest level in the numerous groups now developing quantum technologies and for work in government laboratories.

Employability
Graduates will possess the skills needed to work in the emerging quantum industries as they develop in response to technological advances.

Why study this degree at UCL?

UCL offers one of the leading research programmes in quantum technologies anywhere in the world, as well as outstanding taught programmes in the subjects contributing to the field (including physics, computer science, and engineering). It also hosts the EPSRC Centre for Doctoral Training in Delivering Quantum Technologies.

The programme provides a rigorous grounding across the disciplines underlying quantum technologies, as well as the chance to work with some of the world's leading groups in research projects. The new Quantum Science and Technology Institute ('UCLQ') provides an umbrella where all those working in the field can meet and share ideas, including regular seminars, networking events and opportunities to interact with commercial and government partners.

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Exploration of quantum phenomena has recently led to extraordinary applications of quantum entanglement. The degree of control exerted over these systems is reflected in the term ‘quantum technology’, describing both experimental and theoretical developments in this area.

This course is for you if you’re interested in the wonders of quantum physics and have a desire to exploit its full power. We cover:
-Ion-trap quantum processors
-Ion-photon interfaces for the projected quantum internet
-Quantum simulators
-Superconducting quantum circuits
-Devices for quantum-enhanced metrology

How will I study?

Assessment is split equally between the project and modules.

Your project culminates in a dissertation (with a contribution from a research talk). The modules are assessed by problem sets, with either open-notes tests or unseen examinations. You’ll attend research seminars and contribute to your group’s discussions of the latest journal papers.

You can choose to study this course full time or part time.

Your time is split between taught modules and a research project. The project can take the form of a placement in industry, but usually our faculty supervises them. Supervisors and topics are allocated, in consultation with you, at the start of the autumn term. You work on the project throughout the year. Often the projects form the basis of research papers that are later published in journals. Most projects are theoretical but there is an opportunity for you to become involved in the reduction and analysis of data acquired by faculty members.

In the autumn and spring terms, you take core modules and choose options. You start work on your project and give an assessed talk on this towards the end of the spring term. In the summer term, you focus on examinations and project work.

In the part-time structure, you take the core modules in the autumn and spring terms of your first year. After the examinations in the summer term, you begin work on your project. Project work continues during the second year when you also take options.

Distribution of modules between the two years is relatively flexible and agreed between you, your supervisor and the module conveners. Most of your project work naturally falls into the second year.

Scholarships

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals.

Chancellor's International Scholarship (2017)
-25 scholarships of a 50% tuition fee waiver
-Application deadline: 1 May 2017

HESPAL Scholarship (Higher Education Scholarships Scheme for the Palestinian Territories) (2017)
-Two full fee waivers in conjuction with maintenance support from the British Council
-Application deadline: 1 January 2017

USA Friends Scholarships (2017)
-A scholarship of an amount equivalent to $10,000 for nationals or residents of the USA on a one year taught Masters degree course.
-Application deadline: 3 April 2017

Careers

This course may be attractive to you if you aim to:
-Go on to doctoral study (theory or experiment)
-Work in a high-technology company exploiting cutting-edge technologies related to our research (this could involve development of quantum information technology, high-precision measurements and quantum metrology, and photonics/optical communications)
-Work in business/data analysis, research, computer programming, software development, or teaching

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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Cold Atoms and Quantum Optics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

The MSc by Research Cold Atoms and Quantum Optics enables students to pursue a one year individual programme of research. The Cold Atoms and Quantum Optics programme would normally terminate after a year. However, under appropriate circumstances, this first year of research can also be used in a progression to Year 2 of a PhD degree.

As a student of the Cold Atoms and Quantum Optics programme you will be fully integrated into one of our established research groups and participate in research activities such as seminars, workshops, laboratories, and field work.

Swansea is a research led University to which the Physics department makes a significant contribution, meaning that as a postgraduate Physics student you will benefit from the knowledge and skills of internationally renowned academics.

The Department received top ratings of 4* and 3* in the 2008 RAE, which classified our research as World-leading or Internationally excellent in terms of its originality, significance and rigour.

Links with Industry

Our two research groups, Particle Physics Theory (PPT) and Atomic, Molecular and Quantum Physics (AMQP), deliver impact with commercial benefits both nationally and internationally, complemented by a public engagement programme with a global reach.

Economic impacts are realised by the Department’s Analytical Laser Spectroscopy Unit (ALSU) which, since 1993, has worked with companies developing products eventually sold to customers in the nuclear power industry and military, both in the UK and overseas, and in the global aerospace industry. Computational particle physics work performed by the PPT group has spun-off a computer benchmarking tool, BSMBench, used by several leading software outfits, and has led to the establishment of a start-up company.

The AMQP group’s work on trapping and investigating antihydrogen has generated great media interest and building on this we have developed a significant and on-going programme of public engagement. Activities include the development of a bespoke software simulator (Hands on Antihydrogen) of the antimatter experiment for school students.

Facilities

As a postgraduate Cold Atoms and Quantum Optics student in the Department of Physics you will have access to the following Specialist Facilities:

Low-energy positron beam with a high field superconducting magnet for the study of

positronium

CW and pulsed laser systems

Scanning tunnelling electron and nearfield optical microscopes

Raman microscope

CPU parallel cluster

Access to the IBM-built ‘Blue C’ Super computer at Swansea University and is part of the shared use of the teraflop QCDOC facility based in Edinburgh

Research

The Physics Department carries out world-leading research in experimental and theoretical physics.

The results of the Research Excellence Framework (REF) 2014 show that over 80% of the research outputs from both the experimental and theoretical groups were judged to be world-leading or internationally excellent.

Research groups include:

AMQP Group

The Atomic, Molecular and Quantum Physics Group comprises academic staff, postdoctoral officers and postgraduate research students. Its work is supported by grants from EPSRC, the EU, The Royal Society, the Higher Education Funding Council for Wales and various industrial and government sources. There are two main fields of research: Atomic, Molecular and Laser Physics and Nanoscale Physics.

PPT Group

The Particle Physics Theory Group has fourteen members of staff, in addition to postdoctoral officers and research students. It is the fourth largest particle physics theory group in the UK, and is supported mainly by STFC, but also has grants from EPSRC, the EU, Royal Society and Leverhulme Trust. The group recently expanded by hiring two theoretical cosmologists (Ivonne Zavala and Gianmassimo Tasinato). There are five main fields of research: Quantum Field Theory, Strings, Lattice Field Theory, Beyond the Standard Model Physics and Theoretical Cosmology.

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Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Quantum Fields & String at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).

The MSc by Research Quantum Fields and String enables students to pursue a one year individual programme of research. The Quantum Fields & String programme would normally terminate after a year. However, under appropriate circumstances, this first year of research can also be used in a progression to Year 2 of a PhD degree.

As a student of the MSc by Research in Quantum Fields and String you will be fully integrated into one of our established research groups and participate in research activities such as seminars, workshops, laboratories, and field work.

Key Features

Swansea is a research led University to which the Physics department makes a significant contribution, meaning that as a postgraduate Physics student you will benefit from the knowledge and skills of internationally renowned academics.

The Department received top ratings of 4* and 3* in the 2008 RAE, which classified our research as world-leading or internationally excellent in terms of its originality, significance and rigour.

Links with Industry

Our two research groups, Particle Physics Theory (PPT) and Atomic, Molecular and Quantum Physics (AMQP), deliver impact with commercial benefits both nationally and internationally, complemented by a public engagement programme with a global reach.

Economic impacts are realised by the Department’s Analytical Laser Spectroscopy Unit (ALSU) which, since 1993, has worked with companies developing products eventually sold to customers in the nuclear power industry and military, both in the UK and overseas, and in the global aerospace industry. Computational particle physics work performed by the PPT group has spun-off a computer benchmarking tool, BSMBench, used by several leading software outfits, and has led to the establishment of a start-up company.

The AMQP group’s work on trapping and investigating antihydrogen has generated great media interest and building on this we have developed a significant and on-going programme of public engagement. Activities include the development of a bespoke software simulator (Hands on Antihydrogen) of the antimatter experiment for school students.

Facilities

As a student of the Quantum Fields and String programme in the Department of Physics you will have access to the following Specialist Facilities:

Low-energy positron beam with a high field superconducting magnet for the study of

positronium

CW and pulsed laser systems

Scanning tunnelling electron and nearfield optical microscopes

Raman microscope

CPU parallel cluster

Access to the IBM-built ‘Blue C’ Super computer at Swansea University and is part of the shared use of the teraflop QCDOC facility based in Edinburgh

Research

The Physics Department carries out world-leading research in experimental and theoretical physics.

The results of the Research Excellence Framework (REF) 2014 show that over 80% of the research outputs from both the experimental and theoretical groups were judged to be world-leading or internationally excellent.

Research groups include:

AMQP Group

The Atomic, Molecular and Quantum Physics Group comprises academic staff, postdoctoral officers and postgraduate research students. Its work is supported by grants from EPSRC, the EU, The Royal Society, the Higher Education Funding Council for Wales and various industrial and government sources. There are two main fields of research: Atomic, Molecular and Laser Physics and Nanoscale Physics.

PPT Group

The Particle Physics Theory Group has fourteen members of staff, in addition to postdoctoral officers and research students. It is the fourth largest particle physics theory group in the UK, and is supported mainly by STFC, but also has grants from EPSRC, the EU, Royal Society and Leverhulme Trust. The group recently expanded by hiring two theoretical cosmologists (Ivonne Zavala and Gianmassimo Tasinato). There are five main fields of research: Quantum Field Theory, Strings, Lattice Field Theory, Beyond the Standard Model Physics and Theoretical Cosmology.

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Our Physics MSc is highly flexible, giving you the opportunity to structure your course to meet your individual career aspirations.

The course gives you the opportunity to broaden and deepen your knowledge and skills in physics, at the forefront of research in the area. This will help to prepare you to progress to PhD study, or to work in an industrial or other business related area.

A key feature of the course is that you can choose to study a wide range of optional modules or focus on a particular area of research expertise according to your interests and future career aspirations.

Under the umbrella of an MSc in physics, you can specialise in astrophysics, bionanophysics, soft matter physics, condensed matter physics, quantum technology, optical materials or medical imaging. Or you can take a diverse range of modules to suit your interests and keep their options open.

Course content

The course offers you a very wide range of optional modules, giving you the opportunity to specialise in areas such as astrophysics, bionanophysics, soft matter physics, condensed matter physics, quantum technology, optical materials or medical imaging.

Modules studied may include: quantum field theory; superconductivity; general relativity; medical image analysis; cosmology; bionanophysics; magnetism in condensed matter; statistical mechanics; star and planet formation; elementary particle physics; quantum matter; and photonics.

Alongside your optional modules, you will undertake an advanced and extensive research project in one of the School of Physics and Astronomy’s internationally recognised research groups. This will enable you to develop advanced skills in research planning, execution and reporting, possibly leading to publication of your work in an international journal.

Course structure

Compulsory modules

• MSc Project 75 credits
• Advanced Literature Review 15 credits
• Current Research Topics in Physics 15 credits

Optional modules

• Cardiovascular Medical Imaging 10 credits
• Digital Radiography and X-ray Computed Tomography 10 credits
• Magnetic Resonance Imaging 10 credits
• Ultrasound Imaging 10 credits
• Radionuclide Imaging 10 credits
• Medical Image Analysis 10 credits
• Digital Radiography and X-ray Computed Tomography 15 credits
• Ultrasound Imaging 15 credits
• Radionuclide Imaging 15 credits
• Medical Image Analysis 15 credits
• Cosmology 15 credits
• Photonics 15 credits
• Molecular Simulation: Theory and Practice 15 credits
• Star and Planet Formation 15 credits
• Advanced Quantum Mechanics 15 credits
• Quantum Photonics 15 credits
• Quantum Matter 15 credits
• Magnetism in Condensed Matter 15 credits
• Statistical Mechanics 15 credits
• Advanced Mechanics 15 credits
• Bionanophysics 1 15 credits
• Theoretical Elementary Particle Physics 15 credits
• Soft Matter Physics: Liquid Crystals 15 credits
• Quantum Many-Body Physics 15 credits
• Winds, Bubbles and Explosions 15 credits
• Bionanophysics 2: Advanced Bionanophysics Research 15 credits
• Advanced Group Industrial Project 15 credits
• Superconductivity 15 credits
• Soft Matter Physics: Polymers, Colloids and Glasses 15 credits
• Quantum Transport in Nanostructures 15 credits
• Quantum Field Theory 15 credits
• General Relativity 15 credits
• Quantum Information Science 15 credits
• Advanced Physics in Schools 15 credits

For more information on typical modules, read Physics MSc in the course catalogue

Learning and teaching

Teaching methods include a combination of lectures, seminars, supervisions, problem solving, presentation of work, independent research, and group work (depending on the modules you choose to study).

Assessment

Assessment of modules are by problem solving exams and research assignments. The project is assessed on the ability to plan and conduct research and communicate the results in written and oral format.

Career opportunities

The specialist pathways offered by this course (in astrophysics, bionanophysics, soft matter physics, condensed matter physics, quantum technology, optical materials or medical imaging) allow you to tailor your course and focus on a particular area of research expertise according to your interests and future career aspirations.

Physicists are highly employable due to their high level of numeracy and mathematical competence, their computer skills, and their high level of technical academic scientific knowledge. They are employed by: industry, financial sector, defence, education, and more.

This course is also a clear route to PhD level study.

Careers support

We encourage you to prepare for your career from day one. That’s one of the reasons Leeds graduates are so sought after by employers.

The Careers Centre and staff in your faculty provide a range of help and advice to help you plan your career and make well-informed decisions along the way, even after you graduate. Find out more at the Careers website.

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Recent theoretical and experimental advances mean that we are now able to exert an extraordinary degree of control over individual quantum systems and to prepare and manipulate groups of interacting quantum systems deterministically.

Bringing these techniques to bear upon both fundamental physics and a new swathe of technologies dependent on strange quantum phenomena defines the emerging field of controlled quantum dynamics.

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This one-year research degree is a chance for you to develop your skills in one of the most exciting areas of modern science. It’s a unique opportunity to gain hi-tech skills that are central to the latest advances in electronics, IT and computing.

This course brings together our expertise in quantum photonics and nanomaterials. There is a particular focus on the study of novel fundamental phenomena in condensed matter systems as well as applications in quantum information processing, photovoltaics and optoelectronics.

Our staff are at the forefront of technological advances. We work with support from the UK Engineering and Physical Sciences Research Council, European Research Council and the Horizon 2020 programme, the Royal Society, the Leverhulme Trust and the British Council as well as CONACyT, the National Council of Science and Technology in Mexico.

Our department attracts postgraduate students from around the world.

Core modules

Optical Properties of Solids
Semiconductor Physics and Technology
Advanced Electromagnetism
Solid State Physics
Research Skills in Physics
Research Project in Physics

Examples of optional modules

Magnetic Resonance: Principles and Applications
Physics in an Enterprise Culture
The Physics of Soft Condensed Matter
Statistical Physics
Advanced Quantum Mechanics
Further Quantum Mechanics
Biological Physics

Teaching

Teaching is through lectures, research seminars, small group tutorials and oral presentation.

Your supervisor will help you develop your research skills and support you as you work on your research project.

Assessment

Assessment includes: a project report, literature review, oral presentations, including a viva, formal examinations and short reports and essays.

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This renowned MSc course is designed to prepare students for PhD study in fundamental theoretical physics by bridging the gap between an undergraduate course in physics or mathematics and the research frontier.

The Theoretical Physics Group is internationally recognised for its contribution to our understanding of the unification of fundamental forces, the early universe, quantum gravity, supersymmetry, string theory, and quantum field theory.

The origins of the MSc course date back to the founding of the Theoretical Physics Group by Abdus Salam, one of Imperial’s Nobel Laureates.

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

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

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

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

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

Why study Mathematical Physics at Radboud University?

- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.
- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.
- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.
- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.

Career prospects

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

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad indeed and is why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

PhD positions

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

Our research in this field

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

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

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

Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:
1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.
2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.

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

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Overview

The course provides an introduction to the physical principles and mathematical techniques of current research in general relativity, quantum gravity, particle physics, quantum field theory, quantum information theory, cosmology and the early universe.

The programme of study includes a taught component of closely-related modules in this popular area of mathematical physics. The course also includes a substantial project that will allow students to develop their interest and expertise in a specific topic at the frontier of current research, and develop their skills in writing a full scientific report.

The course will provide training in advanced methods in mathematics and physics which have applications in a wide variety of scientific careers and provide students with enhanced employability compared with undergraduate Bachelors degrees. In particular, it will provide training appropriate for students preparing to study for a PhD in the research areas listed above. For those currently in employment, the course will provide a route back to academic study.

Key facts:

- The course is taught jointly by the School of Mathematical Sciences and the School of Physics and Astronomy.

- Dissertation topics are chosen from among active research themes of the Particle Theory group, the Quantum Gravity group and the Quantum Information group.

- In addition to the lectures there are several related series of research-level seminars to which masters students are welcomed.

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

Module details

Advanced Gravity

Black Holes

Differential Geometry

Gravity

Gravity, Particles and Fields Dissertation

Introduction to Quantum Information Science

Modern Cosmology

Quantum Field Theory

English language requirements for international students

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

Further information

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

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

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

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

Why study Applied Stochastics at Radboud University?

- This specialisation focuses both on theoretical and applied topics. It’s your choice whether you want to specialise in pure theoretical research or perform an internship in a company setting.
- Mathematicians at Radboud University are expanding their knowledge of random graphs and networks, which can be applied in the ever-growing fields of distribution systems, mobile phone networks and social networks.
- In a unique and interesting collaboration with Radboudumc, stochastics students can help researchers at the hospital with very challenging statistical questions.
- Because the Netherlands is known for its expertise in the field of stochastics, it offers a great atmosphere to study this field. And with the existence of the Mastermath programme, you can follow the best mathematics courses in the country, regardless of the university that offers them.
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that you’ll get plenty of one-on-one time with your thesis supervisor at Radboud University .
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating.

Career prospects

Master's programme in Mathematics

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

Job positions

The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad and is the reason why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- Consultant
- ICT developer / software developer
- Policy maker
- Analyst

PhD positions

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

Our research in this field

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

Eric Cator’s research has two main themes, probability and statistics.
1. In probability, he works on interacting particles systems, random polymers and last passage percolation. He has also recently begun working on epidemic models on finite graphs.
2. In statistics, he works on problems arising in mathematical statistics, for example in deconvolution problems, the CAR assumption and more recently on the local minimax property of least squares estimators.

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

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

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

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

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The Department gives MSc students an opportunity to study and perform a research project under the supervision of recognized experts and to acquire specialist knowledge of one or a few topics at the cutting edge of contemporary physics.

The project will be devoted to one of several topical areas of modern physics including high-temperature superconductivity, terahertz semiconductor and superconductor electronics, quantum computing and quantum metamaterials, physics of extreme conditions and astrophysics.

Core study areas currently include mathematical methods for interdisciplinary sciences, research methods in physics, superconductivity and nanoscience and a research project.

Optional study areas currently include characterisation techniques in solid state physics, quantum information, advanced characterisation techniques, quantum computing, and physics of complex systems.

See the website http://www.lboro.ac.uk/study/postgraduate/programmes/departments/physics/advanced-physics/

Programme modules

Compulsory Modules:
- Mathematical Methods for Interdisciplinary Sciences
- Research Methods in Physics
- Superconductivity and Nanoscience
- Research Project Part 1
- Research Project Part 2

Optional Modules:
- Characterisation Techniques in Solid State Physics
- Fundamentals of Quantum Information
- Matlab as a Scientific Programming Language
- Advanced Characterisation Techniques
- Quantum Computing
- Physics of Complex systems

Learning and teaching

Knowledge and understanding are acquired through lectures, tutorials, problem classes and guided independent study. Assessment in taught modules is by a combination of examination and coursework. The MSc includes a significant research project completed through guided independent study with a research supervisor.

Careers and further study

The aim of the course is to equip students with key skills they need for employment in industry, public service or academic research.

Why choose physics at Loughborough?

We are a community of approximately 170 undergraduates, 30 postgraduates, 16 full-time academic staff, seven support staff, and several visiting and part-time academic staff.

Our large research student population and wide international links make the Department a great place to work.

- Research
Our research strengths are in the areas of condensed matter and materials, with a good balance between theory and experiment.
The quality of our researchers is recognised internationally and we publish in highly ranked physics journals; one of our former Visiting Professors, Alexei Abrikosov, was awarded the 2003 Nobel Prize in Physics.

- Career Prospects
100% of our graduates were in employment and/or further study six months after graduating. They have gone on to work with companies such as BT, Nikon Metrology, Prysmian Group, Rutherford Appleton Laboratory ISIS and Smart Manufacturing Technology.

Find out how to apply here http://www.lboro.ac.uk/study/postgraduate/programmes/departments/physics/advanced-physics/

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The Department of Philosophy has exceptional research strength in philosophy of physics, and very strong links with the School of Physics. Our MA draws on these strengths. It is intended both for students who wish to specialise in philosophy of physics at a higher level, and for individuals with a background in physics or mathematics who wish to make a transition to philosophy and foundations of physics. The course consists of five taught units in philosophy, two taught master's units in physics, and a 15,000-word dissertation.

As a postgraduate student, you will be an active member of the department’s flourishing research culture. You will be encouraged to attend and participate in both the weekly departmental research seminar and in the Philosophy and History of Science seminars, which often feature well-known scholars in the field, from Bristol and beyond. There is also a weekly postgraduate seminar, where you may present your own work before your peers and learn to develop your argumentative strategies in a supportive environment.

Programme structure

The MA consists of taught components in philosophy and physics, as well as a dissertation.

Core units
- Philosophical Writing and Research Methods (Philosophy, 20-credit unit)
- A mandatory, two-hour weekly seminar developing ideas, bibliographical and writing skills necessary for philosophical research. The unit is assessed by seminar contributions and presentations.
- Scientific Methodology and Epistemology (Philosophy, 20-credit unit)
This unit concerns core topics in scientific epistemology and metaphysics. The unit is examined on the basis of an essay of 5,000-6,000 words. As with all assessed essays, you may meet with a supervisor to discuss your work and to receive feedback on a draft essay.
- Philosophy of Physics (Philosophy, 20-credit unit)
This unit covers philosophical issues related to basic physical theories, focusing on conceptual issues in the foundations of quantum theory and special relativity. We will cover topics such as the relativity of simultaneity; geometry and the causal structure of relativity physics; the conceptual structure of quantum mechanics, the Einstein-Podolsky-Rosen argument; the measurement problem and Schrödinger’s cat paradox of; locality and action-at-a-distance.
- Advanced Philosophy of Physics (Philosophy, 20-credit unit)
This unit will examine a selection of conceptual issues in the foundations of physical theory with particular focus on the physics of the mid-to-late 20th century. We cover topics such as: the arrow of time in thermal physics; the interpretation of quantum field theory; emergence and universality in condensed matter physics; fine tuning problems and inflationary cosmology; spontaneous symmetry breaking and the Higgs mechanism; and time in quantum gravity.
- Foundations of Modern Physics (Physics, 10-credit unit)
Emphasis is placed on students developing an appreciation of the foundations of different areas of physics, and the unit assessment involves students writing an essay whose detailed subject is partly decided by the student. The lectures are divided into Classical, Spacetime and Quantum Physics.
- Relativistic Field Theory (Physics, 10-credit unit)
This course will give an account of the modern approach to special relativity and Lagrangian field theory, and their role in the covariant description of the classical electromagnetic field, and the relativistic quantum Klein-Gordon and Dirac equations. Formative assessment is through problem sheets discussed in problems classes. Summative assessment is through a 2 hour written examination

Optional units (all Philosophy 20-credit units)
- History of Science
- Logic
- Philosophy and History of Mathematics
- Philosophy and History of Medicine
- Philosophy of Biology
- Philosophy of Psychology
- An individual, supervised research project

Please be aware that optional units may vary from year to year.

Careers

The MA in Philosophy of Physics is an ideal platform for further studies in Philosophy or Foundations of Physics. This course will also provide students with Maths and Physics backgrounds with an opportunity to develop verbal, written and argumentative skills that are highly valued by employers.

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

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

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

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

Why choose this course?

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

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

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

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

Department research and industry highlights

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

Course content and structure

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

Core courses:
Advanced Cipher Systems
Mathematical and security properties of both symmetric key cipher systems and public key cryptography are discussed as well as methods for obtaining confidentiality and authentication.

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

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

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

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

Additional courses:
Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

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

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

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

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

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

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

On completion of the course graduates will have:
- a suitable mathematical foundation for undertaking research or professional employment in cryptography and/or communications

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

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

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

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

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

Assessment

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

Employability & career opportunities

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

How to apply

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

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

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

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

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

Why choose this course?

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

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

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

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

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

Department research and industry highlights

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

Course content and structure

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

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

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

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

Additional courses:
Applications of Field Theory
You will be introduced to some of the basic theory of field extensions, with special emphasis on applications in the context of finite fields.

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

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

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

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

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

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

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

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

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

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

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

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

Assessment

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

Employability & career opportunities

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

How to apply

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

Read less