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Masters Degrees (Quantum Mechanics)

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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. Read more

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.

About this degree

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 three core modules (45 credits), three optional modules (45 credits) and a research project (90 credits).

Core modules

All students take the following core modules:

  • Atom and Photon Physics
  • Advanced Quantum Theory
  • Quantum Communication and Computation

Optional modules

Students choose one optional module from any of the Physics MSc degrees as well as two of the following optional modules:

  • Advanced Photonic Devices
  • 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

Research project and case studies

The MSc programme culminates in the quantum technologies project and attached case studies. All students undertake two case studies related to quantum technologies as well as an independent research project (experimental or theoretical), which will be the subject of a presentation and a dissertation of 10,000-15,000 words. Research-active supervisors will provide topics which will enable the students to make contributions to research in the field.

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.

Further information on modules and degree structure is available on the department website: Quantum Technologies MSc

Funding

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the Scholarships and Funding website.

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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Course description. This masters by research course brings together the University of Sheffield’s expertise in quantum photonics and nanomaterials. Read more

Course description

This masters by research course brings together the University of Sheffield’s 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.

Core modules

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

Examples of optional modules

Choose from a range including:

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

Teaching and assessment

One-year individual programme of research.

Taught material is complemented by a 12-month research project in one of our world-leading research groups.

Your training will cover optical experiments and fabrication of devices in our state-of-the-art laboratories as well as numerical methods and more.



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Master's specialisation in Physics of Molecules and Materials. Revealing the ‘terra incognita’ between quantum mechanics and the classical world and inspiring new technologies. Read more

Master's specialisation in Physics of Molecules and Materials

Revealing the ‘terra incognita’ between quantum mechanics and the classical world and inspiring new technologies.

As a scientist, you’re a problem solver. But how do you tackle a problem when there are no adequate theories and calculations become far too complicated? In the specialisation in Physics of Molecules and Materials you’ll be trained to take up this challenge in a field of physics that is still largely undiscovered: the interface between quantum and classical physics.

We focus on systems from two atoms to complete nanostructures, with time scales in the order of femtoseconds, picoseconds or nanoseconds. One of our challenges is to understand the origin of phenomena like superconductivity and magnetism. As theory and experiment reinforce each other, you’ll learn about both ‘research languages’. In this way, you’ll be able to understand complex problems by dividing them into manageable parts.

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

Why study Physics of Molecules and Materials at Radboud University?

- At Radboud University there’s a strong connection between theory and experiment. Theoretical and experimental physicists will teach you to become acquainted with both methods.

- In your internship(s), you’ll have the opportunity to work with unique research equipment, like free electron lasers and high magnetic fields, and with internationally known scientists.

- We collaborate with several industrial partners, such as Philips and NXP. This extensive network can help you find an internship or job that meets your interests.

If you’re successful in your internship, you have a good chance of obtaining a PhD position at the Institute for Molecules and Materials (IMM).

Admission requirements for international students

1. A completed Bachelor's degree in Physics

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:

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

- An IELTS score of ≥6.5

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

Career prospects

This Master’s specialisation is an excellent preparation for a career in research, either at a university or at a company. However, many of our students end up in business as well. Whatever job you aspire, you can certainly make use of the fact that you have learned to:

- Solve complex problems

- Make accurate approximations

- Combine theory and experiments

- Work with numerical methods

Graduates have found jobs as for example:

- Consultant Billing at KPN

- Communications advisor at the Foundation for Fundamental Research on Matter (FOM)

- Systems analysis engineer at Thales

- Technical consultant at UL Transaction Security

- Business analyst at Capgemini

PhD positions

At Radboud University, we’re capable of offering many successful students in the field of Physics of Molecules and Materials a PhD position. Many of our students have already attained a PhD position, not just at Radboud University, but at universities all over the world.

Our approach to this field

In this specialisation, you’ll discover the interface between quantum mechanics and the classical world, which is still a ‘terra incognita’. We focus on two-atom systems, multi-atom systems, molecules and nanostructures. This is pioneering work, because these systems are often too complex for quantum calculations and too small for the application of classical theories.

- Theory and experiment

At Radboud University, we believe that the combination of theory and experiments is the best way to push the frontiers of our knowledge. Experiments provide new knowledge and data and sometimes also suggest a model for theoretical studies. The theoretical work leads to new theories, and creative ideas for further experiments. That’s why our leading theoretical physicists collaborate intensively with experimental material physicists at the Institute for Molecules and Materials (IMM). Together, they form the teaching staff of the Master’s specialisation in Physics of Molecules and Materials.

- Themes

This specialisation is focused on two main topics:

- Advanced spectroscopy

Spectroscopy is a technique to look at matter in many different ways. Here you’ll learn the physics behind several spectroscopic techniques, and learn how to design spectroscopic experiments. At Radboud University, you also have access to large experimental infrastructure, such as the High Magnetic field Laboratory (HFML), the FELIX facility for free electron lasers and the NMR laboratory.

- Condensed matter and molecular physics

You’ll dive into material science at the molecular level as well as the macroscopic level, on length scales from a single atom up to nanostructure and crystal. In several courses, you’ll get a solid background in both quantum mechanical and classical theories.

- Revolution

We’re not aiming at mere evolution of current techniques, we want to revolutionize them by developing fundamentally new concepts. Take data storage. The current data elements are near the limits of speed and data capacity. That’s why in the IMM we’re exploring a completely new way to store and process data, using light instead of electrical current. And this is but one example of how our research inspires future technology. As a Master’s student you can participate in this research or make breakthroughs in a field your interested in.

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



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

Current faculty projects and research interests:

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

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

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

• Algebraic Number Theory, especially rings of algebraic integers

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

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

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

• Coding theory, especially relation of designs to codes

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

• Partial Differential Equations

• Nonlinear Problems of Mathematical Physics

• Dissipative Dynamical Systems

• Scattering of classical and quantum waves

• Wavelet analysis

• Molecular dynamics

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

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

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

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

• Geometric phases and dynamical invariants

• Supersymmetry and its generalizations

• Pseudo-Hermitian quantum mechanics

• Quantum cosmology

• Numerical Linear Algebra

• Numerical Optimization

• Perturbation Theory of Eigenvalues

• Eigenvalue Optimization

• Mathematical finance

• Stochastic optimal control and dynamic programming

• Stochastic flows and random velocity fields

• Lyapunov exponents of flows

• Unicast and multicast data traffic in telecommunications

• Probabilistic Inference

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

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

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

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

• Arithmetical Algebraic Geometry, Arakelov geometry, Mixed Tate motives

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

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

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

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

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Microsystems Engineering is one of the most dynamic and interdisciplinary engineering fields. The Master of Science program in Microsystems Engineering (MSE) provides the educational basis for your success in this field. Read more
Microsystems Engineering is one of the most dynamic and interdisciplinary engineering fields. The Master of Science program in Microsystems Engineering (MSE) provides the educational basis for your success in this field. The MSE program is designed for highly qualified graduate students holding a Bachelor degree in engineering or science.

In the first year 12 mandatory courses provide the fundamental theoretical framework for a future career in Microsystems. These courses are designed to provide students with a broad knowledge base in the most important aspects of the field:

• MSE technologies and processes
• Microelectronics
• Micro-mechanics
• MSE design laboratory I
• Optical Microsystems
• Sensors
• Probability and statistics
• Assembly and packaging technology
• Dynamics of MEMS
• Micro-actuators
• Biomedical Microsystems
• Micro-fluidics
• MSE design laboratory II
• Signal processing

As part of the mandatory courses, the Microsystems design laboratory is a two-semester course in which small teams of students undertake a comprehensive, hands-on design project in Microsystems engineering. Requiring students to address all aspects of the generation of a microsystem, from conceptualization, through project planning to fabrication and testing, this course provides an essential glimpse into the workings of engineering projects.

In the second year, MSE students can specialise in two of the following seven concentration areas (elective courses), allowing each student to realize individual interests and to obtain an in-depth look at two sub-disciplines of this very broad, interdisciplinary field:

• Circuits and systems
• Design and simulation
• Life sciences: Biomedical engineering
• Life sciences: Lab-on-a-chip
• Materials
• Process engineering
• Sensors and actuators

Below are some examples of subjects offered in the concentration areas. These subjects do not only include theoretical lectures, but also hands-on courses such as labs, projects and seminars.

Circuits and Systems
• Analog CMOS Circuit Design
• Mixed-Signal CMOS Circuit Design
• VLSI – System Design
• RF- und Microwave Devices and Circuits
• Micro-acoustics
• Radio sensor systems
• Optoelectronic devices
• Reliability Engineering
• Lasers
• Micro-optics
• Advanced topics in Macro-, Micro- and Nano-optics


Design and Simulation
• Topology optimization
• Compact Modelling of large Scale Systems
• Lattice Gas Methods
• Particle Simulation Methods
• VLSI – System Design
• Hardware Development using the finite element method
• Computer-Aided Design

Life Sciences: Biomedical Engineering
• Signal processing and analysis of brain signals
• Neurophysiology I: Measurement and Analysis of Neuronal Activity
• Neurophysiology II: Electrophysiology in Living Brain
• DNA Analytics
• Basics of Electrostimulation
• Implant Manufacturing Techologies
• Biomedical Instrumentation I
• Biomedical Instrumentation II

Life Sciences: Lab-on-a-chip
• DNA Analytics
• Biochip Technologies
• Bio fuel cell
• Micro-fluidics 2: Platforms for Lab-on-a-Chip Applications

Materials
• Microstructured polymer components
• Test structures and methods for integrated circuits and microsystems
• Quantum mechanics for Micro- and Macrosystems Engineering
• Microsystems Analytics
• From Microsystems to the nano world
• Techniques for surface modification
• Nanomaterials
• Nanotechnology
• Semiconductor Technology and Devices

MEMS Processing
• Advanced silicon technologies
• Piezoelectric and dielectric transducers
• Nanotechnology

Sensors and Actuators
• Nonlinear optic materials
• CMOS Microsystems
• Quantum mechanics for Micro- and Macrosystems Engineering
• BioMEMS
• Bionic Sensors
• Micro-actuators
• Energy harvesting
• Electronic signal processing for sensors and actuators


Essential for the successful completion of the Master’s degree is submission of a Master’s thesis, which is based on a project performed during the third and fourth semesters of the program. Each student works as a member of one of the 18 research groups of the department, with full access to laboratory and cleanroom infrastructure.

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Course description. You will learn from researchers who were part of the discoveries of the Higgs boson, the third neutrino mixing angle, and gravitational waves. Read more

Course description

You will learn from researchers who were part of the discoveries of the Higgs boson, the third neutrino mixing angle, and gravitational waves.

You’ll be able to take part in front-line experiments at the LHC, in neutrino physics, in the search for dark matter, and in gravitational waves.

You will develop the skills to make new discoveries at the frontiers of physics.

Core modules

  • Dark Matter and the Universe
  • Further Quantum Mechanics
  • The Development of Particle Physics
  • Advanced Electromagnetism
  • Research Skills in Physics
  • Research Project in Physics

Examples of optional modules

Choose from a range including:

  • Introduction to General Relativity
  • Particle Astrophysics
  • Advanced Particle Physics
  • Physics in an Enterprise Culture
  • Advanced Quantum Mechanics
  • Semiconductor Physics and Technology
  • Statistical Physics

Teaching and assessment

One-year individual programme of research.

Taught material is complemented by a 12-month research project in one of our world-leading research groups.

Depending on the subject of your project, it may be possible for you to complete your research at a laboratory outside the University of Sheffield – for example, at CERN.



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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. Read more

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?

You’ll study in a Physics department ranked amongst the top 15 in the UK (Guardian University Guide 2018) where researchers are leading the way on the development of the world’s first quantum computer. We’re also a founder member of SEPnet, the South East Physics Network which supports vital research, teaching and development.

The course is split between taught modules and your individual project and you can choose to study full time or part time.

The taught part of the course comprises core modules plus a choice of options, allowing you to tailor the course towards your own particular interests. You’ll also attend research seminars and contribute to your group’s discussions of the latest journal papers.

Your project can take the form of a placement in industry, but is usually supervised by our faculty. Supervisors and topics are allocated, in consultation with you, at the start of the autumn term. Often the projects form the basis of research papers that are later published in journals.

Assessment is split equally between the project and modules. Modules are assessed with either open-notes tests or unseen examinations. Your project culminates in a dissertation (with a contribution from a research talk).

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

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

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

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

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

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

Why study Mathematical Physics at Radboud University?

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

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

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

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

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

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

Career prospects

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

Job positions

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

PhD positions

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

Our research in this field

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

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

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

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

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

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

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



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

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

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

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

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

Why study Applied Stochastics at Radboud University?

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

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

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

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

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

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

Career prospects

Master's programme in Mathematics

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

Job positions

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

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

PhD positions

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

Our research in this field

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

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

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

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

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

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

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

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



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The Department of Philosophy has exceptional research strength in philosophy of physics, and very strong links with the School of Physics. Read more
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 is a one year advanced taught course. The aim of this course is to bring students in 12 months to the frontier of elementary particle theory. Read more

This is a one year advanced taught course. The aim of this course is to bring students in 12 months to the frontier of elementary particle theory. This course is intended for students who have already obtained a good first degree in either physics or mathematics, including in the latter case courses in quantum mechanics and relativity.

The course consists of three modules: the first two are the Michaelmas and Epiphany graduate lecture courses, which are assessed by examinations in January and March. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics. The dissertation must be submitted by September 15th, the end of the twelve month course period.

Course Structure

The main group of lectures are given in the first two terms of the academic year (Michaelmas and Epiphany). This part of the lecture course is assessed by examinations. In each term there are two teaching periods of four weeks, with a week's break in the middle of the term in which students will be able to revise the material. Most courses are either eight lectures or 16 lectures in length. There are 14 lectures/week in the Michaelmas term and 14 lectures/week in Epiphany term.

Core Modules

  • Introductory Field Theory
  • Group Theory
  • Standard Model
  • General Relativity
  • Quantum Electrodynamics
  • Quantum Field Theory
  • Conformal Field Theory
  • Supersymmetry
  • Anomalies
  • Strong Interaction Physics
  • Cosmology
  • Superstrings and D-branes
  • Non-Perturbative Physics
  • Euclidean Field Theory
  • Flavour Physics and Effective Field Theory
  • Neutrinos and Astroparticle Physics
  • 2d Quantum Field Theory.

Optional Modules available in previous years included:

  • Differential Geometry for Physicists
  • Boundaries and Defects in Integrable Field Theory
  • Computing for Physicists.

Course Learning and Teaching

This is a full-year degree course, starting early October and finishing in the middle of the subsequent September. The aim of the course is to bring students to the frontier of research in elementary particle theory.

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

The lectures begin with a general survey of particle physics and introductory courses on quantum field theory and group theory. These lead on to more specialised topics, amongst others in string theory, cosmology, supersymmetry and more detailed aspects of the standard model.

The main group of lectures is given in the first two terms of the academic year (Michaelmas and Epiphany). This part of the lecture course is assessed by examinations. In each term there are two teaching periods of 4 weeks, with a week's break in the middle of the term in which students will be able to revise the material. Most courses are either 8 lectures or 16 lectures in length. There are 14 lectures/week in the Michaelmas term and 14 lectures/week in Epiphany term they are supported by weekly tutorials. In addition lecturers also set a number of homework assignments which give the student a chance to test his or her understanding of the material.

There are additional optional lectures in the third term. These introduce advanced topics and are intended as preparation for research in these areas.

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



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Why a Physics MSc?. Physics has always remained and still is at the center of science and technology. The laws of physics that are reached through observations and careful experimentation find applications from the subatomic particles to the astronomic formations such as stars and galaxies. Read more

Why a Physics MSc?

Physics has always remained and still is at the center of science and technology. The laws of physics that are reached through observations and careful experimentation find applications from the subatomic particles to the astronomic formations such as stars and galaxies. On the other hand, design of advanced technology materials, fabrication of semiconductor devices, the development of optical communication systems have all evolved as applications of physics.

Our department has both theoretical and experimental research activites. Quantum information theory, gravitation and condensed matter physics are among our theoretical research interests.

On the experimental research side, we have three advanced laboratories where we focus on solid state lasers, optoelectronic and nano-photonic materials and devices.

Our M. Sc. Program aims at teaching fundamental physics at a high level and coupling this knowledge with a research experience in either theoretical or applied physics depending on the interests of the student.

Current faculty projects and research interests:

• Photonic and Laser Materials

• Microphotonics

• Nanophotonics

• Gravitation, Cosmology, and Numerical Relativity

• Mathematical Physics

• Quantum Mechanics and Quantum Information Theory

• Theoretical High Energy Physics

• Quantum Optics, atomic, molecular and optical physics

• Statistical mechanics of biophysical systems

Laboratories



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his is a one year advanced taught course. The aim of this course is to bring students in twelve months to the frontier of elementary particle theory. Read more
his is a one year advanced taught course. The aim of this course is to bring students in twelve months to the frontier of elementary particle theory. This course is intended for students who have already obtained a good first degree in either physics or mathematics, including in the latter case courses in quantum mechanics and relativity.

The course consists of three modules: the first two are the Michaelmas and Epiphany graduate lecture courses, which are assessed by examinations in January and March. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics. The dissertation must be submitted by September 15th, the end of the twelve month course period.

Course Structure
The main group of lectures are given in the first two terms of the academic year (Michaelmas and Epiphany). This part of the lecture course is assessed by examinations. In each term there are two teaching periods of 4 weeks, with a week's break in the middle of the term in which students will be able to revise the material. most courses are either 8 lectures or 16 lectures in length. There are 14 lectures/week in the Michaelmas term and 14 lectures/week in Epiphany term.

Core Modules
- Introductory Field Theory
- Group Theory
- Standard Model
- General Relativity
- Quantum Electrodynamics
- Quantum Field Theory
- Conformal Field Theory
- Supersymmetry
- Anomalies
- Strong Interaction Physics
- Cosmology
- Superstrings and D-branes
- Non-Perturbative Physics
- Euclidean Field Theory
- Flavour Physics and Effective Field Theory
- Neutrinos and Astroparticle Physics
- 2d Quantum Field Theory
- Optional Modules
- Differential Geometry for Physicists
- Boundaries and Defects in Integrable Field Theory
- Computing for Physicists.

For further information on this course, please visit the Centre for Particle Theory website (http://www.cpt.dur.ac.uk/GraduateStudies)

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

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

Course structure and overview

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

Modules: Six of available options

In previous years, optional modules available included:

Modules in Pure Mathematics:

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

Modules in Probability and Statistics:

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

Modules in Applications of Mathematics:

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

Course Learning and Teaching

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

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

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

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



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We offer postgraduate research degrees in Physics at the MPhil and PhD level in all of our major research areas such as Emerging Technology and Materials, Applied Mathematics, and Photoelectron Spectroscopy. Read more
We offer postgraduate research degrees in Physics at the MPhil and PhD level in all of our major research areas such as Emerging Technology and Materials, Applied Mathematics, and Photoelectron Spectroscopy.

We supervise MPhil students whose interests match the expertise we have in our four main research themes.

Condensed matter and nanoscale physics

We research electronic, optical, structural and magnetic properties of novel solid-state materials, particularly novel semi-conductor structures and nanostructured materials such as nanocrystals and nanowires. Theoretical studies use quantum mechanical approaches and involve massively parallel supercomputing.

Our development of new approaches to quantum modelling is changing the size and complexity of systems that can be modelled. Experimental work takes place at synchrotron facilities in Europe and America and related work takes place with colleagues in the Emerging Technology and Materials (ETM) Group in the School of Electrical, Electronic and Computer Engineering.

Biophysics

Our research in biophysics explores the structure and function of cells with the aim of creating artificial life and building machines based on biological parts. Projects include protocell development and the construction of a cyborg robot. An understanding of biological physics is needed that uses techniques including single molecule manipulation, atomic force microscopy and scanning tunnelling microscopy.

Astrophysics

Galaxies and the interstellar medium, the source of the galactic magnetic field and its influence on the structure of the galaxy form the focus of our research in astrophysics. There is also interest in cosmology, particularly the early universe and its origin in the big bang.

Ultrafast optics

Our research focuses on coherent optical control of atomic collisions in ultracold gases by femtosecond laser light for studies of problems in fundamental physics, such as the measurement of time dependence of the fundamental constants of nature. We also research metrological protocols for characterisation of broadband light, specifically those relating to foundational aspects of quantum mechanics and its application.

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