The recent progress in several fields of theoretical physics (such as high energy physics, astrophysics, quantum and nonlinear optics or condensed matter physics) required numerous very sophisticated mathematical tools. In these frontline research fields, it became clear that a new understanding of physical systems going from cold atom gases to black holes is impossible without a new insight into underlying mathematical structures. This kind of problems requires a new interdisciplinary approach and specialists with double competence: in Physics and in different fields of modern Mathematics.
The main aim of the Master Program In Mathematical Physics (Math4Phys) is to provide advanced lectures on the mathematical methods of modern theoretical physics in the framework of a mathematical curriculum. Such an offer exists in France only in Dijon as the Mathematical Physics group of the IMB (Burgundy Mathematical Institute) provides a unique environment for a program requiring a double competence in Mathematics and Physics. The Mathematical Physics group of the IMB laboratory in Dijon is a unique research team in France with a capacity to provide advanced lectures in mathematical problems of modern physics. It permits to create a scientific environment for a master program focused on the most important problems of modern Physics from the mathematical perspective.
We offer lecture courses for the students with background in mathematics or mathematical physics giving an introduction to the mathematical methods used for such branches of theoretical physics as quantum field theory, statistical mechanics, general relativity, gauge theories, string theory, etc. The coursework covers different fields of mathematics (algebra, geometry, analysis) and highlights their applications to the problems of modern theoretical physics. The students are integrated from the very beginning into the mathematical physics group of the IMB and have to prepare by the end of each year a master dissertation.
The first year (M1) of the program is designed to provide the necessary background courses (mostly in mathematics but also in physics) to comply with the coursework of the more advanced second year. In particular, the M1 program includes the following subjects:
1. Differential geometry
2. Fourier analysis
3. Functional analysis
4. Groups and representations
5. Mathematical methods of classical mechanics
6. Partial differential equations
7. Quantum physics
8. Numerical methods
The second year lecture coursework includes the following lecture courses:
1. Mathematical methods of quantum physics
2. Riemann geometry and integrable systems
3. Lie groups and Lie algebras
4. Cohomological field theories
5. Quantum groups
6. Geometry and physics of blackhole spacetimes
We will also provide several mini courses by the research visitors of IMB. More detailed program of the second year courses can be found on the program webpage
The main aim of the master program is to provide sufficient training to start a PhD preparation.
Maximum enrolment 20 in M1 and 15 in M2
To apply for the Master program in Mathematical Physics students should send a CV, a short description of their previous coursework (in Mathematics and Physics) and eventually a motivation letter to the program coordinator:
For M1: Giuseppe Dito ([email protected])
For M2: Nikolai Kitanine ([email protected])
Accepted students should proceed with the formal application procedure available here.
The students applying for the M1 have to complete their undergraduate studies with major in Mathematics or Physics. The students can apply directly for the second year (M2) if they have completed at least one year of graduate courses in Mathematics or Mathematical Physics.
To follow the program the students should have a sufficient proficiency in English (we don’t require TOEFFL or an equivalent certificate but we can suggest an online interview to candidates).
Several fellowship grants (600 € per month, during up to 9 months) will be awarded each year to high quality foreign students,
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
- 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.
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.
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
- ICT developer / software developer
- Policy maker
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.
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
This MSc programme is designed to prepare you for a research career in academia or industry by introducing advanced ideas and techniques that are applicable in a wide range of research areas, while emphasising the underlying physics concepts.
The MSc programme is a core part of the Higgs Centre for Theoretical Physics, which has been created to mark the start of a new era in theoretical physics research, following the discovery of the Higgs boson at CERN. You will take part in the centre’s activities, including weekly seminars, colloquia and workshops involving physicists from around the world, and you will be involved in research-level projects as part of your dissertation.
The partnership between mathematics and physics is an essential one. In theoretical physics we attempt to build abstract constructs that rationalise, explain and predict physical phenomena. To do this we need mathematics: the language of physics. The underlying structure of the physical world can be understood in great detail using mathematics; this is a never-ending source of fascination to theoretical physicists.
You will take two compulsory courses plus a selection of courses that will bring you to an advanced level in subjects such as general relativity, cosmology, statistical physics, condensed matter physics, quantum field theory and the standard model of particle physics. You may also take courses drawn from a wider pool including specialist courses in mathematics, computing and climate science. For the MSc in Mathematical Physics, mathematics courses can account for almost half of the taught course element.
Following the taught component of the programme, you will undertake a three-month research project, which leads to a dissertation.
By engaging with and completing the MSc in Mathematical Physics, graduates will acquire core knowledge of theoretical physics subjects and the research methodologies of modern theoretical and mathematical physics.
The programme aims to develop research skills and problem solving skills, especially in mathematics. It also aims to develop an attitude of mind conductive to critical questioning and creative thinking and the capacity to formulate ideas mathematically.
These degrees are designed to prepare you for a research career by introducing advanced ideas and techniques that are applicable to a wide range of research areas and sectors including academia, industry, education and finance.
Find out more about scholarships and funding opportunities:
The course is run jointly by the Mathematical Institute and the Department of Physics. It provides a high-level, internationally competitive training in mathematical and theoretical physics, right up to the level of modern research. It covers the following main areas:
The course concentrates on the main areas of modern mathematical and theoretical physics: elementary-particle theory, including string theory, condensed matter theory (both quantum and soft matter), theoretical astrophysics, plasma physics and the physics of continuous media (including fluid dynamics and related areas usually associated with courses in applied mathematics in the UK system). If you are a physics student with a strong interest in theoretical physics or a mathematics student keen to apply high-level mathematics to physical systems, this is a course for you.
The course offers considerable flexibility and choice; you will be able to choose a path reflecting your intellectual tastes or career choices. This arrangement caters to you if you prefer a broad theoretical education across subject areas or if you have already firmly set your sights on one of the subject areas, although you are encouraged to explore across sub-field boundaries.
You will have to attend at least ten units' worth of courses, with one unit corresponding to a 16-hour lecture course or equivalent. You can opt to offer a dissertation as part of your ten units. Your performance will be assessed by one or several of the following means:
The modes of assessment for a given course are decided by the course lecturer and will be published at the beginning of each academic year. As a general rule, foundational courses will be offered with an invigilated exam while some of the more advanced courses will typically be relying on the other assessment methods mentioned above. In addition, you will be required to give an oral presentation towards the end of the academic year which will cover a more specialised and advanced topic related to one of the subject areas of the course. At least four of the ten units must be assessed by an invigilated exam and, therefore, have to be taken from lecture courses which provide this type of assessment. A further three units must be assessed by invigilated written exam, take-home exam or mini-project. Apart from these restrictions, you are free to choose from the available programme of lecture courses.
The course offers a substantial opportunity for independent study and research in the form of an optional dissertation (worth at least one unit). The dissertation is undertaken under the guidance of a member of staff and will typically involve investigating and write in a particular area of theoretical physics or mathematics, without the requirement (while not excluding the possibility) of obtaining original results.
This two-year MSc is offered by Royal Holloway as part of its South East Physics Network Partnership (SEPnet). SEPnet is a consortium of six universities: University of Kent, Queen Mary University of London, Royal Holloway University of London, University of Southampton, University of Surrey, and University of Sussex. This consortium consists of around 160 academics, with an exceptionally wide range of expertise linked with world-leading research.
The first year consists mainly of taught courses in the University of London; the second research year can be at Royal Holloway or one of the other consortium members. This is a unique opportunity to collaborate with physics research groups and partner institutions in both the UK and Europe. You will benefit from consortium led events as well as state of the art video conferencing.
The Department of Physics at Royal Holloway is known internationally for its top-class research. Our staff carry out research at the cutting edge of Nanoscience and Nanotechnology, Experimental Quantum Computing, Quantum Matter at Low Temperatures, Theoretical Physics, and Biophysics, as well as other areas.
With access to some of the leading physics departments in the world, there is a wide choice of accommodation options, sporting facilities, international student organisations and careers services. South East England, with its close connections to continental Europe by air, Eurotunnel, and cross channel ferries, is an ideal environment for international students.
All modules are optional
In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.
You will take six from the following:
Only core modules are taken.
This high quality European Masters programme follows the European method of study and involves a year of research working on pioneering projects.
Assessment is carried out by a variety of methods including coursework, examinations and a dissertation.
This course equips you with the subject knowledge and a solid foundation for continued studies in physics, and many of our graduates have gone on to study for a PhD.
On completion of the course graduates will have a systematic understanding of knowledge, and a critical awareness of current problems and/or new insights at the forefront of the discipline a comprehensive understanding of techniques applicable to their own research or advanced scholarship originality in the application of knowledge, together with a practical understanding of how established techniques of research and enquiry are used to create and interpret knowledge in the discipline.
Our graduates are highly employable and, in recent years, have entered many different physics-related areas, including careers in industry, information technology and finance.
The program deepens the knowledge of basic elements of modern physics (atomic and molecular physics, solid state physics, nuclear and particle physics, astrophysics) and of theoretical physics (analytical mechanics, quantum mechanics, mathematical and numerical methods). It is possible to strengthen the knowledge of specific fields like biophysics, nanoscience, physics of matter, nuclear and particle physics, physics of the fundamental interactions, astrophysics. Finally, the program provides direct experience of the laboratory techniques and computer calculation techniques and data analysis.
The graduate in Physics will know and understand the most relevant phenomena of the physical world at different scales, starting from the macroscopic world down to the atomic physics, the physics of condensed matter, nuclear and subnuclear physics up to the physics of the universe. The understanding of the physical world will be based on experimental evidence and a proper use of the theoretical modelling and its mathematical instruments, including numerical techniques.
The second-cycle degree in Physics is divided in three curricula to be chosen by the student: Physics of the fundamental interactions, Physics of matter and Physics of the universe. For further information please check: http://en.didattica.unipd.it
The graduate in Physics can have jobs opportunities in Italy and abroad in industries involving new technologies regardless of the final products, in service companies aiming to innovation and, more generally, in all activities requiring understanding and modelling of processes and ability in analysis and testing. These include startups and high tech industries, software and consulting companies, research centers and public administration. They can also teach physics and mathematics in schools of different levels.
The University of Padova, the Veneto Region and other organisations offer various scholarship schemes to support students. Below is a list of the funding opportunities that are most often used by international students in Padova.
You can find more information below and on our website here: http://www.unipd.it/en/studying-padova/funding-and-fees/scholarships
You can find more information on fee waivers here: http://www.unipd.it/en/fee-waivers
This research oriented Master’s will provide you with a rich toolkit of creative problem solving skills that will turn you into a desired scientist, both in and outside academia. You will dive deep into mathematics, develope genuine research skills in pure, applied and industrial areas and learn to think out of the box.
This Master's is part of the national Mastermath Programme, a collaboration of Dutch Mathematics Departments who joined efforts to enhance their Master's programmes. Due to this collaboration you can benefit from an exceptional list of mathematical courses, offered either by Utrecht University or another Dutch University. Check the courses page for more information and a full overview of the courses you can choose from.
We combine our course offerings with personal and small-scale teaching, including:
Within this Master's you can choose from 8 different tracks, allowing you to tailor the programme to your own personal interest. Depending on the track you choose, you can pursue your degree either in the direction of Fundamental Mathematics or in Mathematical Modeling.
Fundamental Mathematics tracks:
Mathematical Modeling tracks:
You can also choose to do a Research project in History of Mathematics.
If you are up for it, you can also combine the Mathematical Sciences programme with another Master's programmes of the Graduate School of Natural Sciences (e.g. Theoretical Physics, Climate Physics or Computing Science). This will result in a double Master's degree.
The Mathematical Sciences programme will prepare you for a challenging career, either in or outside academia. Mathematicians are desired employees in today's job market since they can easily deal with complex problems and large data sets in an abstract way. About 40% of our students continue with a PhD in mathematics or related research areas such as imaging or physics (in recent years at Harvard, London, Oxford, Stanford, etc). Many find employment in a research oriented environment at governments or in industry. Work fields include risk analysis, security, forensics, consultancy, data analytics, IT, logistics and more.
The programme aims to train physicists capable of working in research institutes or corporate environments. Upon successful completion of the programme, students will have acquired:
This is an initial Master's programme and can be followed on a full-time or part-time basis.
After a semester with advanced courses in different disciplines of physics, you choose a major research specialization consisting of advanced and specialized courses and a master’s thesis of 30 ECTS.
The remaining 30 ECTS allow you to follow one of two options: Research or Physics in Society.
The mission of the Department of Physics and Astronomy is exploring, understanding and modelling physical realities using mathematical, computational, experimental and observational techniques. Fifteen teams perform research at an international level. Publication of research results in leading journals and attracting top-level scientists are priorities for the department.
New physics and innovation in the development of new techniques are important aspects of our mission. The interaction with industry (consulting, patents...) and society (science popularisation) are additional points of interest. Furthermore, the department is responsible for teaching basic physics courses in several study programmes.
The master students will grow into independent and critical scientists. Masters of physics will have developed sufficient knowledge and skills to participate in competitive national or international PhD programmes. Moreover the acquired research methodology will prepare the student for employment as a scientist in any chosen profession.
The curriculum is constructed in a way that the student can specialize in an area of choice by joining one of the research groups of the department. This specialization can be in the field of nuclear physics, condensed matter physics ortheoretical physics. A major part of the curriculum consists of research resulting in a master thesis. The subject of the thesis is chosen by the student during the course of the second semester of the 1st Master year and students join a research team from the 3th semester onwards.
The students can choose an option to prepare themselves better for a future in research or in industry or society related fields.
In the option "research" the student can take courses from another research specialization than its major one, which can be accompanied by an internship in one of the research teams of this minor discipline. As such our students have the possibility to broaden their knowledge in at least two scientific disciplines (in physics or a related field), which is invaluable when a further research career in or out of academia is considered.
In the option "Physics for society" students can choose for an internship of a full semester in a company or they can take courses from the LCIE Entrepreneurship Academy who wants to prepare academics for entrepreneurschip.
The Erasmus programme of the European Union offers an excellent opportunity for Belgian students who would like to combine their study with experience outside the KU Leuven. All research groups of the department have a network of European collaborators and we advise interested students to integrate this exchange with their thesis research during their second Master year. Choices concerning the Erasmus programme need to be made in December of the 1st Master year. Address the Erasmus coordinator to obtain specific information on this European programme.
The Department of Physics and Astronomy at KU Leuven generates substantial research funding. Consequently, many research positions are available, and more than half the students obtaining a master’s degree in physics eventually start a PhD programme in one of the department’s research groups.
A number of graduates prefer to pursue a second master’s degree, with medical radiation physics, environmental sciences, and statistics as the most popular subjects. There are also excellent career opportunities in industry (ICT, material research, electronics), consulting, government, banking (statistics), and higher education. Unemployment is nonexistent among newly graduated physicists.