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

- 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.

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

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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Mathematics is the science of structures, including mathematics itself. Discovery of new patterns and relations, and the construction of models with predictive power are the core of mathematics.
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Frequently, we see an interaction between fundamental and applied research. This versatility is reflected in the Master's programme Mathematical Sciences, which a broad range of courses is offered. Both students who want to specialise and students who aim for a wider background in mathematics.

[Tracks]]

You can tailor your programme by selecting one of the following seven tracks:

-Algebraic Geometry and Number Theory

-Applied Analysis

-Complex Systems

-Differential Geometry and Topology

-Logic

-Probability, Statistics, and Stochastic Modelling

-Pure Analysis

-Scientific Computing

-You can also choose to do a Research project in History of Mathematics.

This Master's programme offers a broad scope in a stimulating international environment which is renowned for its excellent research. Students who prefer to research subjects in depth will feel particularly at home at Mathematical Sciences.

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The Master's programme in Mathematics at Radboud University offers you a thorough theoretical training, while maintaining a clear perspective on concrete applications whenever appropriate.
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Mathematical research of course stands on its own, as is notably the case with the large group in algebraic topology led by Spinoza laureate Ieke Moerdijk. In addition, within IMAPP, researchers link with high-energy physics, including Higgs physics and quantum gravity. Outside IMAPP but within the Faculty of Science, there are close ties with the Institute for Computing and Information Sciences (ICIS) (think of logic and category theory) and outside the Faculty of Science (but within Radboud University) researchers at both the Donders Institute for Neurosciences and the University Medical Center collaborate with the applied stochastics group.

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

- Applied Stochastics

- Mathematical Physics

- Mathematical Foundations of Computer Science

Possible careers for mathematicians include:

- Researcher (at research centres or within corporations)

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

- Risk model validator

- Consultant

- ICT developer / software developer

- Policy maker

- Analyst

- PhD positions

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

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

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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.
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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

Read less

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

- 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.

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

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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