## Applied Mathematics, Complex Systems, and Scientific Computing

The specialisation Applied Mathematics, Complex Systems, and Scientific Computing focuses on applications of mathematics in modern society ranging from Complex systems and Bioinformatics, to Statistics and Scientific Computing.

The course programme provides the students with a broad set of skills, such as analytical thinking, mathematical modelling, programming in Python or C++, and using high-level toolboxes such as Matlab and R.

The master thesis project (45 EC) in this specialisation may be carried out as an internship in industry, a government research institution, or a research group from another department at Utrecht University where mathematics is applied. It is also possible to choose a topic within the Mathematics department.

A special characteristic of the specialisation is the freedom to choose up to 30 EC of courses in other disciplines, provided mathematics is applicable there.

### Complex Systems

Complex systems demonstrate the popular principle that “the whole is greater than the sum of its parts”. More concretely, a complex system is one whose collective behavior cannot readily be deduced by a reductive study of its individual components: Stock markets cannot be predicted by studying individual investors, complex thought cannot be easily understood through the electrochemical processes of neurons, and fluid turbulence is not an obvious consequence of the molecular structure of water.

The science of complex systems is a multidisciplinary effort that draws on mathematically formulated models from a variety of fields. A university-wide focus area “Foundations of Complex Systems” (see website) strives to coordinate research efforts at the Utrecht University on this front.

The mathematical foundations of complex systems are far from mature. Inspired by applications from outside the traditional realm of applied mathematics, the study of complex systems may well lead to truly new forms of mathematics. Additionally, there is a growing demand for mathematical scientists trained to build and analyze models of complex systems in economics, social sciences, biology and medicine, as well as natural sciences, geosciences and ecology. Complex Systems combines mathematical theory in dynamical systems, networks, stochastics and computation, with applications in one of the above disciplines. In particular, a masters research in Complex Systems will be jointly supervised by scientists from at least two disciplines.

### Scientific Computing

Scientific Computing is a rapidly growing field, providing mathematical methods and software for computer simulations in a wide variety of application areas, from particle simulations for the study of protein folding to mesh calculations in climate change prediction. The area is highly interdisciplinary, bringing together methods from numerical analysis, high-performance computing, and application fields. The scientific computing specialisation focuses on analysing the large-scale systems that are central in various fields of science and in many real-world applications. Students willl learn the mathematical tools necessary to tackle these problems in an efficient manner and they will be able to provide generic solutions and apply these to different application areas. They will learn to develop mathematical software and to use modern high-performance computers, such as massively parallel supercomputers, PC clusters, multicore PCs, or machines based on Graphics Processing Units (GPUs). Expertise in scientific computing is in high demand, and graduates will be able to pursue careers in research institutions or in industry or management.

Other topics in the specialisation Applied Mathematics, Complex Systems, and Scientific Computing:

- Bioinformatics
- Data science
- Imaging
- Machine learning
- Parallel algorithms
- Statistics

### Mathematics courses that fit the specialisation:

- Continuous Optimization
- Discrete Optimization
- Introduction to Complex Systems
- Numerical Linear Algebra
- Parallel Algorithms
- Seminar Mathematical Epidemiology
- Seminar Machine Learning
- Advanced Linear Programming
- Inverse Problems in Imaging
- Numerical Bifurcation Analysis of Large-Scale Systems
- Numerical Methods for Time-Dependent Partial Differential Equations
- Algorithms Beyond the Worst Case
- Systems and Control
- Applied Finite Elements
- Scheduling
- Queueing Theory
- Complex Networks
- Mathematical Neuroscience
- Machine Learning Theory
- Stochastic Gradient Techniques in Optimization and Learning
- High-Dimensional Probability Theory in Data Analysis

Note that the above courses may not be offered every academic year.

### Courses outside of mathematics that fit the 30 EC courses in other disciplines:

Computing science courses:

- INFOMDM - Data mining
- INFOGA - Geometric algorithms
- INFOCRWS - Crowd simulation
- INFOMBD - Big data
- INFOAN - Algorithms and networks
- INFOEA - Evolutionary computing
- INFOMGP - Game physics
- INFOMNWSC - Network science

Physics courses:

- NS-MO501M - Simulation of ocean, atmosphere, and climate
- NS-MO402M - Dynamical meteorology
- NS-MO434M - Current themes in climate change
- NS-TP432M - Modelling and Simulation

Biology courses:

- B-MQBIO - Introductory Course Quantitative Biology
- B-MBIEG06 - Bioinformatics and Evolutionary Genomics
- BMB502114 - Advanced Bioinformatics: Data Mining and Data Integration for Life Sciences
- BMB502219 - Introduction to R for Life Sciences

Chemistry courses:

- SK-MCBIM21 - Structural Bioinformatics and Modelling

Students must follow an advanced seminar (at least 7.5 EC) in which they themselves have to give oral presentations. This seminar can also be followed while the student is working on the research project.

### For more information about this specialisation, please contact Prof. dr. Rob Bisseling