# Second year Applied Mathematics

Applied Mathematics (AM) is a three year bachelor programme. Each year is divided into four quarters, each consisting of ten weeks. The academic calendar details the holidays taken into account. Each quarter consists of 15 European Credits (EC). The curriculum has a total of 180 EC, meaning students are expected to earn 60 EC per year. Each year consists of four modules, each with their own theme within the programme. During the first semester of the third year, you as a student have the opportunity to follow a minor of your own choice.

Module 5: Statistics and Analysis

The core of this module (Osiris) is formed by Mathematical Statistics and the project. The project deals with regression analysis. The module consists of the following parts:

• Mathematical Statistics
• Analysis II
• Project
• Prooflab revisited

After successful completion of the module, the student:

• is able to derive mathematically the standard techniques for statistical data analysis and apply them properly.
• is able to work with infinite series of real numbers and functions, with metric spaces and with differentiability of functions in n-dimensional Euclidean spaces.
Module 6: Dynamical Systems

This module (Osiris) is about dynamic phenomena, their mathematical representations, computational aspects and applications in control problems. The subjects of the module are Ordinary Differential Equations (ODEs), Systems & Control and Numerical Analysis. For the project, students model a human movement and study it regarding stability and control, applying the material from the subjects. The module consists of the following parts:

• Differential Equations
• Systems Theory
• Numerical Methods
• Project

After successful completion of the module, the student

• is able to analyse and control solutions of systems of ODEs.
• can model a physical system with ODEs.
• is able to use various numerical and analytical techniques to study the model.
Module 7: Discrete Structures and Efficient Algorithms

This module (Osiris) deals with discrete problems as encountered in various practical problems and solutions thereof using efficient algorithms. The module is a joint effort of Applied Mathematics and Technical Computer Science. Central in the module is a project about graph isomorphisms. The module consists of the following parts:

• Algorithms and Data Structures
• Discrete Mathematics
• Languages & Machines
• Algebra
• Project

After successful completion of the module the student:

• has knowledge of and insight into discrete structures as studied in mathematics and computer science.
• is able to apply the techniques to analyse these structures and to solve relevant problems through appropriate algorithms.
• is able to deduce the complexity and efficiency of such algorithms.
Module 8: Modelling and Analysis of Stochastic Processes for Math

This module (Osiris) is about modelling situations with uncertainty using stochastic processes. The module is a joint effort of Applied Mathematics, Industrial Engineering and Management and Civil Engineering. The theoretical parts are closely connected (Stochastic Models being focused on applicability, while Markov Chains is more in depth), and Project Stochastic Models is closely related to Stochastic Models itself. Furthermore, all three projects are about the same context, the final project serving to integrate all acquired knowledge. The module consists of the following parts:

• Stochastic Models
• Project Stochastic Models
• Markov Chains
• Project Stochastic Simulation
• Multidisciplinary Project

After successful completion of the module the student:

• knows how to recognise when a situation or system should be modelled using stochastic models.
• is able to select the most appropriate models.
• has knowledge of and insight into methods to analyse and/or simulate such models.
• is able to interpret the outcomes of the analysis or simulation.