Master of Science in Computational Mathematics
In addition to being a science in its own right, mathematics plays a fundamental role in the quantitative areas of practically all other academic disciplines, particularly in the natural sciences, engineering, business administration, economics, medicine and psychology. Mathematical results permeate nearly all facets of life and are a necessary prerequisite for the vast majority of modern technologies – and as our IT systems become increasingly powerful, we are able to mathematically handle enormous amounts of data and solve ever more complex problems. Special emphasis is placed on developing the students' ability to formalise given problems in a way that facilitates algorithmic processing. Also, they are enabled to choose or develop, and subsequently apply, suitable algorithms to solve problems in an appropriate manner. The degree programme is theoretical in its orientation, with strongly application-oriented components. Studying this programme, you can gain advanced knowledge in the mathematical areas of cryptography, computer algebra, algorithmic algebra and geometry, image and signals processing, statistics and stochastic simulation, dynamical systems and control theory as well as expert knowledge in computer science fields such as data management, machine learning and data mining. Furthermore, you will have the chance to learn how to apply your knowledge to tackle problems in areas as diverse as marketing, predictive analytics, computational finance, digital humanities, IT security and robotics.
The core modules consist of two mathematics seminars and the presentation of your Master's thesis. The compulsory elective modules are divided into eight module groups: Algebra, Geometry and Cryptography This module group imparts advanced results in the areas of algebra and geometry, which constitute the foundation for algorithmic calculations, particularly in cryptography, but also in many other mathematical areas. Mathematical Logic and Discrete Mathematics The theoretical possibilities and limitations of algorithm-based solutions are treated in this module group. Analysis, Numerics and Approximation Theory Methods from the fields of mathematical analysis, applied harmonic analysis and approximation theory for modelling and approximating continuous and discrete data and systems as well as efficient numerical implementation and evaluation of these methods are the scope of this module group. Dynamical Systems and Optimisation Dynamical systems theory deals with the description of change over time. This module group is concerned with methods used for the modelling, analysis, optimisation and design of dynamical systems as well as the numerical implementation of such techniques. Stochastics, Statistics This module group deals with methods for modelling and analysing complex random phenomena as well as the construction, analysis and optimisation of stochastic algorithms and techniques used in statistical data analysis. Data Analysis and Data Management and Programming This module group examines the core methods used in computer science for the analysis of data of heterogeneous modalities (e.g., multimedia data, social networks and sensor data) and for the realisation of data analysis systems. Applications In this module group, you will practise applying the mathematical methods learned in module groups 1 to 6 to real-world applications such as marketing, predictive analytics and computational finance. Key Competencies and Language Training In this module group, you will choose seminars that develop your non-subject-specific skills, such as public speaking and academic writing and other soft skills. You may also participate in internships. This will serve to complement your technical expertise gained during your degree studies and will help to prepare you for your professional life after the university. Your performance throughout the programme is evaluated by way of module assessments. In order to obtain the degree, you must pass a certain number of prescribed modules. However, you will be given the freedom to decide at which point in your degree programme you wish to complete specific modules. This also means that you need to rely on your organisational skills, as you will have to put together your own timetable every semester, avoiding scheduling conflicts between modules that may be administered by different faculties. Nonetheless, the student committees and other units of the university will be on hand to advise you on timetabling issues and module selections.
You are eligible for this degree programme if you have an undergraduate university degree in mathematics or a closely related degree with a mathematics component of at least 110 ECTS credits and a final grade of 2.7 (German grading system) or the equivalent grade in a foreign grading system. Applicants who have not attained this minimum grade may still apply if they are among the best 70% of graduates of their cohort. Language requirements Unless English was the language of instruction of your prior university or secondary education, you should provide a language certificate at level B2 of the Common European Framework of Reference for Languages (CEFR). Similarly, unless German was the language of instruction of your prior university or secondary education, you should provide proof of German language skills at level A1 CEFR (i.e., introductory level). If you do not have German language skills at the time of application or enrolment, you will complete a compulsory, free-of-charge German language course during the first two semesters of the programme.