The subject profile Modelling and Simulation

In the following you will find some explanations of the courses offered by the subject profile “Modelling and Simulation” for the Master’s programmes in Mathematics and Industrial Mathematics (CAM programme: see below). This information complements the general notes. The Master’s programme in Industrial Mathematics is expiring. Enrolments were accepted for the last time for WS16/17. It was replaced by the Computational and Applied Mathematics programme.

The offer of the subject profile ” Modelling and Simulation” is realised by the two chairs Applied Mathematics I and Applied Mathematics III. The courses are coordinated in a way that a mixture of courses of both chairs is possible and reasonable.

For the Master’s programme in Industrial Mathematics, this subject profile “Modelling and Simulation” corresponds to the programme of the same name. For the Master’s program in Mathematics it is, together with the subject profile “Optimization”, part of the field of study ” Modeling, Simulation and Optimization”.

The basic core module is the course “Advanced Numerics of Partial Differential Equations”. This is the former “Numerics of Partial Differential Equations II”, which was held earlier in the summer semester following the “Numerics of Partial Differential Equations I”. In order to be able to listen to this course in the first semester, it will be offered from now on in the winter semester. Prerequisite is the successful participation in the module “Introduction to Numerics of Partial Differential Equations”, the former “Numerics of Partial Differential Equations I”. This course was already a compulsory module of the bachelor’s programme for the master’s students who have completed a bachelor’s degree in Industrial Mathematics in Erlangen. If you belong to a group of students (Industrial Mathematics Bachelor from another university or Bachelor Mathematics) who have not yet included this course as a module in the Bachelor’s programme, this course, which will also take place in winter semester, will take on the role of the core module of the first Master’s programme. For this group of students, the “Advanced Studies in Numerics of Partial Differential Equations” will then follow in the third master’s semester. A further change is the additional course “Introduction Numerics of Partial Differential Equations II”, a two-hour lecture in the summer semester, which is graded with 5 ECTS. With this course it is taken into account that by integrating contents from the field of analysis of partial differential equations and also linear functional analysis into the “Introduction Numerics of Partial Differential Equations” in the winter semester only stationary (time-independent) problems can be treated. The additional course in summer semester is supplemented by prototypes of time-dependent problems. This course is recommended either in the Bachelor’s programme in Industrial Mathematics, especially if a Bachelor’s thesis is aimed at in this field, then this course is parallel to the corresponding Bachelor’s seminar. If the “Introduction to Numerics of Partial Differential Equations” is a course of the Master’s program, then the respective second part is also recommended.

Further core modules with 5 ECTS belong to the subject area Mathematical Modelling, whereby here, in analogy to the previous course, either the “Advanced Mathematical Modelling” is the core module of the first master’s semester, if the “Introduction to Mathematical Modelling” was already part of the bachelor’s programme or in the other case both courses are recommended for the first or third semester.

These core modules are grouped around in-depth and research modules, which cover the following Topics

numerical fluid mechanics
flow and transport in porous media
multiscale modelling
solving large systems
application areas such as mathematical image processing or option pricing

At the same time, these thematic groups are strongly interrelated and also overlapping. In the following you will find the module planning for the next four semesters with the planned lecturers, or in the table: General course offering “Modelling and Simulation” then the basic planning with all modules in view.

The planning for the next four semesters should be implemented as far as possible as indicated. However, it can always happen that an exchange of lecturers has to take place at short notice or that a course in the in-depth and research module area has to be cancelled for capacity reasons. For the core modules it is guaranteed that they will take place in the form described here.

In the following you will find some explanations of the courses offered by the subject profile ” Modelling and Applied Analysis (MApA)” and “Numerical Analysis and Simulation (NASi)” for the Master’s programmes Computational and Applied Mathematics (CAM) and Mathematics.

The offer of the subject profile “Modelling and Simulation” is realised by the two chairs of Applied Mathematics I and Applied Mathematics III, whereby the courses are coordinated in such a way that a mixture of courses of both chairs is possible and reasonable.

In the winter semester 2017/18, the international master’s degree programme CAM was introduced, replacing the master’s degree programme in Industrial Mathematics, which expires with it. Therefore, all courses in the subject profile Modelling and Simulation for the Master’s programme are in English from this date on and replace the respective German courses. For the Master’s programme in Mathematics, the subject profile together with the subject profile ” Optimization (Opti)” is part of the subject area ” Modelling, Simulation and Optimization”.

Therefore, please inform yourself about the possible modules and the frequency of their offer, especially through the module manual of CAM. From now on there are 2 basic core modules, namely ” Modelling and Analysis in Continuum Mechanics I” (10 ECTS, compulsory for CAM), which replaces and extends the master course “Mathematical Modelling” and the lecture “Advanced Discretization Techniques” (10 ECTS), which replaces the lecture “Advanced Numerical Methods of Partial Differential Equations”.

A further prerequisite is the successful participation in the module “Introduction of Numerics of Partial Differential Equations”. If you have not yet included this course as a module in your Bachelor’s programme, there is the possibility to make up for this course, which was also offered in the winter semester, in your 1st Master’s semester and to include it in your Master’s programme according to the 10 ECTS regulations, which, however, postpones the lecture “Advanced Discretization Techniques” and its subsequent courses into the 3rd and following semester.

The two large lectures mentioned above open up the CAM course of studies and correspond to the lines ” Modelling and Applied Analysis” (MApA) and “Numerical Analysis and Simulation” (NASi) in the course of studies Mathematics with the subject profile Modelling and Simulation within the field of study Modelling, Simulation and Optimization. For these, corresponding in-depth courses are offered in the 2nd (or for lateral entrants, see above, 4th semester), which are all highly recommended (Module Handbook CAM, Module 2, Module 3, Module 9).

We also recommend the Department of Computer Science’s courses in “High Performance Computing”, which are integrated into CAM, which are available from the summer semester onwards. It is guaranteed that the previously mentioned course will be held once a year in the respective semester.

For studies from the 5th semester onwards, a variety of more specialised 5 ECTS modules are offered. Please inform yourself here in good time whether these courses will take place in the semester you have planned. Only in general can a sufficiently comprehensive range of courses be guaranteed to ensure that you are fit to study. These are in-depth and research modules, which are offered in the following subject areas

numerical fluid mechanics
flow and transport in porous media
multiscale modelling
stochastic evolution equations
application areas such as mathematical image processing or option pricing or life sciences

(Module handbook CAM Modules 11-20, 23-25 Due to personnel changes, Modules 21, 22 cannot be guaranteed in this way.)