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Department of Mathematics

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Studying Mathematics at Karlsruhe

Master program in English

Study plan

Study plan

The official descriptions of the program (in German) can be found in study plan and study regulations. Unofficial translation of these documents in English are study plan and study regulations.

Here we summarise the essential information informally.

Program: The program of study Master of Mathematics is a continuation of the "Bachelor of Mathematics" program. The main goals are to gain knowledge in mathematical methods and results, to gain the ability for discovering and analyzing structures, to learn about new subjects independently, to deepen knowledge in subjects of own choice, to get to the front of current research in a chosen area of mathematics, and to learn about practical techniques for solving complex problems. Successful completion of the program results in the degree Master of Science (in short, M.Sc.).

Registration: Typically there is no need to register for classes, but students must register for the exams later on. For lectures: Show up for the first lecture of a class you are interested in and you will get specific information on how it is run. Most classes now are supported by the ILIAS platform, it contains class information, forum, assignment submission site etc. A few days before the lectures start, look at the open ILIAS pages for courses you are interested in and sign up. For seminars: Show up at the end of the previous semester for the preliminary meeting, and register for the seminar in Campus-System when you succeed in finishing your presentation/participation. If you would like to take a seminar during your first semester, please contact the respective instructors directly.

Examination: There are two forms of examination for the lectures: written examination or oral examination. The examination format is typically determined at the beginning of the course. To earn credit points for a seminar, students are typically required to give a presentation and actively participate in the seminar.

Required credit points

Altogether 120 CPs (Credit Points) are required for the masters degree -- roughly equally distributed over four semesters. Credit points can be earned by successfully attending lectures (possibly with tutorials), seminars, and writing a Master Thesis. 70 CPs are required for the admission to the master’s thesis module.

Description of different types of Pedagogical Activities

Types of Pedagogical Activities		Offers
Mathematical Lectures		Lectures in subjects such as Algebra and Geometry (Ag), Analysis (An), Applied and Numerical Mathematics (Nu), and Stochastics (St)
Mathematical Seminars		Seminars (Sem)
Non-Mathematical Lectures		Lectures in subjects such as Computer Science (CS), Physics (PH), Economics (EC), Mechanical Engineering (ME), and Electrical Engineering (EE)
Key Qualifications		Activities associated to corresponding Key Qualifications (KeyQua)

Activities corresponding to Key qualifications (KeyQua) can be for example language courses offered by the Sprachenzentrum, House of Competence, or ZAK Zentrum für Angewandte Kulturwissenschaft und Studium Generale.
We recommend for students to do voluntary practical work in a company for example. It corresponds to 8 credit points, which can be given provided there is a report and a presentation of the practical work. These credits are counted as "additional qualifications", they could not be counted towards 120 credit points for the degree, but they may be listed in the final certificate.

Description of Master Study Programme in Mathematics

Main Subject 1 (Fach 1- $F_1$ , 24+ CP)		Main Subject 2 (Fach 2- $F_2$ , 16+ CP)
Supplementary Subject (Fach 3- $F_3$ , 16 - 24 CP)		Specialization Subject (Fach 5- $F_5$ , 14 - 22 CP)
Mathematical Seminar (Fach 4- $F_4$ , 6 CP)		Key Qualifications (Fach 6- $F_6$ , 6+ CP)
Master's thesis (30 CP)

A student should choose two main subjects (Fach 1, Fach 2), one of which must be Ag or An. In the first main subject at least 24 credit points must be obtained, in the second main subject at least 16 credit points must be obtained. Between 16 and 24 credit points should be acquired by taking courses in a supplementary subject (Fach 3) that is one of Ag, An, Nu, and St which are not the main subjects, or from CS, PH, EC, ME, EE. Between 14 and 22 credit points must be acquired by taking any courses from specialization subject (Fach 5) from Ag, An, Nu, and St. In total, specialization points and supplementary points should add up to at least 38. There must be two seminars (Fach 4) from Ag, An, Nu, or St taken, each worth 3 credit points. Another, third seminar could be counted towards specialization subject. Moreover, 6 credit points for key qualifications (Fach 6) have to be obtained.

Requirements for the Choice of Subjects - A mathematical Description
To describe the degree requirements more formally, let $Ag, An, Nu, St,$ $CS, PH, EC, ME, EE$ , $Sem$ and $KeyQua$ denote the set of master courses in (respective) subjects. Let $S_1$ and $S_2$ be two selected main subjects, i.e.,

$\{S_1, S_2\}\subseteq \{Ag, An, Nu, St\}$ ,
$\{S_1, S_2\}\cap \{Ag, An\}\neq \emptyset$ ,
$S_1\neq S_2.$

Let $F_1, F_2,\ldots, F_6$ be the sets of courses and seminars taken towards Master Degree (corresponding to Fach 1-6), such that

$F_1 \subseteq S_1$ , $F_2 \subseteq S_2$ ,

$F_3 \subseteq F \in \{Ag, An, Nu, St, CS, PH, EC, ME, EE\}$ - $\{S_1, S_2\},$

$F_5\subseteq \{Ag \cup An \cup Nu \cup St \cup Sem\}$ ,

$F_4 \subseteq Sem$ ,

$F_6\subseteq KeyQua$ .

Let $|F_i|$ denote the total number of credit points in $F_i, ~ i=1,\ldots,6$ . The following requirements must be satisfied:

$|F_1|+|F_2|+|F_3|+|F_4|+|F_5|+|F_6| \geq 90$ ,

$|F_1|\geq 24, ~|F_2|\geq 16,$

$22\geq |F_5| \geq 14,$

$24\geq |F_3|\geq 16,$

$|F_3|+|F_5|\geq 38,$

$|F_4|= 6,$

$|F_6|\geq 6,$

$|F_5\cap Sem|\leq 3,$

30 credit points should be obtained by writing a Master Thesis. 70 credit points are required for the admission of the master thesis module.

In addition, it is sometimes possible to obtain credit points towards $F_3$ by taking seminars in non-mathematics subjects. Credit points for graded seminars sometimes could be counted toward the credit points for the courses. Choosing courses in a non-mathematics subject and special seminars should be discussed with an advisor and sometimes must be approved by the examination board.

Exemplary Courses of Studies

In the following examples, modules from the four mathematical areas are chosen for the supplementary subject. As credits in the range from 16 to 24 are to be acquired in the complementary subject, selection is quite easy.

The module handbooks, which include the complete list and detailed descriptions (e.g. credit points) of courses in mathematics and in other complementary fields, can be found here.

Example 1 (Start in the summer semester)

Semester 1: 30 credits, 4 examinations, 2 courseworks

• Subject 1 (Analysis, analysis): Spektraltheorie (spectral theory) 8 credits
• Subject 2 (Stochastik, stochastics): Zeitreihenanalyse (time series analysis) 4 credits, Generalisierte Regressionsmodelle (generalized regression models) 4 credits
• Subject 3 (Algebra und Geometrie, algebra and geometry): Geometrische Gruppentheorie (geometrical group theory) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 2: 32 credits, 4 examinations

• Subject 1 (Analysis, analysis): Funktionalanalysis (functional analysis) 8 credits, Klassische Methoden für Partielle Differentialgleichungen (classical methods for partial differential equations) 8 credits
• Subject 2 (Stochastik, stochastics): Mathematische Statistik (mathematical statistics) 8 credits
• Subject 3 (Algebra und Geometrie, algebra and geometry): Geometrische Gruppentheorie 2 (geometrical group theory 2) 8 credits or Algebraische Topologie (algebraic topology) 8 credits

Semester 3: 28 credits, 3 examinations, 2 courseworks

• Subject 5 Mathematische Vertiefung (mathematical specialization): Finanzmathematik in stetiger Zeit (financial mathematics in continuous time), Einführung in das Wissenschaftliche Rechnen (introduction to scientific computing) or Spezielle Themen der Numerischen Linearen Algebra (special topics of numerical linear algebra) with 8 credits each, special lecture with 6 credits, such as Perkolation (percolation) or Der Poissonprozess (Poisson’s process) or Numerische Verfahren für Maxwellgleichungen (numerical methods for Maxwell equations) or Geometrische Numerische Integration (geometrical numerical integration) or Steuerungstheorie (control theory)
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits

Semester 4: 30 credits

• Master’s thesis

Example 2 (Start in the summer semester)

Semester 1: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Stochastik, stochastics): Finanzmathematik in stetiger Zeit (financial mathematics in continuous time) 8 credits, Statistical Learning 8 credits
• Subject 2 (Algebra und Geometrie, algebra and geometry): Geometrische Gruppentheorie (geometrical group theory) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 2: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Stochastik, stochastics): Räumliche Stochastik (spatial stochastics) 8 credits
• Subject 2 (Algebra und Geometrie, algebra and geometry): Algebraische Topologie (algebraic topology) 8 credits
• Subject 3 (Angewandte und Numerische Mathematik, applied and numerical mathematics): Numerische Methoden für Differentialgleichungen (numerical methods for differential equations) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 3: 30 credits, 4 examinations

• Subject 3 (Angewandte und Numerische Mathematik, applied and numerical mathematics): Einführung in das Wissenschaftliche Rechnen (introduction to scientific computing) 8 credits
• Subject 5 Mathematische Vertiefung (mathematical specialization): Stochastische Geometrie (stochastic geometry) 8 credits, Algebraische Topologie 2 (algebraic topology 2) 8 credits, special lecture 6 credits (or two seminars or one seminar and a special lecture of 3 credits)

Semester 4: 30 credits

• Master’s thesis

Example 3 (Start in the winter semester)

Semester 1: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Algebra und Geometrie, algebra and geometry): Algebra (algebra) 8 credits, another module (Algebra und Geometrie, algebra and geometry) 8 credits
• Subject 2 (Analysis, analysis): Funktionalanalysis (functional analysis) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 2: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Algebra und Geometrie, algebra and geometry): Geometrische Gruppentheorie (geometrical group theory) 8 credits
• Subject 2 (Analysis, analysis): Rand- und Eigenwertprobleme (boundary value and eigenvalue problems) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 5 Mathematische Vertiefung (mathematical specialization): Geometrie der Schemata (geometry of schemes) 8 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 3: 30 credits, 4 examinations

• Subject 5 Mathematische Vertiefung (mathematical specialization): Geometrische Gruppentheorie 2 (geometrical group theory 2) 8 credits
• Subject 3 (Stochastik, stochastics): Mathematische Statistik (mathematical statistics) 8 credits, Räumliche Stochastik (spatial stochastics) 8 credits, Der Poissonprozess (Poisson’s process) 6 credits (or another course of 6 credits)

Semester 4: 30 credits

• Master’s thesis

Example 4 (Start in the winter semester)

Semester 1: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Analysis, analysis): Funktionalanalysis (functional analysis) 8 credits
• Subject 2 (Stochastik, stochastics): Räumliche Stochastik (spatial stochastics) 8 credits or Finanzmathematik in diskreter Zeit (financial mathematics in discrete time) 8 credits
• Subject 3 (Angewandte und Numerische Mathematik, applied and numerical mathematics): Numerische Methoden für Differentialgleichungen (numerical methods for differential equations) 8 credits
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 2: 30 credits, 3 examinations, 2 courseworks

• Subject 1 (Analysis, analysis): Spektraltheorie (spectral theory) 8 credits
• Subject 2 (Stochastik, stochastics): Stochastische Geometrie (stochastic geometry) 8 credits or Finanzmathematik in stetiger Zeit (financial mathematics in continuous time) 8 credits
• Subject 3 (Angewandte und Numerische Mathematik, applied and numerical mathematics): Einführung in das Wissenschaftliche Rechnen (introduction to scientific computing) or Spezielle Themen der Numerischen Linearen Algebra (special topics of numerical linear algebra) 8 credits each
• Subject 4 Mathematisches Seminar (mathematical seminar) 3 credits
• Subject 6 Überfachliche Qualifikation (transferable skill) 3 credits

Semester 3: 30 credits, 4 examinations or 3 examinations + 2 courseworks

• Subject 1 (Analysis, analysis): Klassische Methoden für Partielle Differentialgleichungen (classical methods for partial differential equations) 8 credits
• Subject 3 (Angewandte und Numerische Mathematik, applied and numerical mathematics): Finite Elemente Methoden (finite element methods) 8 credits
• Subject 5 Mathematische Vertiefung (mathematical specialization): module from Algebra und Geometrie (algebra and geometry) with 8 credits or Mathematische Statistik (mathematical statistics) 8 credits
• Subject 5 Mathematische Vertiefung (mathematical specialization): special lecture with 6 credits or two seminars with a total of 6 credits

Semester 4: 30 credits

• Master’s thesis