Master in Mathematics

- First year: Essential modern mathematical skills. Specialization via optional activities.

- Second year: Exclusively specialized courses matching the individual student’s professional project - 60 ECTS can be acquired within the following directions:

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Semester 1 (Winter 2021-2022)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Computational Science 2 [F1_BAINFOR-47] (optional)	Mathematics 1	28	28	4
Commutative Algebra [MAMATH-1] (optional)	Mathematics 1	30	30	8
Riemannian Geometry [MAMATH-124] (optional)	Mathematics 1	30	30	8
Partial Differential Equations I [MAMATH-3] (optional)	Mathematics 1	30	30	8
Algorithmic Number Theory [MAMATH-104] (optional)	Mathematics 1	30		4
Basics of Discrete Mathematics [MAMATH-6] (optional)	Mathematics 1	30		4
Probabilistic Models in Finance [MAMATH-9] (optional)	Mathematics 1	45		6
Student Project [MAMATH-109] (optional)	Mathematics 1	0		4
Numerical Analysis [MAMATH-82] (optional)	Mathematics 1		45	6
Probability (Stochastic Analysis) [MAMATH-23] (optional)	Mathematics 1	30	15	6
Discrete-time stochastic processes [MAMATH-4] (optional)	Mathematics 1	30	15	6
Mathematical Statistics [MA_DS-1] (optional)	Mathematics 1	60	30	5
Introduction to Graph Theory [MA_DS-8] (optional)	Mathematics 1	30		3

Semester 2 (Summer 2020-2021)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Probability (stochastic analysis) [MAMATH-23] (optional)	Module 2.1	45		5
Homological Algebra [MAMATH-50]	Module 2.1	45		5
Partial Differential Equations II [MAMATH-22]	Module 2.1	45		5
Graph theory [MAMATH-132] (optional)	Module 2.1	45		5
Student Seminar [MAMATH-32]	Module 2.2	60		4
Algebraic Number Theory [MAMATH-24] (optional)	Module 2.2	30		4
Introduction to Continuous Time Models in Mathematical Finance [MAMATH-26] (optional)	Module 2.2	30		4
Numerical Analysis [MAMATH-82] (optional)	Module 2.2	30		4
An introduction to mathematical statistics [MAMATH-123] (optional)	Module 2.2	30		4
Reading course "complements to Homological Algebra" [MAMATH-137] (optional)	Module 2.2	15		1
Reading course "complements to Partial Differential Equation II" [MAMATH-138] (optional)	Module 2.2	15		1
Reading course "complements to Graph Theory" [MAMATH-139] (optional)	Module 2.2	15		1
Reading course "complements to Probability (stochastic analysis) [MAMATH-140] (optional)	Module 2.2	15		1

Semester 3 (Winter 2021-2022)

option Financial Mathematics (2021-2022)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Stochastic Analysis on Manifolds [MAMATH-149] (optional)	Financial Mathematics 3	30		5
Advanced Stochastic Modelling [MAMATH-89] (optional)	Financial Mathematics 3	30		5
Advanced Discretization Methods [MAMATH-99] (optional)	Financial Mathematics 3	30		5
American options: Optimal Stopping Theory and numerical methods [MAMATH-75] (optional)	Financial Mathematics 3	30		5
Data Science [MAMATH-80] (optional)	Financial Mathematics 3	30		5
Advanced Econometrics [QTECOFIN-2] (optional)	Financial Mathematics 3	45	15	6
Continuous-Time Stochastic Calculus and Interest Rate Models [MAMATH-90] (optional)	Financial Mathematics 3	30		5
Numerical solution of partial differential equations and applications [MAMATH-81] (optional)	Financial Mathematics 3		30	5
Intelligent Systems - Problem Solving [MICS2-38] (optional)	Financial Mathematics 3	20	10	3
Gaussian processes and applications [MAMATH-93] (optional)	Financial Mathematics 3	30		5
Numerical Methods in Finance [MAMATH-39] (optional)	Financial Mathematics 3	30		5
Internship in a financial institution [MAMATH-115] (optional)	Financial Mathematics 3	1		5

option General Mathematics (Winter 2021-2022)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Arithmetic Geometry [MAMATH-147] (optional)	General Mathematics 3	45		6
Stochastic Analysis on Manifolds [MAMATH-149] (optional)	General Mathematics 3	30		5
Advanced Stochastic Modelling [MAMATH-89] (optional)	General Mathematics 3	30		5
Advanced Discretization Methods [MAMATH-99] (optional)	General Mathematics 3	30		5
Data Science [MAMATH-80] (optional)	General Mathematics 3	30		5
Numerical solution of partial differential equations and applications [MAMATH-81] (optional)	General Mathematics 3		30	5
Continuous-Time Stochastic Calculus and Interest Rate Models [MAMATH-90] (optional)	General Mathematics 3	30		5
Lie Algebras and Lie Groups [MAMATH-21] (optional)	General Mathematics 3	45		6
Combinatorial Geometry [MAMATH-120] (optional)	General Mathematics 3	30	15	6
Gaussian processes and applications [MAMATH-93] (optional)	General Mathematics 3	30		5

option Industrial Mathematics (Winter 2021-2022)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Arithmetic Geometry [MAMATH-147] (optional)	Industrial Mathematics 3	45		6
Selected Topics in Industrial Mathematics 1 [MAMATH-148] (optional)	Industrial Mathematics 3	30		4
Advanced Stochastic Modelling [MAMATH-89] (optional)	Industrial Mathematics 3	30		5
Advanced Discretization Methods [MAMATH-99] (optional)	Industrial Mathematics 3	30		5
American options: Optimal Stopping Theory and numerical methods [MAMATH-75] (optional)	Industrial Mathematics 3	30		5
Data Science [MAMATH-80] (optional)	Industrial Mathematics 3	30		5
Numerical solution of partial differential equations and applications [MAMATH-81] (optional)	Industrial Mathematics 3		30	5
Continuous-Time Stochastic Calculus and Interest Rate Models [MAMATH-90] (optional)	Industrial Mathematics 3	30		5
Intelligent Systems - Problem Solving [MICS2-38] (optional)	Industrial Mathematics 3	20	10	3
Lie Algebras and Lie Groups [MAMATH-21] (optional)	Industrial Mathematics 3	45		6
Combinatorial Geometry [MAMATH-120] (optional)	Industrial Mathematics 3	30	15	6
Gaussian processes and applications [MAMATH-93] (optional)	Industrial Mathematics 3	30		5
Numerical Methods in Finance [MAMATH-39] (optional)	Industrial Mathematics 3	30		5

Semester 4 (Summer 2020-2021)

option Financial Mathematics (2020-2021)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Internship in a financial institution [MAMATH-114]	Module 4.1	1		5
Stochastic calculus of variations in finance & statistics [MAMATH-108]	Module 4.1	30		5
SDE and PDE (Solving PDE by Running a Brownian Motion) [MAMATH-42]	Module 4.1	30		5
Master Thesis [MAMATH-7]	Module 4.2	1		20

option General Mathematics (Summer 2020-2021)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Complex geometry [MAMATH-136]	Module 4.1	30		5
K3 Surfaces [MAMATH-135]	Module 4.1	30		5
SDE and PDE (Solving PDE by Running a Brownian Motion) [MAMATH-42] (optional)	Module 4.1	30		5
Master Thesis [MAMATH-30]	Module 4.2			20

option Industrial Mathematics (Summer 2020-2021)

		Lecture (hours)	Exercise (hours)	ECTS
TOTAL (mandatory / optional)		0 / 0	0 / 0	0 / 0
Internship in Industry including a Master Thesis [MAMATH-117] (optional)	Internship in Industry including a Master Thesis			30
Reading course I: Statistics [MAMATH-118] (optional)	Reading course I: Statistics	30		1
Reading course II: Probability theory [MAMATH-119] (optional)	Reading course II: Probability theory	30		5