Advanced and Computational Mathematics

-Real-world Problem

-New Knowledge

Application Modelling

Computation

Optimization-Mathematical model

Nowadays the use of mathematics is indispensable for an efficient treatment of complex real-world problems coming from engineering, computer science, economics, finance etc. To list a few but rather influential and striking examples, we refer to household automatic control systems, Google ranking, portfolio optimization, weather forecasting or big data analysis. Here, the first step is to identify essential variables and model those links between them which crucially determine a real-world problem. This then allows to analyze the resulting mathematical model in a quantitative way. In particular, computation and optimization issues become important in order to obtain new cutting-edge knowledge about the problem and its solution. We arrive at a more thorough understanding and efficient treatments of the real-world application.

Basic courses

18ECTS

Optimization MethodsNonlinear Optimization

Algorithms for Convex Optimization

Algebraic and Geometric MethodsAlgeabraic and Differenial Geometry

Topology and Complex Geometry

Data ScienceMachine Learning, Big Data Analytics

Matrix Methods, Statistics

Stochastic ModelsStochastic Analysis

Stochastic Processes

18ECTS

sem. 1

and 2

Applications and Specialization

Optimization with PDEs, Optimization under Uncertainty, Randomized Algorithms andOnline Optimization, Combinatorial Optimization, Infinite-Dimensional Optimization

Inverse Problems, Regularization Theory and Practice, Fast solvers for PDEs, Model Reduction, Fourier Analysis, Introduction to Wavelets, Analysis and Numerics of

Integral Methods, Orthogonal Polynomials, Distributions and Differential Operators

Graph Theory, Singularity Theory, Game Theory, Mathematics of Big Data, AlgebraicGeometry, Convex and Toric Geometry, Low-dimensional geometry and topology

Time Series Analysis, Quantitative Finance, Asymptotic and Extreme Value Statistics,Mathematical Methods od Uncertainty Quantification, Methods of Algebraic Statistics

Minor inMechanical Engeneering, Electrical Engineering and Information Technology,

Computer Science, Economics and Business Administration

24ECTS

3 Research Seminars and/or Summer schools

Master Thesis

Ph.D. program

Seminars, additional lectures

Research for Ph. D. Thesis

18ECTS

12ECTS

sem.3

and 4

30ECTS

sem6 to 10

Master program

(Advanced Theoretical Mathematics, Computational Mathematics, Data Science)

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Basics for the Master program (Phase 1)There is no admission restriction for this degree program. However, there will be a review of the credits which were obtained in the previous study program (usually within a Bachelor program). Normal period of study: 4 semestersDegree: MasterStart of study: in winter or summer term

Basics for the Ph.D. program (Phase 2)Students with excellent results in their Master degree (externally or in Phase 1) qualify for the Ph.D. program.

Normal period of study: 6 semestersDegree: Ph.D.Start of study: in winter or summer term.

https://www.tu-chemnitz.de/mathematik/mscphd/index.phphttps://www.tu-chemnitz.de/mathematik/mscphd/content.php

All information around this program:

Apply using the form available athttps://www.tu-chemnitz.de/mathematik/mscphd/admission_form.pdfTogether with the form, please hand in the following documents: - curriculum vitae (with a description of your school career) - a list of all passed mathematical courses with a short description of contents - a list of all passed exams - two recommendation letters - Certified copy/translation into English or German of the bachelor's or Master's degree certificate, respectively

Please send your application with the complete documents to: Technische Universität Chemnitz Studentensekretariat Abteilung Zulassung ausländischer Studienbewerber 09107 Chemnitz GermanyIn order to process applications as quickly as possible, it would be helpful to send a copy of all of the documents mentioned above as a single pdf-file to int-mast-math@mathematik.tu-chemnitz.de

Application

Dr. Thomas Kalmesthomas.kalmes@mathematik.tu-chemnitz.dePhone: +49 371 531 34991

Academic advisor for the international Master and Ph.D. program

International Master- andPh. D. Program in MathematicsFaculty of Mathematics

Master- and Ph. D. Program

The integrated Master- and Ph.D. programat the Chemnitz University of Technologyleads after four semesters to the masters degree and after additional six semesters to the Ph. D.