MathMods :: Joint MSc

Semester2 Numerics

Numerics  @  TUW   OR TUHH   OR UHH  30 ECTS credits

The second semester will focus on Numerics and will be spent from March to August in one of the following universities:

  1. Vienna University of Technology (TUW)
  2. Hamburg University of Technology (TUHH) OR University of Hamburg (UHH)

Semester 2 is designed with the goal of providing the student with advanced skills in both the design of fast and efficient numerical schemes and their implementation. Both skills are essential in the formation of the modern applied mathematician, and are nowadays considered essential in the implementation of mathematical models arising in modern applications of mathematics such as social sciences, urban sciences, economics.
Both optional branches (Vienna and Hamburg) will offer courses centered on numerical methods for ordinary and partial differential equations as main subject. Optional units covering modern scientific computing, optimization, statistics, computer science, and industrial applications will complete this semester.

The Consortium will address each student to either Vienna or Hamburg depending on the student's background and will provide assistance in the choice of the optional courses in such a way to design the best study plan to approach the chosen Year 2 option.

 

Below you can find more information about the two branches.

when  WHEN

what  WHAT

where  WHERE

Semester 2 Numerics  
     •  Numerics - TUW TUW, Austria
     •  Numerics - (T)UHH TUHH or UHH, Germany

 
  

Semester 2: Numerics @ TUW, Vienna

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TUW smallSemester 2: Numerics @ TUW, Vienna University of Technology

The second semester at TUW provides a stronger background on advanced methods for the implementation of numerical codes (computer programming). Moreover, the student will have the opportunity to acquire basic skills in parallel computing and high performance computing. This semester will also include optional units in Numerical Optimization and Statistics.

 

  • Computer programming [5 credits]

    Computer programming

    • ECTS credits 5
    • Semester 2
    • University Vienna University of Technology
    • Topics

       

      Introduction to Computer Programming: introductory knowledge of Matlab and C++ as needed for the parallel numerical methods courses.
      MATLAB syntax (command- and object-oriented), graphical representations, toolboxes, selected problems from engineering and statistics.


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  • Numerics of differential equations [15 credits]

    Numerics of differential equations

    • ECTS credits 15
    • Semester 2
    • University Vienna University of Technology
    • Topics

       

      1. Numerics of differential equations: Knowledge of standard numerical methods for the approximation of solutions of ordinary and partial differential equations (discretization methods).
      2. Numerical methods for PDEs: Knowledge of numerical standard models for partial differential equations. Finite element methods. Discontinuous Galerkin methods. Instationary PDEs.

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  • German language and culture for foreigners (level A1) [4 credits]

    German language and culture for foreigners (level A1)

    • ECTS credits 4
    • Semester 2
    • University Vienna University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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  • Introduction to parallel computing [6 credits]

    Introduction to parallel computing

    • ECTS credits 6
    • Semester 2
    • University Vienna University of Technology
    • Topics

       

      Basic of parallel computing, parallel architectures, programming models, languages and interfaces, performance analysis and modeling, pitfalls, basic programming skills


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  • Numerical optimization [6 credits]

    Numerical optimization

    • ECTS credits 6
    • Semester 2
    • University Vienna University of Technology
    • Topics

       

      Unconstrained optimisation: gradient methods, classical Newton method, quasi-Newton method. Constrained optimisation: trust region methods, linear programming, (sequential) quadratic programming


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  • Stationary processes and time series analysis [6 credits]

    Stationary processes and time series analysis

    • ECTS credits 6
    • Semester 2
    • University Vienna University of Technology
    • Topics

       

      Stationary processes, autocovariance function, spectral representati- on, linear filters, transfer function, AR/ARMA processes, forecasting, Wold representation, estimation


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Semester 2: Numerics @ (T)UHH, Hamburg

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T UHH logoSemester 2: Numerics @ (T)UHH, Hamburg

The second semester in Hamburg is characterized by a stronger "engineering oriented" perspective, in that it provides optional units at the interface of Computer Science and case studies of industrial applications of mathematics. The Hamburg semester will be spent at TUHH in case the programme is funded by the Erasmus Mundus scheme, at UHH otherwise. In any case, the two universities at Hamburg will work in synergy with each other for the delivery of the semester 2 courses.

Semester 2 @ TUHH

TUHH logo smallSemester 2 @ TUHH, Hamburg University of Technology

To be activated in case the programme is funded by the Erasmus Mundus scheme

 

  • Numerical approximation of PDEs by finite differences and finite volumes [6 credits]

    Numerical approximation of PDEs by finite differences and finite volumes

    • ECTS credits 6
    • Semester 1
    • University University of Hamburg
    • Objectives

       

      The overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for non-linear systems of conservation laws, particularly for problems involving shock waves.

    • Topics

       

      Numerical methods for linear equations. Computing discontinuous solutions. Conservative methods for non-linear problems. Godunov's methods. Approximate Riemann solvers. Nonlinear stability. High resolution methods. Semi-discrete methods.


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  • Numerics of ODEs [6 credits]

    Numerics of ODEs

    • ECTS credits 6
    • Semester 2
    • University Hamburg University of Technology
    • Topics

       

      TBD

    • Prerequisites

       

      TBD


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  • German language and culture for foreigners (level A1) [4 credits]

    German language and culture for foreigners (level A1)

    • ECTS credits 4
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      - To understand sentences and frequently used expressions related to familiar everyday expressions, university life and its requirements.
      - To describe your place of residence and the city of Hamburg
      - To complete simple forms
      - To impart basic grammar structures and vocabulary
      - To enable to read and understand.

    • Topics

       

      - To introduce sb to sb + talking about yourself; alphabet, spelling, so called "w-questions", numbers (1-1 Mio), time, days of the week, pronunciation

      - Simple role plays

      - Grammar: word order, construction of German sentences , affirmative sentence, questions, regular verbs → present tense, auxiliary verbs "haben" and "sein", pronouns (Nominativ ), negative answer to a question "nicht" and "kein"

       


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  • Approximation and stability [6 credits]

    Approximation and stability

    • ECTS credits 6
    • Semester 2
    • University Hamburg University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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  • Optimisation [6 credits]

    Optimisation

    • ECTS credits 6
    • Semester 2
    • University Hamburg University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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  • Random graphs and randomized algorithms [6 credits]

    Random graphs and randomized algorithms

    • ECTS credits 6
    • Semester 2
    • University Hamburg University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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  • Intercultural communication [2 credits]

    Intercultural communication

    • ECTS credits 2
    • Semester 2
    • University Hamburg University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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  • Creative processes in technology [2 credits]

    Creative processes in technology

    • ECTS credits 2
    • Semester 2
    • University Hamburg University of Technology
    • Objectives

       

      TBD

    • Topics

       

      TBD


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Semester 2 @ UHH

uhh smallSemester 2 @ UHH, University of Hamburg

To be activated in case the programme is NOT funded by the Erasmus Mundus scheme

 

  • Numerical approximation of PDEs by finite differences and finite volumes [6 credits]

    Numerical approximation of PDEs by finite differences and finite volumes

    • ECTS credits 6
    • Semester 1
    • University University of Hamburg
    • Objectives

       

      The overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for non-linear systems of conservation laws, particularly for problems involving shock waves.

    • Topics

       

      Numerical methods for linear equations. Computing discontinuous solutions. Conservative methods for non-linear problems. Godunov's methods. Approximate Riemann solvers. Nonlinear stability. High resolution methods. Semi-discrete methods.


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  • Numerical methods for PDEs - Galerkin Methods [6 credits]

    Numerical methods for PDEs - Galerkin Methods

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      In this course the basic principles of the FE element method applied to the numerical treatment of elliptic PDEs are considered. Successful applicants will be able to use the FE method as analytic and numerical tool for the mathematical investigation of l

    • Topics

       

      Topics include construction of FE spaces, derivation and numerical solution of the resulting linear algebra systems, error analysis in Sobolev spaces including interpolation estimates, basic principles of residual based a posteriori error analysis.


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  • Advanced Optimisation [6 credits]

    Advanced Optimisation

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      The objective of this lecture is first, to familiarize the participants with concepts for nonsmooth convex optimization in theory as well as in computation. Second, to give an understanding of the differences and similarities between smooth and nonsmooth

    • Topics

       

      Fundamentals of convex analysis; subdifferential and epsilon-subdifferential; cutting palane algorithms; bundle methods; regularization.


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  • Scientific computing [6 credits]

    Scientific computing

    • ECTS credits 6
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      ...

    • Topics

       

      ...


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  • Modelling camp [2 credits]

    Modelling camp

    • ECTS credits 2
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      In this seminar we face the students with real world problems. We discuss the interface between the real world  industrial problems and applied mathematics.

    • Topics

       

      A series of 22 small real world industrial problems where mathematics has been applied successfully.


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  • German language and culture for foreigners (level A1) [4 credits]

    German language and culture for foreigners (level A1)

    • ECTS credits 4
    • Semester 2
    • University University of Hamburg
    • Objectives

       

      - To understand sentences and frequently used expressions related to familiar everyday expressions, university life and its requirements.
      - To describe your place of residence and the city of Hamburg
      - To complete simple forms
      - To impart basic grammar structures and vocabulary
      - To enable to read and understand.

    • Topics

       

      - To introduce sb to sb + talking about yourself; alphabet, spelling, so called "w-questions", numbers (1-1 Mio), time, days of the week, pronunciation

      - Simple role plays

      - Grammar: word order, construction of German sentences , affirmative sentence, questions, regular verbs → present tense, auxiliary verbs "haben" and "sein", pronouns (Nominativ ), negative answer to a question "nicht" and "kein"

       


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Connect with us

Our partners' addresses

University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

Vienna Univ. of Technology, Austria (TUW)

Technische Universität Wien
Institute of Analysis & Scientific Computing
Wiedner Hauptstr. 8, 1040 Vienna - Austria

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