MathMods :: Joint MSc

Sem3 UHH Complex Sys.

Sem3 UHH Complex Sys.

Applications @ UHH 30 ECTS credits

Modelling and simulation of complex systems

The semester in Hamburg focuses on fundamental principles of contemporary computational mathematics. Concrete model scenarios arising from academic and industrial applications are used as case studies.

The portfolio of the offered courses ranges from theoretical fundamentals of mathematical modelling and numerical simulation to concrete applications in computational science and engineering.

 

Below you can find information about the subjects for this semester.

 

  • Optimisation of complex systems governed by ODEs and PDEs [6 credits]

    Optimisation of complex systems governed by ODEs and PDEs

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Lecturer 1 Michael HINZE
    • Objectives

       

      Optimization techniques in function space
      Applications to elliptic partial differential equations
      Optimal control with partial differential equations
    • Topics

       

      Existence of minimizers in function space
      Optimality conditions for the unconstrained case
      Elliptic PDEs as energy minimization problem
      Convex analysis and optimality conditions in the constrained case
      Optimal control problems with PDEs

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  • Advanced topics in fluid dynamics [6 credits]

    Advanced topics in fluid dynamics

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Lecturer 1 J. Struckmeier
    • Objectives

       

      The module concerns advanced topics in fluid dynamics with a focus on applications in gasdynamics and semiconductor modelling.
    • Topics

       

      Gasdynamics: Boltzmann equation, Macroscopic limits, Euler equations of gasdynamics, Navier Stokes equations, Incompressible equations, Acoustics, Shallow water equations, Boussinesq approximation. Charged fluids: Semiconductors and plasmas, Hydrodynamic models, Energy transport models, Drift diffusion models, Quantum mechanical models. 

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  • Computer tomography [6 credits]

    Computer tomography

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Lecturer 1 Armin ISKE
    • Objectives

       

      This course gives an introduction to mathematical methods of medical imaging, where particular focus is placed on computer(ized) tomography (CT). But also algebraic reconstruction techniques (ART) will be discussed. If time allows, a short overview over m...
    • Topics

       

      X-rays; the Radon transform; the back projection; the central slice theorem; the filtered back projection formula; discrete image reconstruction; algebraic reconstruction techniques; magnetic resonance imaging.

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  • Traffic flow models [6 credits]

    Traffic flow models

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Lecturer 1 Ingenuin GASSER
    • Objectives

       

      The module introduces basic modelling concepts and the related mathematical methods for the description of vehicular traffic flow.
    • Topics

       

      Vehicular traffic flow phenomena, Modelling approaches, Cellular automata. Microscopic models: models based on ODE's. Macroscopic models: models based on PDE’s.

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  • Advanced Machine Learning [6 credits]

    Advanced Machine Learning

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Topics

       

      1. Basics: analogy; layout of neural nets, universal approximation, NP-completeness
      2. Feedforward nets: backpropagation, variants of Stochastistic Gradients
      3. Deep Learning: problems and solution strategies
      4. Deep Belief Networks: energy based models, Contrastive Divergence
      5. CNN: idea, layout, FFT and Winograds algorithms, implementation details
      6. RNN: idea, dynamical systems, training, LSTM
      7. ResNN: idea, relation to neural ODEs
      8. Standard libraries: Tensorflow, Keras, PyTorch
      9. Recent trends
    • Prerequisites

       

      1. Skript
      2. Online-Werke:

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  • Medical Imaging [6 credits]

    Medical Imaging

    • ECTS credits 6
    • Semester 3
    • University University of Hamburg
    • Topics

       

      • Overview about different imaging methods
      • Signal processing
      • Inverse problems
      • Computed tomography
      • Magnetic resonance imaging
      • Compressed Sensing
      • Magnetic particle imaging
    • Books

       

      1. Introduction to the Mathematics of Medical Imaging; C. L.Epstein; Siam, Philadelphia, 2008

      2. Medical Image Processing, Reconstruction and Restoration; J. Jan; Taylor and Francis, Boca Raton, 2006

      3. Principles of Magnetic Resonance Imaging; Z.-P. Liang and P. C. Lauterbur; IEEE Press, New York, 1999

      4. Bildgebende Verfahren in der Medizin; O. Dössel; Springer, Berlin, 2000

      5. Bildgebende Systeme für die medizinische Diagnostik; H. Morneburg (Hrsg.); Publicis MCD, München, 1995

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