MathMods :: Joint MSc

Semester 2 UHH Numerics (OLD)

Semester 2 UHH Numerics (OLD)

(to be discontinued - valid up to batch 2017)

Numerics  @  UHH  30 ECTS credits

The second semester will be focused on Numerics and will be spent at UHH - University of Hamburg in Germany from April to August.

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

Fluid dynamics [3 credits]

  • ECTS credits 3
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Rodolfo Repetto
  • Objectives

     

    Applications to the study of models in fluid dynamics.
  • Topics

     

    Introduction to fluid dynamics. Continuum approach. Statics and kinematics of fluids. Mass conservation and balance laws. Constitutive laws: ideal fluids, Newtonian viscous fluids. The Navier-Stokes equations. Ideal fluids: Bernoulli's theorem and Kelvin theorem. Viscous fluids: unidirectional flows, the vorticity
    
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Algorithms and data structures [6 credits]

  • ECTS credits 6
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Jörn BEHRENS
  • Objectives

     

    - Students get to know the most important classes of modern machine learning algorithms. - They are going to develop an understanding why certain algorithms work well and others don't. - They learn how to evaluate and compare the results of different learning algorithms. - They learn how to model machine learning problems and what are common pitfalls.
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Numerical approximation of PDEs by finite differences and finite volumes [6 credits]

  • ECTS credits 6
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Jens Struckmeier
  • 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]

  • ECTS credits 6
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Christian KAHLE
  • 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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Optimisation [6 credits]

  • ECTS credits 6
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Thomas BERGER
  • 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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German language and culture for foreigners (A1 level) [3 credits]

  • ECTS credits 3
  • University University of Hamburg
  • Semester 2
  • 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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Modelling camp (elective) [3 credits]

  • ECTS credits 3
  • University University of Hamburg
  • Semester 2
  • Lecturer 1 Ingenuin Gasser
  • Lecturer 2 Elisabetta Felaco
  • 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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