# MathMods :: Joint MSc ## Sem2 Numerics TUW

Numerics  @  TUW  30 ECTS credits

The second semester at TUW (Vienna University of Technology) 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
• Objectives

This course aims at providing the students with a minimal knowledge of Matlab and C++ needed to tackle the numerical methods courses of this semester. It will be concentrated in the first weeks.

• 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
• Objectives

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

• Topics

Initial- and boundary value problems for ordinary and partial differential equations: One-step and multi-step methods, adaptivity. Introduction to numerical methods for partial differential equations of elliptic, parabolic, and hyperbolic type. Variational formulation of PDEs and function spaces. Finite element convergence theory. Discontinuous Galerkin methods for convection dominated problems. Mixed methods and applications in fluid mechanics. Nonlinear equations and applications in solid mechanics. Vectorial function spaces and applications in electromagnetics. Instationary PDEs and time-stepping methods. Analysis of iterative solvers and preconditioners. A posteriori error estimates and adaptivity. Exercises: Apply these methods to solve pde problems; exercises with NGSolve-Python; verify qualitative and quantitative properties.

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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
• Objectives

Motivation, goals of parallel computing. Parallel architectures, programming models, performance measurement and analysis. Problems in parallel algorithms. Introduction to MPI (Message-Passing interface), hreads and OpenMP. Task-parallel models and interfaces (Cilk). Other languages for multi-core processors.

• Topics

Basic understanding of motivation and goals of parallel computing, basic knowledge of parallel architectures, programming models, languages and interfaces (concrete examples OpenMP, Cilk, MPI), performance analysis and modeling, pitfalls, basic programming skills in the discussed parallel interfaces (C or C++ with MPI and OpenMP; pthreads and Cilk or related).

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• ## Numerical optimization [6 credits]

Numerical optimization

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

Learn the basic concepts and methods of unconstrained and constrained optimization.

• Topics

Unconstrained optimisation: gradient methods, classical Newton method, quasi-Newton method (e.g. BFGS method). Constrained optimisation: trust region methods, linear programming (simplex method, interior point method), quadratic programming (inner point method, active sets method), 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
• Objectives

Introduction to the theory of stationary processe and time series analysis.

• Topics

Stationary processes, basics, autocovariance function, spectral representation, spectrum, linear filters, transfer function, AR/ARMA processes, forecasting, estimation.

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### Our partners' addresses

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#### University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 â€“ 67100 Lâ€™Aquila (Italy)
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#### University of Hamburg , Germany (UHH)

Department of Mathematics
Bundesstr. 55
20146 Hamburg - Germany
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