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Search result: Catalogue data in Autumn Semester 2016

Mathematics Master Information
Core Courses
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Core Courses: Applied Mathematics and Further Appl.-Oriented Fields
401-3651-00LNumerical Methods for Elliptic and Parabolic Partial Differential Equations Information
Course audience at ETH: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students.
Other ETH-students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester.
W10 credits4V + 1UC. Schwab
AbstractThis course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods.
ObjectiveParticipants of the course should become familiar with
* concepts underlying the discretization of elliptic and parabolic boundary value problems
* analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems
* methods for the efficient solution of discrete boundary value problems
* implementational aspects of the finite element method
ContentA selection of the following topics will be covered:

* Elliptic boundary value problems
* Galerkin discretization of linear variational problems
* The primal finite element method
* Mixed finite element methods
* Discontinuous Galerkin Methods
* Boundary element methods
* Spectral methods
* Adaptive finite element schemes
* Singularly perturbed problems
* Sparse grids
* Galerkin discretization of elliptic eigenproblems
* Non-linear elliptic boundary value problems
* Discretization of parabolic initial boundary value problems
Lecture notesCourse slides will be made available to the audience.
Prerequisites / NoticePractical exercises based on MATLAB
401-3621-00LFundamentals of Mathematical StatisticsW10 credits4V + 1UF. Balabdaoui
AbstractThe course covers the basics of inferential statistics.
401-4889-00LMathematical FinanceW11 credits4V + 2UM. Schweizer
AbstractAdvanced introduction to mathematical finance:
- absence of arbitrage and martingale measures
- option pricing and hedging
- optimal investment problems
- additional topics
ObjectiveAdvanced level introduction to mathematical finance, presupposing knowledge in probability theory and stochastic processes
ContentThis is an advanced level introduction to mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this in both discrete- and continuous-time models. Topics include absence of arbitrage and martingale measures, option pricing and hedging, optimal investment problems, and probably others.
Prerequisites are probability theory and stochastic processes (for which lecture notes are available).
Lecture notesNone available
LiteratureDetails will be announced in the course.
Prerequisites / NoticePrerequisites are probability theory and stochastic processes (for which lecture notes are available).
401-3901-00LMathematical Optimization Information W11 credits4V + 2UR. Weismantel
AbstractMathematical treatment of diverse optimization techniques.
ObjectiveAdvanced optimization theory and algorithms.
Content1. Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming.

2. Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.

3. Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory.

4. Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings and, more generally, independence systems.
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