# Search result: Catalogue data in Autumn Semester 2016

Computational Science and Engineering Master | ||||||

Core Courses Two core courses out of three must be attended and examinations must be taken in both. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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252-0543-01L | Computer Graphics | W | 6 credits | 3V + 2U | M. Gross, J. Novak | |

Abstract | This course covers some of the fundamental concepts of computer graphics, namely 3D object representations and generation of photorealistic images from digital representations of 3D scenes. | |||||

Objective | At the end of the course the students will be able to build a rendering system. The students will study the basic principles of rendering and image synthesis. In addition, the course is intended to stimulate the students' curiosity to explore the field of computer graphics in subsequent courses or on their own. | |||||

Content | This course covers fundamental concepts of modern computer graphics. Students will learn about 3D object representations and the details of how to generate photorealistic images from digital representations of 3D scenes. Starting with an introduction to 3D shape modeling and representation, texture mapping and ray-tracing, we will move on to acceleration structures, the physics of light transport, appearance modeling and global illumination principles and algorithms. We will end with an overview of modern image-based image synthesis techniques, covering topics such as lightfields and depth-image based rendering. | |||||

Lecture notes | no | |||||

Prerequisites / Notice | Prerequisites: Fundamentals of calculus and linear algebra, basic concepts of algorithms and data structures, programming skills in C++, Visual Computing course recommended. The programming assignments will be in C++. This will not be taught in the class. | |||||

Fields of Specialization | ||||||

Astrophysics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-7851-00L | Theoretical Astrophysics (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: AST512 Mind the enrolment deadlines at UZH: http://www.uzh.ch/studies/application/mobilitaet_en.html | W | 10 credits | 4V + 2U | R. Teyssier | |

Abstract | Radiative processes in the interstellar medium; stellar structure and evolution; supernovae; white dwarfs; neutron stars; black holes; planet formation | |||||

Objective | ||||||

Literature | (1) "Formation of stars" (S. Stahler and F. Palla - Wiley editions, this is the book on which about half of the classes will be based and photocopies will be organized during first lecture) (2) "Radiative processes in astrophysics" (R. Ribycki and A. Lightman) (3) "The Physics of Stars" (A.C. Philllips) (4) "Black Holes, White Dwarfs and Neutron Stars: The physics of compact objects" (S. Shapiro and S.A. Teukolski). Additionally PowerPoint slides will be prepared by the lecturer on these and extra topics (e.g. planet formation). | |||||

Prerequisites / Notice | Prerequisites: Elementary atomic physics, thermodynamics, mechanics, fluid dynamics. Introduction to astrophysics (preferred but not obligatory). | |||||

401-7855-00L | Computational Astrophysics (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: AST245 Mind the enrolment deadlines at UZH: http://www.uzh.ch/studies/application/mobilitaet_en.html | W | 6 credits | 2V | L. M. Mayer | |

Abstract | Acquire knowledge of main methodologies for computer-based models of astrophysical systems,the physical equations behind them, and train such knowledge with simple examples of computer programmes | |||||

Objective | Acquire knowledge of main methodologies for computer-based models of astrophysical systems,the physical equations behind them, and train such knowledge with simple examples of computer programmes | |||||

Content | 1. Integration of ODE, Hamiltonians and Symplectic integration techniques, time adaptivity, time reversibility 2. Large-N gravity calculation, collisionless N-body systems and their simulation 3. Fast Fourier Transform and spectral methods in general 4. Eulerian Hydrodynamics: Upwinding, Riemann solvers, Limiters 5. Lagrangian Hydrodynamics: The SPH method 6. Resolution and instabilities in Hydrodynamics 7. Initial Conditions: Cosmological Simulations and Astrophysical Disks 8. Physical Approximations and Methods for Radiative Transfer in Astrophysics | |||||

Literature | Galactic Dynamics (Binney & Tremaine, Princeton University Press), Computer Simulation using Particles (Hockney & Eastwood CRC press), Targeted journal reviews on computational methods for astrophysical fluids (SPH, AMR, moving mesh) | |||||

Prerequisites / Notice | Some knowledge of UNIX, scripting languages (see www.physik.uzh.ch/lectures/informatik/python/ as an example), some prior experience programming, knowledge of C, C++ beneficial | |||||

Physics of the Atmosphere | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

701-0023-00L | Atmosphere | W | 3 credits | 2V | H. Wernli, E. M. Fischer, T. Peter | |

Abstract | Basic principles of the atmosphere, physical structure and chemical composition, trace gases, atmospheric cycles, circulation, stability, radiation, condensation, clouds, oxidation capacity and ozone layer. | |||||

Objective | Understanding of basic physical and chemical processes in the atmosphere. Understanding of mechanisms of and interactions between: weather - climate, atmosphere - ocean - continents, troposhere - stratosphere. Understanding of environmentally relevant structures and processes on vastly differing scales. Basis for the modelling of complex interrelations in the atmospehre. | |||||

Content | Basic principles of the atmosphere, physical structure and chemical composition, trace gases, atmospheric cycles, circulation, stability, radiation, condensation, clouds, oxidation capacity and ozone layer. | |||||

Lecture notes | Written information will be supplied. | |||||

Literature | - John H. Seinfeld and Spyros N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, Wiley, New York, 1998. - Gösta H. Liljequist, Allgemeine Meteorologie, Vieweg, Braunschweig, 1974. | |||||

651-4053-05L | Boundary Layer Meteorology | W | 4 credits | 3G | M. Rotach, P. Calanca | |

Abstract | The Planetary Boundary Layer (PBL) constitutes the interface between the atmosphere and the Earth's surface. Theory on transport processes in the PBL and their dynamics is provided. This course treats theoretical background and idealized concepts. These are contrasted to real world applications and current research issues. | |||||

Objective | Overall goals of this course are given below. Focus is on the theoretical background and idealised concepts. Students have basic knowledge on atmospheric turbulence and theoretical as well as practical approaches to treat Planetary Boundary Layer flows. They are familiar with the relevant processes (turbulent transport, forcing) within, and typical states of the Planetary Boundary Layer. Idealized concepts are known as well as their adaptations under real surface conditions (as for example over complex topography). | |||||

Content | - Introduction - Turbulence - Statistical tratment of turbulence, turbulent transport - Conservation equations in a turbulent flow - Closure problem and closure assumptions - Scaling and similarity theory - Spectral characteristics - Concepts for non-ideal boundary layer conditions | |||||

Lecture notes | available (i.e. in English) | |||||

Literature | - Stull, R.B.: 1988, "An Introduction to Boundary Layer Meteorology", (Kluwer), 666 pp. - Panofsky, H. A. and Dutton, J.A.: 1984, "Atmospheric Turbulence, Models and Methods for Engineering Applications", (J. Wiley), 397 pp. - Kaimal JC and Finningan JJ: 1994, Atmospheric Boundary Layer Flows, Oxford University Press, 289 pp. - Wyngaard JC: 2010, Turbulence in the Atmosphere, Cambridge University Press, 393pp. | |||||

Prerequisites / Notice | Umwelt-Fluiddynamik (701-0479-00L) (environment fluid dynamics) or equivalent and basic knowledge in atmospheric science | |||||

701-1221-00L | Dynamics of Large-Scale Atmospheric Flow | W | 4 credits | 2V + 1U | H. Wernli, S. Pfahl | |

Abstract | Dynamic, synoptic Meteorology | |||||

Objective | Understanding the dynamics of large-scale atmospheric flow | |||||

Content | Dynamical Meteorology is concerned with the dynamical processes of the earth's atmosphere. The fundamental equations of motion in the atmosphere will be discussed along with the dynamics and interactions of synoptic system - i.e. the low and high pressure systems that determine our weather. The motion of such systems can be understood in terms of quasi-geostrophic theory. The lecture course provides a derivation of the mathematical basis along with some interpretations and applications of the concept. | |||||

Lecture notes | Dynamics of large-scale atmospheric flow | |||||

Literature | - Holton J.R., An introduction to Dynamic Meteorogy. Academic Press, fourth edition 2004, - Pichler H., Dynamik der Atmosphäre, Bibliographisches Institut, 456 pp. 1997 | |||||

Prerequisites / Notice | Physics I, II, Environmental Fluid Dynamics | |||||

401-5930-00L | Seminar in Physics of the Atmosphere for CSE | W | 4 credits | 2S | H. Joos, C. Schär | |

Abstract | The students of this course are provided with an introduction into presentation techniques (talks and posters) and practice this knowledge by making an oral presentation about a classical or recent scientific publication. | |||||

Objective | ||||||

Chemistry | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

529-0004-00L | Computer Simulation in Chemistry, Biology and Physics | W | 7 credits | 4G | P. H. Hünenberger | |

Abstract | Molecular models, Force fields, Boundary conditions, Electrostatic interactions, Molecular dynamics, Analysis of trajectories, Quantum-mechanical simulation, Structure refinement, Application to real systems. Exercises: Analysis of papers on computer simulation, Molecular simulation in practice, Validation of molecular dynamics simulation. For more information: www.csms.ethz.ch/education/CSCBP | |||||

Objective | Introduction to computer simulation of (bio)molecular systems, development of skills to carry out and interpret computer simulations of biomolecular systems. | |||||

Content | Molecular models, Force fields, Spatial boundary conditions, Calculation of Coulomb forces, Molecular dynamics, Analysis of trajectories, Quantum-mechanical simulation, Structure refinement, Application to real systems. Exercises: Analysis of papers on computer simulation, Molecular simulation in practice, Validation of molecular dynamics simulation. | |||||

Lecture notes | Available (copies of powerpoint slides distributed before each lecture) | |||||

Literature | See: www.csms.ethz.ch/education/CSCBP | |||||

Prerequisites / Notice | Since the exercises on the computer do convey and test essentially different skills as those being conveyed during the lectures and tested at the oral exam, the results of the exercises are taken into account when evaluating the results of the exam. For more information about the lecture: www.csms.ethz.ch/education/CSCBP | |||||

529-0003-00L | Advanced Quantum Chemistry | W | 7 credits | 3G | M. Reiher, S. Knecht | |

Abstract | Advanced, but fundamental topics central to the understanding of theory in chemistry and for solving actual chemical problems with a computer. Examples are: * Operators derived from principles of relativistic quantum mechanics * Relativistic effects + methods of relativistic quantum chemistry * Open-shell molecules + spin-density functional theory * New electron-correlation theories | |||||

Objective | The aim of the course is to provide an in-depth knowledge of theory and method development in theoretical chemistry. It will be shown that this is necessary in order to be able to solve actual chemical problems on a computer with quantum chemical methods. The relativistic re-derivation of all concepts known from (nonrelativistic) quantum mechanics and quantum-chemistry lectures will finally explain the form of all operators in the molecular Hamiltonian - usually postulated rather than deduced. From this, we derive operators needed for molecular spectroscopy (like those required by magnetic resonance spectroscopy). Implications of other assumptions in standard non-relativistic quantum chemistry shall be analyzed and understood, too. Examples are the Born-Oppenheimer approximation and the expansion of the electronic wave function in a set of pre-defined many-electron basis functions (Slater determinants). Overcoming these concepts, which are so natural to the theory of chemistry, will provide deeper insights into many-particle quantum mechanics. Also revisiting the workhorse of quantum chemistry, namely density functional theory, with an emphasis on open-shell electronic structures (radicals, transition-metal complexes) will contribute to this endeavor. It will be shown how these insights allow us to make more accurate predictions in chemistry in practice - at the frontier of research in theoretical chemistry. | |||||

Content | 1) Introductory lecture: basics of quantum mechanics and quantum chemistry 2) Einstein's special theory of relativity and the (classical) electromagnetic interaction of two charged particles 3) Klein-Gordon and Dirac equation; the Dirac hydrogen atom 4) Numerical methods based on the Dirac-Fock-Coulomb Hamiltonian, two-component and scalar relativistic Hamiltonians 5) Response theory and molecular properties, derivation of property operators, Breit-Pauli-Hamiltonian 6) Relativistic effects in chemistry and the emergence of spin 7) Spin in density functional theory 8) New electron-correlation theories: Tensor network and matrix product states, the density matrix renormalization group 9) Quantum chemistry without the Born-Oppenheimer approximation | |||||

Lecture notes | A set of detailed lecture notes will be provided, which will cover the whole course. | |||||

Literature | 1) M. Reiher, A. Wolf, Relativistic Quantum Chemistry, Wiley-VCH, 2014, 2nd edition 2) F. Schwabl: Quantenmechanik für Fortgeschrittene (QM II), Springer-Verlag, 1997 [english version available: F. Schwabl, Advanced Quantum Mechanics] 3) R. McWeeny: Methods of Molecular Quantum Mechanics, Academic Press, 1992 4) C. R. Jacob, M. Reiher, Spin in Density-Functional Theory, Int. J. Quantum Chem. 112 (2012) 3661 http://onlinelibrary.wiley.com/doi/10.1002/qua.24309/abstract 5) K. H. Marti, M. Reiher, New Electron Correlation Theories for Transition Metal Chemistry, Phys. Chem. Chem. Phys. 13 (2011) 6750 http://pubs.rsc.org/en/Content/ArticleLanding/2011/CP/c0cp01883j 6) K.H. Marti, M. Reiher, The Density Matrix Renormalization Group Algorithm in Quantum Chemistry, Z. Phys. Chem. 224 (2010) 583 http://www.oldenbourg-link.com/doi/abs/10.1524/zpch.2010.6125 7) E. Mátyus, J. Hutter, U. Müller-Herold, M. Reiher, On the emergence of molecular structure, Phys. Rev. A 83 2011, 052512 http://pra.aps.org/abstract/PRA/v83/i5/e052512 Note also the standard textbooks: A) A. Szabo, N.S. Ostlund. Verlag, Dover Publications B) I. N. Levine, Quantum Chemistry, Pearson C) T. Helgaker, P. Jorgensen, J. Olsen: Molecular Electronic-Structure Theory, Wiley, 2000 D) R.G. Parr, W. Yang: Density-Functional Theory of Atoms and Molecules, Oxford University Press, 1994 E) R.M. Dreizler, E.K.U. Gross: Density Functional Theory, Springer-Verlag, 1990 | |||||

Prerequisites / Notice | Strongly recommended (preparatory) courses are: quantum mechanics and quantum chemistry | |||||

401-5940-00L | Seminar in Chemistry for CSE | W | 4 credits | 2S | P. H. Hünenberger, M. Reiher | |

Abstract | The student will carry out a literature study on a topic of his or her liking or suggested by the supervisor in the area of computer simulation in chemistry, the results of which are to be presented both orally and in written form. For more information: www.csms.ethz.ch/education/RW | |||||

Objective | ||||||

Fluid Dynamics One of the course units 151-0103-00L Fluid Dynamics II 151-0109-00L Turbulent Flows is compulsory. Students able to follow courses in German are advised to choose 151-0103-00L Fluid Dynamics II. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0103-00L | Fluid Dynamics II | O | 3 credits | 2V + 1U | P. Jenny | |

Abstract | Two-dimensional irrotational (potential) flows: stream function and potential, singularity method, unsteady flow, aerodynamic concepts. Vorticity dynamics: vorticity and circulation, vorticity equation, vortex theorems of Helmholtz and Kelvin. Compressible flows: isentropic flow along stream tube, normal and oblique shocks, Laval nozzle, Prandtl-Meyer expansion, viscous effects. | |||||

Objective | Expand basic knowledge of fluid dynamics. Concepts, phenomena and quantitative description of irrotational (potential), rotational, and one-dimensional compressible flows. | |||||

Content | Two-dimensional irrotational (potential) flows: stream function and potential, complex notation, singularity method, unsteady flow, aerodynamic concepts. Vorticity dynamics: vorticity and circulation, vorticity equation, vortex theorems of Helmholtz and Kelvin. Compressible flows: isentropic flow along stream tube, normal and oblique shocks, Laval nozzle, Prandtl-Meyer expansion, viscous effects. | |||||

Lecture notes | Lecture notes are available (in German). (See also info on literature below.) | |||||

Literature | Relevant chapters (corresponding to lecture notes) from the textbook P.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 5th ed., 2011 (includes a free copy of the DVD "Multimedia Fluid Mechanics") P.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 6th ed., 2015 (does NOT include a free copy of the DVD "Multimedia Fluid Mechanics") | |||||

Prerequisites / Notice | Analysis I/II, Knowledge of Fluid Dynamics I, thermodynamics of ideal gas | |||||

151-0109-00L | Turbulent Flows | W | 4 credits | 2V + 1U | P. Jenny | |

Abstract | Contents - Laminar and turbulent flows, instability and origin of turbulence - Statistical description: averaging, turbulent energy, dissipation, closure problem - Scalings. Homogeneous isotropic turbulence, correlations, Fourier representation, energy spectrum - Free turbulence: wake, jet, mixing layer - Wall turbulence: Channel and boundary layer - Computation and modelling of turbulent flows | |||||

Objective | Basic physical phenomena of turbulent flows, quantitative and statistical description, basic and averaged equations, principles of turbulent flow computation and elements of turbulence modelling | |||||

Content | - Properties of laminar, transitional and turbulent flows. - Origin and control of turbulence. Instability and transition. - Statistical description, averaging, equations for mean and fluctuating quantities, closure problem. - Scalings, homogeneous isotropic turbulence, energy spectrum. - Turbulent free shear flows. Jet, wake, mixing layer. - Wall-bounded turbulent flows. - Turbulent flow computation and modeling. | |||||

Lecture notes | Lecture notes are available | |||||

Literature | S.B. Pope, Turbulent Flows, Cambridge University Press, 2000 | |||||

151-0182-00L | Fundamentals of CFD Methods | W+ | 4 credits | 3G | A. Haselbacher | |

Abstract | This course is focused on providing students with the knowledge and understanding required to develop simple computational fluid dynamics (CFD) codes to solve the incompressible Navier-Stokes equations and to critically assess the results produced by CFD codes. As part of the course, students will write their own codes and verify and validate them systematically. | |||||

Objective | 1. Students know and understand basic numerical methods used in CFD in terms of accuracy and stability. 2. Students have a basic understanding of a typical simple CFD code. 3. Students understand how to assess the numerical and physical accuracy of CFD results. | |||||

Content | 1. Governing and model equations. Brief review of equations and properties 2. Overview of basic concepts: Overview of discretization process and its consequences 3. Overview of numerical methods: Finite-difference and finite-volume methods 4. Analysis of spatially discrete equations: Consistency, accuracy, stability, convergence of semi-discrete methods 5. Time-integration methods: LMS and RK methods, consistency, accuracy, stability, convergence 6. Analysis of fully discrete equations: Consistency, accuracy, stability, convergence of fully discrete methods 7. Solution of one-dimensional advection equation: Motivation for and consequences of upwinding, Godunov's theorem, TVD methods, DRP methods 8. Solution of two-dimensional advection equation: Dimension-by-dimension methods, dimensional splitting, multidimensional methods 9. Solution of one- and two-dimensional diffusion equations: Implicit methods, ADI methods 10. Solution of one-dimensional advection-diffusion equation: Numerical vs physical viscosity, boundary layers, non-uniform grids 11. Solution of incompressible Navier-Stokes equations: Incompressibility constraint and consequences, fractional-step and pressure-correction methods 12. Solution of incompressible Navier-Stokes equations on unstructured grids | |||||

Lecture notes | The course is based mostly on notes developed by the instructor. | |||||

Literature | Literature: There is no required textbook. Suggested references are: 1. H.K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, 2nd ed., Pearson Prentice Hall, 2007 2. R.H. Pletcher, J.C. Tannehill, and D. Anderson, Computational Fluid Mechanics and Heat Transfer, 3rd ed., Taylor & Francis, 2011 | |||||

Prerequisites / Notice | Prior knowledge of fluid dynamics, applied mathematics, basic numerical methods, and programming in Fortran and/or C++ (knowledge of MATLAB is *not* sufficient). | |||||

151-0105-00L | Quantitative Flow Visualization | W | 4 credits | 2V + 1U | T. Rösgen | |

Abstract | The course provides an introduction to digital image analysis in modern flow diagnostics. Different techniques which are discussed include image velocimetry, laser induced fluorescence, liquid crystal thermography and interferometry. The physical foundations and measurement configurations are explained. Image analysis algorithms are presented in detail and programmed during the exercises. | |||||

Objective | Introduction to modern imaging techniques and post processing algorithms with special emphasis on flow analysis and visualization. Understanding of hardware and software requirements and solutions. Development of basic programming skills for (generic) imaging applications. | |||||

Content | Fundamentals of optics, flow visualization and electronic image acquisition. Frequently used mage processing techniques (filtering, correlation processing, FFTs, color space transforms). Image Velocimetry (tracking, pattern matching, Doppler imaging). Surface pressure and temperature measurements (fluorescent paints, liquid crystal imaging, infrared thermography). Laser induced fluorescence. (Digital) Schlieren techniques, phase contrast imaging, interferometry, phase unwrapping. Wall shear and heat transfer measurements. Pattern recognition and feature extraction, proper orthogonal decomposition. | |||||

Lecture notes | available | |||||

Prerequisites / Notice | Prerequisites: Fluiddynamics I, Numerical Mathematics, programming skills. Language: German on request. | |||||

151-0213-00L | Fluid Dynamics with the Lattice Boltzmann Method | W | 4 credits | 3G | I. Karlin | |

Abstract | The course provides an introduction to theoretical foundations and practical usage of the Lattice Boltzmann Method for fluid dynamics simulations. | |||||

Objective | Methods like molecular dynamics, DSMC, lattice Boltzmann etc are being increasingly used by engineers all over and these methods require knowledge of kinetic theory and statistical mechanics which are traditionally not taught at engineering departments. The goal of this course is to give an introduction to ideas of kinetic theory and non-equilibrium thermodynamics with a focus on developing simulation algorithms and their realizations. During the course, students will be able to develop a lattice Boltzmann code on their own. Practical issues about implementation and performance on parallel machines will be demonstrated hands on. Central element of the course is the completion of a lattice Boltzmann code (using the framework specifically designed for this course). The course will also include a review of topics of current interest in various fields of fluid dynamics, such as multiphase flows, reactive flows, microflows among others. Optionally, we offer an opportunity to complete a project of student's choice as an alternative to the oral exam. Samples of projects completed by previous students will be made available. | |||||

Content | The course builds upon three parts: I Elementary kinetic theory and lattice Boltzmann simulations introduced on simple examples. II Theoretical basis of statistical mechanics and kinetic equations. III Lattice Boltzmann method for real-world applications. The content of the course includes: 1. Background: Elements of statistical mechanics and kinetic theory: Particle's distribution function, Liouville equation, entropy, ensembles; Kinetic theory: Boltzmann equation for rarefied gas, H-theorem, hydrodynamic limit and derivation of Navier-Stokes equations, Chapman-Enskog method, Grad method, boundary conditions; mean-field interactions, Vlasov equation; Kinetic models: BGK model, generalized BGK model for mixtures, chemical reactions and other fluids. 2. Basics of the Lattice Boltzmann Method and Simulations: Minimal kinetic models: lattice Boltzmann method for single-component fluid, discretization of velocity space, time-space discretization, boundary conditions, forcing, thermal models, mixtures. 3. Hands on: Development of the basic lattice Boltzmann code and its validation on standard benchmarks (Taylor-Green vortex, lid-driven cavity flow etc). 4. Practical issues of LBM for fluid dynamics simulations: Lattice Boltzmann simulations of turbulent flows; numerical stability and accuracy. 5. Microflow: Rarefaction effects in moderately dilute gases; Boundary conditions, exact solutions to Couette and Poiseuille flows; micro-channel simulations. 6. Advanced lattice Boltzmann methods: Entropic lattice Boltzmann scheme, subgrid simulations at high Reynolds numbers; Boundary conditions for complex geometries. 7. Introduction to LB models beyond hydrodynamics: Relativistic fluid dynamics; flows with phase transitions. | |||||

Lecture notes | Lecture notes on the theoretical parts of the course will be made available. Selected original and review papers are provided for some of the lectures on advanced topics. Handouts and basic code framework for implementation of the lattice Boltzmann models will be provided. | |||||

Prerequisites / Notice | The course addresses mainly graduate students (MSc/Ph D) but BSc students can also attend. | |||||

151-0207-00L | Theory and Modeling of Reactive Flows | W | 4 credits | 3G | C. E. Frouzakis, I. Mantzaras | |

Abstract | The course first reviews the governing equations and combustion chemistry, setting the ground for the analysis of homogeneous gas-phase mixtures, laminar diffusion and premixed flames. Catalytic combustion and its coupling with homogeneous combustion are dealt in detail, and turbulent combustion modeling approaches are presented. Available numerical codes will be used for modeling. | |||||

Objective | Theory of combustion with numerical applications | |||||

Content | The analysis of realistic reactive flow systems necessitates the use of detailed computer models that can be constructed starting from first principles i.e. thermodynamics, fluid mechanics, chemical kinetics, and heat and mass transport. In this course, the focus will be on combustion theory and modeling. The reacting flow governing equations and the combustion chemistry are firstly reviewed, setting the ground for the analysis of homogeneous gas-phase mixtures, laminar diffusion and premixed flames. Heterogeneous (catalytic) combustion, an area of increased importance in the last years, will be dealt in detail along with its coupling with homogeneous combustion. Finally, approaches for the modeling of turbulent combustion will be presented. Available numerical codes will be used to compute the above described phenomena. Familiarity with numerical methods for the solution of partial differential equations is expected. | |||||

Lecture notes | Handouts | |||||

Prerequisites / Notice | NEW course | |||||

401-5950-00L | Seminar in Fluid Dynamics for CSE | W | 4 credits | 2S | P. Jenny, T. Rösgen | |

Abstract | Enlarged knowledge and practical abilities in fundamentals and applications of Computational Fluid Dynamics | |||||

Objective | Enlarged knowledge and practical abilities in fundamentals and applications of Computational Fluid Dynamics | |||||

Prerequisites / Notice | Contact Prof. P. Jenny or Prof. T. Rösgen before the beginning of the semester | |||||

Systems and Control | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

227-0103-00L | Control Systems | W | 6 credits | 2V + 2U | F. Dörfler | |

Abstract | Study of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems. | |||||

Objective | Study of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems. | |||||

Content | Process automation, concept of control. Modelling of dynamical systems - examples, state space description, linearisation, analytical/numerical solution. Laplace transform, system response for first and second order systems - effect of additional poles and zeros. Closed-loop control - idea of feedback. PID control, Ziegler - Nichols tuning. Stability, Routh-Hurwitz criterion, root locus, frequency response, Bode diagram, Bode gain/phase relationship, controller design via "loop shaping", Nyquist criterion. Feedforward compensation, cascade control. Multivariable systems (transfer matrix, state space representation), multi-loop control, problem of coupling, Relative Gain Array, decoupling, sensitivity to model uncertainty. State space representation (modal description, controllability, control canonical form, observer canonical form), state feedback, pole placement - choice of poles. Observer, observability, duality, separation principle. LQ Regulator, optimal state estimation. | |||||

Literature | K. J. Aström & R. Murray. Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press, 2010. R. C. Dorf and R. H. Bishop. Modern Control Systems. Prentice Hall, New Jersey, 2007. G. F. Franklin, J. D. Powell, and A. Emami-Naeini. Feedback Control of Dynamic Systems. Addison-Wesley, 2010. J. Lunze. Regelungstechnik 1. Springer, Berlin, 2014. J. Lunze. Regelungstechnik 2. Springer, Berlin, 2014. | |||||

Prerequisites / Notice | Prerequisites: Signal and Systems Theory II. MATLAB is used for system analysis and simulation. | |||||

227-0045-00L | Signals and Systems I | W | 4 credits | 2V + 2U | H. Bölcskei | |

Abstract | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | |||||

Objective | Introduction to mathematical signal processing and system theory. | |||||

Content | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | |||||

Lecture notes | Lecture notes, problem set with solutions. | |||||

227-0225-00L | Linear System Theory | W | 6 credits | 5G | M. Kamgarpour | |

Abstract | The class is intended to provide a comprehensive overview of the theory of linear dynamical systems, their use in control, filtering, and estimation and their applications to areas ranging from avionics to systems biology. | |||||

Objective | By the end of the class students should be comfortable with the fundamental results in linear system theory and the mathematical tools used to derive them. | |||||

Content | - Rings, fields and linear spaces, normed linear spaces and inner product spaces. - Ordinary differential equations, existence and uniqueness of solutions. - Continuous and discrete time, time varying linear systems. Time domain solutions. Time invariant systems treated as a special case. - Controllability and observability, canonical forms, Kalman decomposition. Time invariant systems treated as a special case. - Stability and stabilization, observers, state and output feedback, separation principle. - Realization theory. | |||||

Lecture notes | F.M. Callier and C.A. Desoer, "Linear System Theory", Springer-Verlag, 1991. | |||||

Prerequisites / Notice | Prerequisites: Control Systems I (227-0103-00) or equivalent and sufficient mathematical maturity. | |||||

252-0535-00L | Machine Learning | W | 8 credits | 3V + 2U + 2A | J. M. Buhmann | |

Abstract | Machine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects. | |||||

Objective | Students will be familiarized with the most important concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. A machine learning project will provide an opportunity to test the machine learning algorithms on real world data. | |||||

Content | The theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data. Topics covered in the lecture include: - Bayesian theory of optimal decisions - Maximum likelihood and Bayesian parameter inference - Classification with discriminant functions: Perceptrons, Fisher's LDA and support vector machines (SVM) - Ensemble methods: Bagging and Boosting - Regression: least squares, ridge and LASSO penalization, non-linear regression and the bias-variance trade-off - Non parametric density estimation: Parzen windows, nearest nieghbour - Dimension reduction: principal component analysis (PCA) and beyond | |||||

Lecture notes | No lecture notes, but slides will be made available on the course webpage. | |||||

Literature | C. Bishop. Pattern Recognition and Machine Learning. Springer 2007. R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley & Sons, second edition, 2001. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, 2001. L. Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer, 2004. | |||||

Prerequisites / Notice | The course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments. Students should at least have followed one previous course offered by the Machine Learning Institute (e.g., CIL or LIS) or an equivalent course offered by another institution. | |||||

151-0575-01L | Signals and Systems | W | 4 credits | 2V + 2U | R. D'Andrea | |

Abstract | Signals arise in most engineering applications. They contain information about the behavior of physical systems. Systems respond to signals and produce other signals. In this course, we explore how signals can be represented and manipulated, and their effects on systems. We further explore how we can discover basic system properties by exciting a system with various types of signals. | |||||

Objective | Master the basics of signals and systems. Apply this knowledge to problems in the homework assignments and programming exercise. | |||||

Content | Discrete-time signals and systems. Fourier- and z-Transforms. Frequency domain characterization of signals and systems. System identification. Time series analysis. Filter design. | |||||

Lecture notes | Lecture notes available on course website. | |||||

151-0563-01L | Dynamic Programming and Optimal Control | W | 4 credits | 2V + 1U | R. D'Andrea | |

Abstract | Introduction to Dynamic Programming and Optimal Control. | |||||

Objective | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||

Content | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||

Literature | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||

Prerequisites / Notice | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||

401-5850-00L | Seminar in Systems and Control for CSE | W | 4 credits | 2S | J. Lygeros | |

Abstract | ||||||

Objective | ||||||

Robotics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0601-00L | Theory of Robotics and Mechatronics | W | 4 credits | 3G | P. Korba, S. Stoeter, B. Nelson | |

Abstract | This course provides an introduction and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. It’s a requirement for the Robotics Vertiefung and for the Masters in Mechatronics and Microsystems. | |||||

Objective | Robotics is often viewed from three perspectives: perception (sensing), manipulation (affecting changes in the world), and cognition (intelligence). Robotic systems integrate aspects of all three of these areas. This course provides an introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. This course is a requirement for the Robotics Vertiefung and for the Masters in Mechatronics and Microsystems. | |||||

Content | An introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. | |||||

Lecture notes | available. | |||||

Prerequisites / Notice | The course will be taught in English. | |||||

252-0535-00L | Machine Learning | W | 8 credits | 3V + 2U + 2A | J. M. Buhmann | |

Abstract | Machine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects. | |||||

Objective | Students will be familiarized with the most important concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. A machine learning project will provide an opportunity to test the machine learning algorithms on real world data. | |||||

Content | The theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data. Topics covered in the lecture include: - Bayesian theory of optimal decisions - Maximum likelihood and Bayesian parameter inference - Classification with discriminant functions: Perceptrons, Fisher's LDA and support vector machines (SVM) - Ensemble methods: Bagging and Boosting - Regression: least squares, ridge and LASSO penalization, non-linear regression and the bias-variance trade-off - Non parametric density estimation: Parzen windows, nearest nieghbour - Dimension reduction: principal component analysis (PCA) and beyond | |||||

Lecture notes | No lecture notes, but slides will be made available on the course webpage. | |||||

Literature | C. Bishop. Pattern Recognition and Machine Learning. Springer 2007. R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley & Sons, second edition, 2001. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, 2001. L. Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer, 2004. | |||||

Prerequisites / Notice | The course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments. Students should at least have followed one previous course offered by the Machine Learning Institute (e.g., CIL or LIS) or an equivalent course offered by another institution. | |||||

263-5902-00L | Computer Vision | W | 6 credits | 3V + 1U + 1A | L. Van Gool, V. Ferrari, A. Geiger | |

Abstract | The goal of this course is to provide students with a good understanding of computer vision and image analysis techniques. The main concepts and techniques will be studied in depth and practical algorithms and approaches will be discussed and explored through the exercises. | |||||

Objective | The objectives of this course are: 1. To introduce the fundamental problems of computer vision. 2. To introduce the main concepts and techniques used to solve those. 3. To enable participants to implement solutions for reasonably complex problems. 4. To enable participants to make sense of the computer vision literature. | |||||

Content | Camera models and calibration, invariant features, Multiple-view geometry, Model fitting, Stereo Matching, Segmentation, 2D Shape matching, Shape from Silhouettes, Optical flow, Structure from motion, Tracking, Object recognition, Object category recognition | |||||

Prerequisites / Notice | It is recommended that students have taken the Visual Computing lecture or a similar course introducing basic image processing concepts before taking this course. | |||||

151-0563-01L | Dynamic Programming and Optimal Control | W | 4 credits | 2V + 1U | R. D'Andrea | |

Abstract | Introduction to Dynamic Programming and Optimal Control. | |||||

Objective | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||

Content | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||

Literature | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||

Prerequisites / Notice | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||

151-0851-00L | Robot Dynamics | W | 4 credits | 2V + 1U | M. Hutter, R. Siegwart, T. Stastny | |

Abstract | We will provide an overview on how to kinematically and dynamically model typical robotic systems such as robot arms, legged robots, rotary wing systems, or fixed wing. | |||||

Objective | The primary objective of this course is that the student deepens an applied understanding of how to model the most common robotic systems. The student receives a solid background in kinematics, dynamics, and rotations of multi-body systems. On the basis of state of the art applications, he/she will learn all necessary tools to work in the field of design or control of robotic systems. | |||||

Content | The course consists of three parts: First, we will refresh and deepen the student's knowledge in kinematics, dynamics, and rotations of multi-body systems. In this context, the learning material will build upon the courses for mechanics and dynamics available at ETH, with the particular focus on their application to robotic systems. The goal is to foster the conceptual understanding of similarities and differences among the various types of robots. In the second part, we will apply the learned material to classical robotic arms as well as legged systems and discuss kinematic constraints and interaction forces. In the third part, focus is put on modeling fixed wing aircraft, along with related design and control concepts. In this context, we also touch aerodynamics and flight mechanics to an extent typically required in robotics. The last part finally covers different helicopter types, with a focus on quadrotors and the coaxial configuration which we see today in many UAV applications. Case studies on all main topics provide the link to real applications and to the state of the art in robotics. | |||||

Prerequisites / Notice | The contents of the following ETH Bachelor lectures or equivalent are assumed to be known: Mechanics and Dynamics, Control, Basics in Fluid Dynamics. | |||||

401-5860-00L | Seminar in Robotics for CSE | W | 4 credits | 2S | R. Siegwart | |

Abstract | This course provides an opportunity to familiarize yourself with the advanced topics of robotics and mechatronics research. The study plan has to be discussed with the lecturer based on your specific interests and/or the relevant seminar series such as the IRIS's Robotics Seminars and BiRONZ lectures, for example. | |||||

Objective | The students are familiar with the challenges of the fascinating and interdisciplinary field of Robotics and Mechatronics. They are introduced in the basics of independent non-experimental scientific research and are able to summarize and to present the results efficiently. | |||||

Content | This 4 ECTS course requires each student to discuss a study plan with the lecturer and select minimum 10 relevant scientific publications to read through, or attend 5-10 lectures of the public robotics oriented seminars (e.g. Public robotics seminars such as the IRIS's Robotics Seminars http://www.iris.ethz.ch/iris/series/, and BiRONZ lectures http://www.birl.ethz.ch/bironz/index are good examples). At the end of semester, the results should be presented in an oral presentation and summarized in a report, which takes the discussion of the presentation into account. | |||||

Physics For the field of specialization `Physics' basic knowledge in quantum mechanics is required. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

402-0809-00L | Introduction to Computational Physics | W | 8 credits | 2V + 2U | H. J. Herrmann | |

Abstract | This course offers an introduction to computer simulation methods for physics problems and their implementation on PCs and super computers: classical equations of motion, partial differential equations (wave equation, diffusion equation, Maxwell's equation), Monte Carlo simulations, percolation, phase transitions | |||||

Objective | ||||||

Content | Einführung in die rechnergestützte Simulation physikalischer Probleme. Anhand einfacher Modelle aus der klassischen Mechanik, Elektrodynamik und statistischen Mechanik sowie interdisziplinären Anwendungen werden die wichtigsten objektorientierten Programmiermethoden für numerische Simulationen (überwiegend in C++) erläutert. Daneben wird eine Einführung in die Programmierung von Vektorsupercomputern und parallelen Rechnern, sowie ein Überblick über vorhandene Softwarebibliotheken für numerische Simulationen geboten. | |||||

Prerequisites / Notice | Lecture and exercise lessons in english, exams in German or in English | |||||

402-0205-00L | Quantum Mechanics I | W | 10 credits | 3V + 2U | T. K. Gehrmann | |

Abstract | Introduction to non-relativistic single-particle quantum mechanics. In particular, the basic concepts of quantum mechanics, such as the quantisation of classical systems, wave functions and the description of observables as operators on a Hilbert space, and the formulation of symmetries will be discussed. Basic phenomena will be analysed and illustrated by generic examples. | |||||

Objective | Introduction to single-particle quantum mechanics. Familiarity with basic ideas and concepts (quantisation, operator formalism, symmetries, perturbation theory) and generic examples and applications (bound states, tunneling, scattering states, in one- and three-dimensional settings). Ability to solve simple problems. | |||||

Content | Keywords: Schrödinger equation, basic formalism of quantum mechanics (states, operators, commutators, measuring process), symmetries (translations, rotations), quantum mechanics in one dimension, spherically symmetric problems in three dimensions, scattering theory, perturbation theory, variational techniques, spin, addition of angular momenta, relation between QM and classical physics. | |||||

Literature | F. Schwabl: Quantum mechanics J.J. Sakurai: Modern Quantum Mechanics C. Cohen-Tannoudji: Quantum mechanics I | |||||

401-5810-00L | Seminar in Physics for CSE | W | 4 credits | 2S | A. Soluyanov, M. Troyer | |

Abstract | In this seminar the students present a talk on an advanced topic in modern theoretical or computational physics. | |||||

Objective | ||||||

Computational Finance | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3913-01L | Mathematical Foundations for Finance | W | 4 credits | 3V + 2U | E. W. Farkas, M. Schweizer | |

Abstract | First introduction to main modelling ideas and mathematical tools from mathematical finance | |||||

Objective | This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims at a double audience: mathematicians who want to learn the modelling ideas and concepts for finance, and non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs. | |||||

Content | Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula | |||||

Lecture notes | Lecture notes will be sold at the beginning of the course. | |||||

Literature | Lecture notes will be sold at the beginning of the course. Additional (background) references are given there. | |||||

Prerequisites / Notice | Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared. | |||||

401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 credits | 3V + 1U | A. Jentzen | |

Abstract | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | |||||

Objective | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||

Content | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Multilevel Monte Carlo methods for SODEs Applications to computational finance: Option valuation | |||||

Lecture notes | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | |||||

Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | |||||

Prerequisites / Notice | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 21, 2016 For more details, please follow the link in the Learning materials section. | |||||

401-8905-00L | Financial Engineering (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: MFOEC103 Mind the enrolment deadlines at UZH: http://www.uzh.ch/studies/application/mobilitaet_en.html | W | 4.5 credits | 3G | University lecturers | |

Abstract | This lecture is intended for students who would like to learn more on equity derivatives modelling and pricing. | |||||

Objective | Quantitative models for European option pricing (including stochastic volatility and jump models), volatility and variance derivatives, American and exotic options. | |||||

Content | After introducing fundamental concepts of mathematical finance including no-arbitrage, portfolio replication and risk-neutral measure, we will present the main models that can be used for pricing and hedging European options e.g. Black- Scholes model, stochastic and jump-diffusion models, and highlight their assumptions and limitations. We will cover several types of derivatives such as European and American options, Barrier options and Variance- Swaps. Basic knowledge in probability theory and stochastic calculus is required. Besides attending class, we strongly encourage students to stay informed on financial matters, especially by reading daily financial newspapers such as the Financial Times or the Wall Street Journal. | |||||

Lecture notes | Script. | |||||

Prerequisites / Notice | Basic knowledge of probability theory and stochastic calculus. Asset Pricing. | |||||

401-5820-00L | Seminar in Computational Finance for CSE | W | 4 credits | 2S | J. Teichmann | |

Abstract | ||||||

Objective | ||||||

Content | We aim to comprehend recent and exciting research on the nature of stochastic volatility: an extensive econometric research [4] lead to new in- sights on stochastic volatility, in particular that very rough fractional pro- cesses of Hurst index about 0.1 actually provide very attractive models. Also from the point of view of pricing [1] and microfoundations [2] these models are very convincing. More precisely each student is expected to work on one specified task consisting of a theoretical part and an implementation with financial data, whose results should be presented in a 45 minutes presentation. | |||||

Literature | [1] C. Bayer, P. Friz, and J. Gatheral. Pricing under rough volatility. Quantitative Finance , 16(6):887-904, 2016. [2] F. M. Euch, Omar El and M. Rosenbaum. The microstructural founda- tions of leverage effect and rough volatility. arXiv:1609.05177 , 2016. [3] O. E. Euch and M. Rosenbaum. The characteristic function of rough Heston models. arXiv:1609.02108 , 2016. [4] J. Gatheral, T. Jaisson, and M. Rosenbaum. Volatility is rough. arXiv:1410.3394 , 2014. | |||||

Prerequisites / Notice | Requirements: sound understanding of stochastic concepts and of con- cepts of mathematical Finance, ability to implement econometric or simula- tion routines in MATLAB. | |||||

Electromagnetics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

227-0110-00L | Advanced Electromagnetic WavesThis course has been moved from the spring to the fall semester for the academic year of 2016/17. It will therefore not take place in spring 2017. | W | 6 credits | 2V + 2U | P. Leuchtmann | |

Abstract | This course provides advanced knowledge of electromagnetic waves in linear materials including negative index and other non classical materials. | |||||

Objective | The behavior of electromagnetic waves both in free space and in selected environments including stratified media, material interfaces and waveguides is understood. Material models in the time harmonic regime including negative index and plasmonic materials are clarified. | |||||

Content | Description of generic time harmonic electromagnetic fields; the role of the material in Maxwell's equations; energy transport and power loss mechanism; EM-waves in homogeneous space: ordinary and evanescent plane waves, cylindrical and spherical waves, "complex origin"-waves and beams; EM-waves in stratified media; generic guiding mechanism for EM waves; classical wave guides, dielectric wave guides. | |||||

Lecture notes | A skript including animated wave representations is provided in electronic form. | |||||

Literature | See literature list in the script. | |||||

Prerequisites / Notice | The lecture is taught in German while both the script and the viewgraphs are in English. | |||||

227-2037-00L | Physical Modelling and Simulation | W | 5 credits | 4G | C. Hafner, J. Leuthold, J. Smajic | |

Abstract | This module consists of (a) an introduction to fundamental equations of electromagnetics, mechanics and heat transfer, (b) a detailed overview of numerical methods for field simulations, and (c) practical examples solved in form of small projects. | |||||

Objective | Basic knowledge of the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. Knowledge of the main concepts of numerical methods for physical modelling and simulation. Ability (a) to develop own simple field simulation programs, (b) to select an appropriate field solver for a given problem, (c) to perform field simulations, (d) to evaluate the obtained results, and (e) to interactively improve the models until sufficiently accurate results are obtained. | |||||

Content | The module begins with an introduction to the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. After the introduction follows a detailed overview of the available numerical methods for solving electromagnetic, thermal and mechanical boundary value problems. This part of the course contains a general introduction into numerical methods, differential and integral forms, linear equation systems, Finite Difference Method (FDM), Boundary Element Method (BEM), Method of Moments (MoM), Multiple Multipole Program (MMP) and Finite Element Method (FEM). The theoretical part of the course finishes with a presentation of multiphysics simulations through several practical examples of HF-engineering such as coupled electromagnetic-mechanical and electromagnetic-thermal analysis of MEMS. In the second part of the course the students will work in small groups on practical simulation problems. For solving practical problems the students can develop and use own simulation programs or chose an appropriate commercial field solver for their specific problem. This practical simulation work of the students is supervised by the lecturers. | |||||

227-0301-00L | Optical Communication Fundamentals | W | 6 credits | 2V + 1U + 1P | J. Leuthold | |

Abstract | The path of an analog signal in the transmitter to the digital world in a communication link and back to the analog world at the receiver is discussed. The lecture covers the fundamentals of all important optical and optoelectronic components in a fiber communication system. This includes the transmitter, the fiber channel and the receiver with the electronic digital signal processing elements. | |||||

Objective | An in-depth understanding on how information is transmitted from source to destination. Also the mathematical framework to describe the important elements will be passed on. Students attending the lecture will further get engaged in critical discussion on societal, economical and environmental aspects related to the on-going exponential growth in the field of communications. | |||||

Content | * Chapter 1: Introduction: Analog/Digital conversion, The communication channel, Shannon channel capacity, Capacity requirements. * Chapter 2: The Transmitter: Components of a transmitter, Lasers, The spectrum of a signal, Optical modulators, Modulation formats. * Chapter 3: The Optical Fiber Channel: Geometrical optics, The wave equations in a fiber, Fiber modes, Fiber propagation, Fiber losses, Nonlinear effects in a fiber. * Chapter 4: The Receiver: Photodiodes, Receiver noise, Detector schemes (direct detection, coherent detection), Bit-error ratios and error estimations. * Chapter 5: Digital Signal Processing Techniques: Digital signal processing in a coherent receiver, Error detection teqchniques, Error correction coding. * Chapter 6: Pulse Shaping and Multiplexing Techniques: WDM/FDM, TDM, OFDM, Nyquist Multiplexing, OCDMA. * Chapter 7: Optical Amplifiers : Semiconductor Optical Amplifiers, Erbium Doped Fiber Amplifiers, Raman Amplifiers. | |||||

Lecture notes | Lecture notes are handed out. | |||||

Literature | Govind P. Agrawal; "Fiber-Optic Communication Systems"; Wiley, 2010 | |||||

Prerequisites / Notice | Fundamentals of Electromagnetic Fields & Bachelor Lectures on Physics. | |||||

401-5870-00L | Seminar in Electromagnetics for CSE | W | 4 credits | 2S | C. Hafner, J. Leuthold | |

Abstract | Various topics of electromagnetics, including electromagnetic theory, computational electromagnetics, electromagnetic wave propagation, applications from statics to optics. Traditional problems such as antennas, electromagnetic scattering, waveguides, resonators, etc. as well as modern topics such as photonic crystals, metamaterials, plasmonics, etc. are considered. | |||||

Objective | Knowledge of the fundamentals of electromagnetic theory, development and application of numerical methods for solving Maxwell equations, analysis and optimal design of electromagnetic structures | |||||

Geophysics Recommended combinations: Subject 1 + Subject 2 Subject 1 + Subject 3 Subject 2 + Subject 3 Subject 3 + Subject 4 Subject 5 + Subject 6 Subject 5 + Subject 4 | ||||||

Geophysics: Subject 1 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4007-00L | Continuum Mechanics | W | 3 credits | 2V | T. Gerya | |

Abstract | In this course, students learn crucial partial differential equations (conservation laws) that are applicable to any continuum including the Earth's mantle, core, atmosphere and ocean. The course will provide step-by-step introduction into the mathematical structure, physical meaning and analytical solutions of the equations. The course has a particular focus on solid Earth applications. | |||||

Objective | The goal of this course is to learn and understand few principal partial differential equations (conservation laws) that are applicable for analysing and modelling of any continuum including the Earth's mantle, core, atmosphere and ocean. By the end of the course, students should be able to write, explain and analyse the equations and apply them for simple analytical cases. Numerical solving of these equations will be discussed in the Numerical Modelling I and II course running in parallel. | |||||

Content | A provisional week-by-week schedule (subject to change) is as follows: Week 1: The continuity equation Theory: Definition of a geological media as a continuum. Field variables used for the representation of a continuum.Methods for definition of the field variables. Eulerian and Lagrangian points of view. Continuity equation in Eulerian and Lagrangian forms and their derivation. Advective transport term. Continuity equation for an incompressible fluid. Exercise: Computing the divergence of velocity field. Week 2: Density and gravity Theory: Density of rocks and minerals. Thermal expansion and compressibility. Dependence of density on pressure and temperature. Equations of state. Poisson equation for gravitational potential and its derivation. Exercise: Computing density, thermal expansion and compressibility from an equation of state. Week 3: Stress and strain Theory: Deformation and stresses. Definition of stress, strain and strain-rate tensors. Deviatoric stresses. Mean stress as a dynamic (nonlithostatic) pressure. Stress and strain rate invariants. Exercise: Analysing strain rate tensor for solid body rotation. Week 4: The momentum equation Theory: Momentum equation. Viscosity and Newtonian law of viscous friction. Navier-–Stokes equation for the motion of a viscous fluid. Stokes equation of slow laminar flow of highly viscous incompressible fluid and its application to geodynamics. Simplification of the Stokes equation in case of constant viscosity and its relation to the Poisson equation. Exercises: Computing velocity for magma flow in a channel. Week 5: Viscous rheology of rocks Theory: Solid-state creep of minerals and rocks as themajor mechanism of deformation of the Earth’s interior. Dislocation and diffusion creep mechanisms. Rheological equations for minerals and rocks. Effective viscosity and its dependence on temperature, pressure and strain rate. Formulation of the effective viscosity from empirical flow laws. Exercise: Deriving viscous rheological equations for computing effective viscosities from empirical flow laws. Week 6: The heat conservation equation Theory: Fourier’s law of heat conduction. Heat conservation equation and its derivation. Radioactive, viscous and adiabatic heating and their relative importance. Heat conservation equation for the case of a constant thermal conductivity and its relation to the Poisson equation. Exercise: steady temperature profile in case of channel flow. Week 7: Elasticity and plasticity Theory: Elastic rheology. Maxwell viscoelastic rheology. Plastic rheology. Plastic yielding criterion. Plastic flow potential. Plastic flow rule. GRADING will be based on honeworks (30%) and oral exams (70%). Exam questions: http://www.erdw.ethz.ch/people/geophysics/tgerya/EXAM_QUESTIONS | |||||

Lecture notes | Script is available by request to taras.gerya@erdw.ethz.ch Exam questions: http://www.erdw.ethz.ch/people/geophysics/tgerya/EXAM_QUESTIONS | |||||

Literature | Taras Gerya Introduction to Numerical Geodynamic Modelling Cambridge University Press, 2010 | |||||

Geophysics: Subject 2 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4241-00L | Numerical Modelling I and II: Theory and Applications | W | 6 credits | 4G | T. Gerya | |

Abstract | In this 13-week sequence, students learn how to write programs from scratch to solve partial differential equations that are useful for Earth science applications. Programming will be done in MATLAB and will use the finite-difference method and marker-in-cell technique. The course will emphasise a hands-on learning approach rather than extensive theory. | |||||

Objective | The goal of this course is for students to learn how to program numerical applications from scratch. By the end of the course, students should be able to write state-of-the-art MATLAB codes that solve systems of partial-differential equations relevant to Earth and Planetary Science applications using finite-difference method and marker-in-cell technique. Applications include Poisson equation, buoyancy driven variable viscosity flow, heat diffusion and advection, and state-of-the-art thermomechanical code programming. The emphasis will be on commonality, i.e., using a similar approach to solve different applications, and modularity, i.e., re-use of code in different programs. The course will emphasise a hands-on learning approach rather than extensive theory, and will begin with an introduction to programming in MATLAB. | |||||

Content | A provisional week-by-week schedule (subject to change) is as follows: Week 1: Introduction to the finite difference approximation to differential equations. Introduction to programming in Matlab. Solving of 1D Poisson equation. Week 2: Direct and iterative methods for obtaining numerical solutions. Solving of 2D Poisson equation with direct method. Solving of 2D Poisson equation with Gauss-Seidel and Jacobi iterative methods. Week 3: Solving momentum and continuity equations in case of constant viscosity with stream function/vorticity formulation. Weeks 4: Staggered grid for formulating momentum and continuity equations. Indexing of unknowns. Solving momentum and continuity equations in case of constant viscosity using pressure-velocity formulation with staggered grid. Weeks 5: Conservative finite differences for the momentum equation. "Free slip" and "no slip" boundary conditions. Solving momentum and continuity equations in case of variable viscosity using pressure-velocity formulation with staggered grid. Week 6: Advection in 1-D. Eulerian methods. Marker-in-cell method. Comparison of different advection methods and their accuracy. Week 7: Advection in 2-D with Marker-in-cell method. Combining flow calculation and advection for buoyancy driven flow. Week 8: "Free surface" boundary condition and "sticky air" approach. Free surface stabilization. Runge-Kutta schemes. Week 9: Solving 2D heat conservation equation in case of constant thermal conductivity with explicit and implicit approaches. Week 10: Solving 2D heat conservation equation in case of variable thermal conductivity with implicit approach. Temperature advection with markers. Creating thermomechanical code by combining mechanical solution for 2D buoyancy driven flow with heat diffusion and advection based on marker-in-cell approach. Week 11: Subgrid diffusion of temperature. Implementing subgrid diffusion to the thermomechanical code. Week 12: Implementation of radioactive, adiabatic and shear heating to the thermomechanical code. Week 13: Implementation of temperature-, pressure- and strain rate-dependent viscosity, temperature- and pressure-dependent density and temperature-dependent thermal conductivity to the thermomechanical code. Final project description. GRADING will be based on weekly programming homeworks (50%) and a term project (50%) to develop an application of their choice to a more advanced level. | |||||

Literature | Taras Gerya, Introduction to Numerical Geodynamic Modelling, Cambridge University Press 2010 | |||||

Geophysics: Subject 3 Offered in the spring semester | ||||||

Geophysics: Subject 4 Offered in the spring semester | ||||||

Geophysics: Subject 5 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4014-00L | Seismic Tomography | W | 3 credits | 2G | E. Kissling, T. Diehl | |

Abstract | Seismic tomography is the science of interpreting seismic measurements (seismograms) to derive information about the structure of the Earth. The subject of this course is the formal relationship existing between a seismic measurement and the nature of the Earth, or of certain regions of the Earth, and the ways to use it, to gain information about the Earth. | |||||

Objective | ||||||

Literature | Aki, K. and P. G. Richards, Quantitative Seismology, second edition, University Science Books, Sausalito, 2002. The most standard textbook in seismology, for grad students and advanced undergraduates. Dahlen, F. A. and J. Tromp, Theoretical Global Seismology, Princeton University Press, Princeton, 1998. A very good book, suited for advanced graduate students with a strong math background. Kennett B.L.N., The Seismic Wavefield. Volume I: Introduction and Theoretical Development (2001). Volume II: Interpretation of Seismograms on Regional and Global Scales (2002). Cambridge University Press. Lay, T. and T. C. Wallace, Modern Global Seismology, Academic Press, San Diego, 1995. A very basic seismology textbook. Chapters 2 through 4 provide a useful introduction to the contents of this course. Menke, W., Geophysical Data Analysis: Discrete Inverse Theory, revised edition, Academic Press, San Diego, 1989. A very complete textbook on inverse theory in geophysics. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes, Cambridge University Press. The art of scientific computing. Trefethen, L. N. and D. Bau III, Numerical Linear Algebra, Soc. for Ind. and Appl. Math., Philadelphia, 1997. A textbook on the numerical solution of large linear inverse problems, designed for advanced math undergraduates. | |||||

Geophysics: Subject 6 Offered in the spring semester | ||||||

Biology | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

636-0007-00L | Computational Systems Biology | W | 6 credits | 3V + 2U | J. Stelling | |

Abstract | Study of fundamental concepts, models and computational methods for the analysis of complex biological networks. Topics: Systems approaches in biology, biology and reaction network fundamentals, modeling and simulation approaches (topological, probabilistic, stoichiometric, qualitative, linear / nonlinear ODEs, stochastic), and systems analysis (complexity reduction, stability, identification). | |||||

Objective | The aim of this course is to provide an introductory overview of mathematical and computational methods for the modeling, simulation and analysis of biological networks. | |||||

Content | Biology has witnessed an unprecedented increase in experimental data and, correspondingly, an increased need for computational methods to analyze this data. The explosion of sequenced genomes, and subsequently, of bioinformatics methods for the storage, analysis and comparison of genetic sequences provides a prominent example. Recently, however, an additional area of research, captured by the label "Systems Biology", focuses on how networks, which are more than the mere sum of their parts' properties, establish biological functions. This is essentially a task of reverse engineering. The aim of this course is to provide an introductory overview of corresponding computational methods for the modeling, simulation and analysis of biological networks. We will start with an introduction into the basic units, functions and design principles that are relevant for biology at the level of individual cells. Making extensive use of example systems, the course will then focus on methods and algorithms that allow for the investigation of biological networks with increasing detail. These include (i) graph theoretical approaches for revealing large-scale network organization, (ii) probabilistic (Bayesian) network representations, (iii) structural network analysis based on reaction stoichiometries, (iv) qualitative methods for dynamic modeling and simulation (Boolean and piece-wise linear approaches), (v) mechanistic modeling using ordinary differential equations (ODEs) and finally (vi) stochastic simulation methods. | |||||

Lecture notes | Link | |||||

Literature | U. Alon, An introduction to systems biology. Chapman & Hall / CRC, 2006. Z. Szallasi et al. (eds.), System modeling in cellular biology. MIT Press, 2006. | |||||

636-0706-00L | Spatio-Temporal Modelling in Biology | W | 5 credits | 3G | D. Iber | |

Abstract | This course focuses on modeling spatio-temporal problems in biology, in particular on the cell and tissue level. A wide range of mathematical techniques will be presented as part of the course, including concepts from non-linear dynamics (ODE and PDE models), stochastic techniques (SDE, Master equations, Monte Carlo simulations), and thermodynamic descriptions. | |||||

Objective | The aim of the course is to introduce students to state-of-the-art mathematical modelling of spatio-temporal problems in biology. Students will learn how to chose from a wide range of modelling techniques and how to apply these to further our understanding of biological mechanisms. The course aims at equipping students with the tools and concepts to conduct successful research in this area; both classical as well as recent research work will be discussed. | |||||

Content | 1. Introduction to Modelling in Biology 2. Morphogen Gradients 3. Turing Pattern 4. Travelling Waves & Wave Pinning 5. Application Example 1: Dorso-ventral axis formation 6. Chemotaxis, Cell Adhesion & Migration 7. Introduction to Numerical Methods 8. Simulations on Growing Domains 9. Image-Based Modelling 10. Branching Processes 11. Cell-based Simulation Frameworks 12. Application Example 2: Limb Development 13. Summary | |||||

Lecture notes | All lecture material will be made available online Link | |||||

Literature | Murray, Mathematical Biology, Springer Forgacs and Newman, Biological Physics of the Developing Embryo, CUP Keener and Sneyd, Mathematical Physiology, Springer Fall et al, Computational Cell Biology, Springer Szallasi et al, System Modeling in Cellular Biology, MIT Press Wolkenhauer, Systems Biology Kreyszig, Engineering Mathematics, Wiley | |||||

Prerequisites / Notice | The course builds on introductory courses in Computational Biology. The course assumes no background in biology but a good foundation regarding mathematical and computational techniques. | |||||

Electives | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0113-00L | Applied Fluid Dynamics | W | 4 credits | 2V + 1U | J.‑P. Kunsch | |

Abstract | Applied Fluid Dynamics The methods of fluid dynamics play an important role in the description of a chain of events, involving the release, spreading and dilution of dangerous fluids in the environment. Tunnel ventilation systems and strategies are studied, which must meet severe requirements during normal operation and in emergency situations (tunnel fires etc.). | |||||

Objective | Generally applicable methods in fluid dynamics and gas dynamics are illustrated and practiced using selected current examples. | |||||

Content | Often experts fall back on the methodology of fluid dynamics when involved in the construction of environmentally friendly processing and incineration facilities, as well as when choosing safe transport and storage options for dangerous materials. As a result of accidents, but also in normal operations, dangerous gases and liquids may escape and be transported further by wind or flowing water. There are many possible forms that the resulting damage may take, including fire and explosion when flammable substances are mixed. The topics covered include: Emissions of liquids and gases from containers and pipelines, evaporation from pools and vaporization of gases kept under pressure, the spread and dilution of waste gas plumes in the wind, deflagration and detonation of inflammable gases, fireballs in gases held under pressure, pollution and exhaust gases in tunnels (tunnel fires etc.) | |||||

Lecture notes | not available | |||||

Prerequisites / Notice | Requirements: successful attendance at lectures "Fluiddynamik I und II", "Thermodynamik I und II" | |||||

151-0709-00L | Stochastic Methods for Engineers and Natural Scientists | W | 4 credits | 3G | D. W. Meyer-Massetti, N. Noiray | |

Abstract | The course provides an introduction into stochastic methods that are applicable for example for the description and modeling of turbulent and subsurface flows. Moreover, mathematical techniques are presented that are used to quantify uncertainty in various engineering applications. | |||||

Objective | By the end of the course you should be able to mathematically describe random quantities and their effect on physical systems. Moreover, you should be able to develop basic stochastic models of such systems. | |||||

Content | - Probability theory, single and multiple random variables, mappings of random variables - Stochastic differential equations, Ito calculus, PDF evolution equations - Polynomial chaos and other expansion methods All topics are illustrated with application examples from engineering. | |||||

Lecture notes | Detailed lecture notes will be provided. | |||||

Literature | Some textbooks related to the material covered in the course: Stochastic Methods: A Handbook for the Natural and Social Sciences, Crispin Gardiner, Springer, 2010 The Fokker-Planck Equation: Methods of Solutions and Applications, Hannes Risken, Springer, 1996 Turbulent Flows, S.B. Pope, Cambridge University Press, 2000 Spectral Methods for Uncertainty Quantification, O.P. Le Maitre and O.M. Knio, Springer, 2010 | |||||

151-0317-00L | Visualization, Simulation and Interaction - Virtual Reality II | W | 4 credits | 3G | A. Kunz | |

Abstract | This lecture provides deeper knowledge on the possible applications of virtual reality, its basic technolgy, and future research fields. The goal is to provide a strong knowledge on Virtual Reality for a possible future use in business processes. | |||||

Objective | Virtual Reality can not only be used for the visualization of 3D objects, but also offers a wide application field for small and medium enterprises (SME). This could be for instance an enabling technolgy for net-based collaboration, the transmission of images and other data, the interaction of the human user with the digital environment, or the use of augmented reality systems. The goal of the lecture is to provide a deeper knowledge of today's VR environments that are used in business processes. The technical background, the algorithms, and the applied methods are explained more in detail. Finally, future tasks of VR will be discussed and an outlook on ongoing international research is given. | |||||

Content | Introduction into Virtual Reality; basisc of augmented reality; interaction with digital data, tangible user interfaces (TUI); basics of simulation; compression procedures of image-, audio-, and video signals; new materials for force feedback devices; intorduction into data security; cryptography; definition of free-form surfaces; digital factory; new research fields of virtual reality | |||||

Lecture notes | The handout is available in German and English. | |||||

Prerequisites / Notice | Prerequisites: "Visualization, Simulation and Interaction - Virtual Reality I" is recommended. Didactical concept: The course consists of lectures and exercises. | |||||

151-0833-00L | Principles of Nonlinear Finite-Element-Methods | W | 5 credits | 2V + 2U | N. Manopulo, B. Berisha, P. Hora | |

Abstract | Most problems in engineering are of nonlinear nature. The nonlinearities are caused basically due to the nonlinear material behavior, contact conditions and instability of structures. The principles of the nonlinear Finite-Element-Method (FEM) will be introduced in the scope of this lecture for treating such problems. | |||||

Objective | The goal of the lecture is to provide the students with the fundamentals of the non linear Finite Element Method (FEM). The lecture focuses on the principles of the nonlinear Finite-Element-Method based on explicit and implicit formulations. Typical applications of the nonlinear Finite-Element-Methods are simulations of: - Crash - Collapse of structures - Materials in Biomechanics (soft materials) - General forming processes Special attention will be paid to the modeling of the nonlinear material behavior, thermo-mechanical processes and processes with large plastic deformations. The ability to independently create a virtual model which describes the complex non linear systems will be acquired through accompanying exercises. These will include the Matlab programming of important model components such as constitutive equations | |||||

Content | - Fundamentals of continuum mechanics to characterize large plastic deformations - Elasto-plastic material models - Updated-Lagrange (UL), Euler and combined Euler-Lagrange (ALE) approaches - FEM implementation of constitutive equations - Element formulations - Implicit and explicit FEM methods - FEM formulations of coupled thermo-mechanical problems - Modeling of tool contact and the influence of friction - Solvers and convergence - Modeling of crack propagation - Introduction of advanced FE-Methods | |||||

Lecture notes | yes | |||||

Literature | Bathe, K. J., Finite-Element-Procedures, Prentice-Hall, 1996 | |||||

Prerequisites / Notice | If we will have a large number of students, two dates for the exercises will be offered. | |||||

263-5001-00L | Introduction to Finite Elements and Sparse Linear System Solving | W | 4 credits | 2V + 1U | P. Arbenz | |

Abstract | The finite element (FE) method is the method of choice for (approximately) solving partial differential equations on complicated domains. In the first third of the lecture, we give an introduction to the method. The rest of the lecture will be devoted to methods for solving the large sparse linear systems of equation that a typical for the FE method. We will consider direct and iterative methods. | |||||

Objective | Students will know the most important direct and iterative solvers for sparse linear systems. They will be able to determine which solver to choose in particular situations. | |||||

Content | I. THE FINITE ELEMENT METHOD (1) Introduction, model problems. (2) 1D problems. Piecewise polynomials in 1D. (3) 2D problems. Triangulations. Piecewise polynomials in 2D. (4) Variational formulations. Galerkin finite element method. (5) Implementation aspects. II. DIRECT SOLUTION METHODS (6) LU and Cholesky decomposition. (7) Sparse matrices. (8) Fill-reducing orderings. III. ITERATIVE SOLUTION METHODS (9) Stationary iterative methods, preconditioning. (10) Preconditioned conjugate gradient method (PCG). (11) Incomplete factorization preconditioning. (12) Multigrid preconditioning. (13) Nonsymmetric problems (GMRES, BiCGstab). (14) Indefinite problems (SYMMLQ, MINRES). | |||||

Literature | [1] M. G. Larson, F. Bengzon: The Finite Element Method: Theory, Implementation, and Applications. Springer, Heidelberg, 2013. [2] H. Elman, D. Sylvester, A. Wathen: Finite elements and fast iterative solvers. OUP, Oxford, 2005. [3] Y. Saad: Iterative methods for sparse linear systems (2nd ed.). SIAM, Philadelphia, 2003. [4] T. Davis: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006. [5] H.R. Schwarz: Die Methode der finiten Elemente (3rd ed.). Teubner, Stuttgart, 1991. | |||||

Prerequisites / Notice | Prerequisites: Linear Algebra, Analysis, Computational Science. The exercises are made with Matlab. | |||||

263-3010-00L | Big Data | W | 6 credits | 2V + 2U + 1A | G. Fourny | |

Abstract | The key challenge of the information society is to turn data into information, information into knowledge, knowledge into value. This has become increasingly complex. Data comes in larger volumes, diverse shapes, from different sources. Data is more heterogeneous and less structured than forty years ago. Nevertheless, it still needs to be processed fast, with support for complex operations. | |||||

Objective | This combination of requirements, together with the technologies that have emerged in order to address them, is typically referred to as "Big Data." This revolution has led to a completely new way to do business, e.g., develop new products and business models, but also to do science -- which is sometimes referred to as data-driven science or the "fourth paradigm". Unfortunately, the quantity of data produced and available -- now in the Zettabyte range (that's 21 zeros) per year -- keeps growing faster than our ability to process it. Hence, new architectures and approaches for processing it were and are still needed. Harnessing them must involve a deep understanding of data not only in the large, but also in the small. The field of databases evolves at a fast pace. In order to be prepared, to the extent possible, to the (r)evolutions that will take place in the next few decades, the emphasis of the lecture will be on the paradigms and core design ideas, while today's technologies will serve as supporting illustrations thereof. After visiting this lecture, you should have gained an overview and understanding of the Big Data landscape, which is the basis on which one can make informed decisions, i.e., pick and orchestrate the relevant technologies together for addressing each business use case efficiently and consistently. | |||||

Content | This course gives an overview of database technologies and of the most important database design principles that lay the foundations of the Big Data universe. The material is organized along three axes: data in the large, data in the small, data in the very small. A broad range of aspects is covered with a focus on how they fit all together in the big picture of the Big Data ecosystem. - physical storage (HDFS, S3) - logical storage (key-value stores, document stores, column stores, key-value stores, data warehouses) - data formats and syntaxes (XML, JSON, CSV, XBRL) - data shapes and models (tables, trees, graphs, cubes) - an overview of programming languages with a focus on their type systems (SQL, XQuery, MDX) - the most important query paradigms (selection, projection, joining, grouping, ordering, windowing) - paradigms for parallel processing (MapReduce) and technologies (Hadoop, Spark) - optimization techniques (functional and declarative paradigms, query plans, rewrites, indexing) - applications. We will also host two guest lectures to get insights from the industry: UBS and Google. Large scale analytics and machine learning are outside of the scope of this course. | |||||

Literature | Papers from scientific conferences and journals. References will be given as part of the course material during the semester. | |||||

263-5200-00L | Data Mining: Learning from Large Data Sets | W | 4 credits | 2V + 1U | A. Krause | |

Abstract | Many scientific and commercial applications require insights from massive, high-dimensional data sets. This courses introduces principled, state-of-the-art techniques from statistics, algorithms and discrete and convex optimization for learning from such large data sets. The course both covers theoretical foundations and practical applications. | |||||

Objective | Many scientific and commercial applications require us to obtain insights from massive, high-dimensional data sets. In this graduate-level course, we will study principled, state-of-the-art techniques from statistics, algorithms and discrete and convex optimization for learning from such large data sets. The course will both cover theoretical foundations and practical applications. | |||||

Content | Topics covered: - Dealing with large data (Data centers; Map-Reduce/Hadoop; Amazon Mechanical Turk) - Fast nearest neighbor methods (Shingling, locality sensitive hashing) - Online learning (Online optimization and regret minimization, online convex programming, applications to large-scale Support Vector Machines) - Multi-armed bandits (exploration-exploitation tradeoffs, applications to online advertising and relevance feedback) - Active learning (uncertainty sampling, pool-based methods, label complexity) - Dimension reduction (random projections, nonlinear methods) - Data streams (Sketches, coresets, applications to online clustering) - Recommender systems | |||||

Prerequisites / Notice | Prerequisites: Solid basic knowledge in statistics, algorithms and programming. Background in machine learning is helpful but not required. | |||||

263-2800-00L | Design of Parallel and High-Performance Computing | W | 7 credits | 3V + 2U + 1A | T. Hoefler, M. Püschel | |

Abstract | Advanced topics in parallel / concurrent programming. | |||||

Objective | Understand concurrency paradigms and models from a higher perspective and acquire skills for designing, structuring and developing possibly large concurrent software systems. Become able to distinguish parallelism in problem space and in machine space. Become familiar with important technical concepts and with concurrency folklore. | |||||

263-3210-00L | Deep Learning Number of participants limited to 120. | W | 4 credits | 2V + 1U | T. Hofmann | |

Abstract | Deep learning is an area within machine learning that deals with algorithms and models that automatically induce multi-level data representations. | |||||

Objective | In recent years, deep learning and deep networks have significantly improved the state-of-the-art in many application domains such as computer vision, speech recognition, and natural language processing. This class will cover the fundamentals of deep learning and provide a rich set of hands-on tasks and practical projects to familiarize students with this emerging technology. | |||||

Prerequisites / Notice | The participation in the course is subject to the following conditions: 1) The number of participants is limited to 120 students (MSc and PhDs). 2) Students must have taken the exam in Machine Learning (252-0535-00) or have acquired equivalent knowledge. | |||||

227-0102-00L | Discrete Event Systems | W | 6 credits | 4G | L. Thiele, L. Vanbever, R. Wattenhofer | |

Abstract | Introduction to discrete event systems. We start out by studying popular models of discrete event systems. In the second part of the course we analyze discrete event systems from an average-case and from a worst-case perspective. Topics include: Automata and Languages, Specification Models, Stochastic Discrete Event Systems, Worst-Case Event Systems, Verification, Network Calculus. | |||||

Objective | Over the past few decades the rapid evolution of computing, communication, and information technologies has brought about the proliferation of new dynamic systems. A significant part of activity in these systems is governed by operational rules designed by humans. The dynamics of these systems are characterized by asynchronous occurrences of discrete events, some controlled (e.g. hitting a keyboard key, sending a message), some not (e.g. spontaneous failure, packet loss). The mathematical arsenal centered around differential equations that has been employed in systems engineering to model and study processes governed by the laws of nature is often inadequate or inappropriate for discrete event systems. The challenge is to develop new modeling frameworks, analysis techniques, design tools, testing methods, and optimization processes for this new generation of systems. In this lecture we give an introduction to discrete event systems. We start out the course by studying popular models of discrete event systems, such as automata and Petri nets. In the second part of the course we analyze discrete event systems. We first examine discrete event systems from an average-case perspective: we model discrete events as stochastic processes, and then apply Markov chains and queuing theory for an understanding of the typical behavior of a system. In the last part of the course we analyze discrete event systems from a worst-case perspective using the theory of online algorithms and adversarial queuing. | |||||

Content | 1. Introduction 2. Automata and Languages 3. Smarter Automata 4. Specification Models 5. Stochastic Discrete Event Systems 6. Worst-Case Event Systems 7. Network Calculus | |||||

Lecture notes | Available | |||||

Literature | [bertsekas] Data Networks Dimitri Bersekas, Robert Gallager Prentice Hall, 1991, ISBN: 0132009161 [borodin] Online Computation and Competitive Analysis Allan Borodin, Ran El-Yaniv. Cambridge University Press, 1998 [boudec] Network Calculus J.-Y. Le Boudec, P. Thiran Springer, 2001 [cassandras] Introduction to Discrete Event Systems Christos Cassandras, Stéphane Lafortune. Kluwer Academic Publishers, 1999, ISBN 0-7923-8609-4 [fiat] Online Algorithms: The State of the Art A. Fiat and G. Woeginger [hochbaum] Approximation Algorithms for NP-hard Problems (Chapter 13 by S. Irani, A. Karlin) D. Hochbaum [schickinger] Diskrete Strukturen (Band 2: Wahrscheinlichkeitstheorie und Statistik) T. Schickinger, A. Steger Springer, Berlin, 2001 [sipser] Introduction to the Theory of Computation Michael Sipser. PWS Publishing Company, 1996, ISBN 053494728X | |||||

227-0197-00L | Wearable Systems I | W | 6 credits | 4G | G. Tröster, U. Blanke | |

Abstract | Context recognition in mobile communication systems like mobile phone, smart watches and wearable computer will be studied using advanced methods from sensor data fusion, pattern recognition, statistics, data mining and machine learning. Context comprises the behavior of individuals and of groups, their activites as well as the local and social environment. | |||||

Objective | Using internal sensors and sensors in our environment including data from the wristwatch, bracelet or internet (crowd sourcing), our 'smart phone' detects our context continuously, e.g. where we are, what we are doing, with whom we are together, what is our constitution, what are our needs. Based on this information our 'smart phone' offers us the appropriate services like a personal assistant.Context comprises user's behavior, his activities, his local and social environment. In the data path from the sensor level to signal segmentation to the classification of the context, advanced methods of signal processing, pattern recognition and machine learning will be applied. Sensor data generated by crowdsouring methods are integrated. The validation using MATLAB is followed by implementation and testing on a smart phone. Context recognition as the crucial function of mobile systems is the main focus of the course. Using MatLab the participants implement and verify the discussed methods also using a smart phone. | |||||

Content | Using internal sensors and sensors in our environment including data from the wristwatch, bracelet or internet (crowd sourcing), our 'smart phone' detects our context continuously, e.g. where we are, what we are doing, with whom we are together, what is our constitution, what are our needs. Based on this information our 'smart phone' offers us the appropriate services like a personal assistant. Context recognition - what is the situation of the user, his activity, his environment, how is he doing, what are his needs - as the central functionality of mobile systems constitutes the focus of the course. The main topics of the course include Sensor nets, sensor signal processing, data fusion, time series (segmentation, similariy measures), supervised learning (Bayes Decision Theory, Decision Trees, Random Forest, kNN-Methods, Support Vector Machine, Adaboost, Deep Learning), clustering (k-means, dbscan, topic models), Recommender Systems, Collaborative Filtering, Crowdsourcing. The exercises show concrete design problems like motion and gesture recognition using distributed sensors, detection of activity patterns and identification of the local environment. Presentations of the PhD students and the visit at the Wearable Computing Lab introduce in current research topics and international research projects. Language: german/english (depending on the participants) | |||||

Lecture notes | Lecture notes for all lessons, assignments and solutions. http://www.ife.ee.ethz.ch/education/wearable_systems_1 | |||||

Literature | Literature will be announced during the lessons. | |||||

Prerequisites / Notice | No special prerequisites | |||||

227-0447-00L | Image Analysis and Computer Vision | W | 6 credits | 3V + 1U | L. Van Gool, O. Göksel, E. Konukoglu | |

Abstract | Light and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition. | |||||

Objective | Overview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises. | |||||

Content | The first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed. | |||||

Lecture notes | Course material Script, computer demonstrations, exercises and problem solutions | |||||

Prerequisites / Notice | Prerequisites: Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C. The course language is English. | |||||

227-0417-00L | Information Theory I | W | 6 credits | 4G | A. Lapidoth | |

Abstract | This course covers the basic concepts of information theory and of communication theory. Topics covered include the entropy rate of a source, mutual information, typical sequences, the asymptotic equi-partition property, Huffman coding, channel capacity, the channel coding theorem, the source-channel separation theorem, and feedback capacity. | |||||

Objective | The fundamentals of Information Theory including Shannon's source coding and channel coding theorems | |||||

Content | The entropy rate of a source, Typical sequences, the asymptotic equi-partition property, the source coding theorem, Huffman coding, Arithmetic coding, channel capacity, the channel coding theorem, the source-channel separation theorem, feedback capacity | |||||

Literature | T.M. Cover and J. Thomas, Elements of Information Theory (second edition) | |||||

227-0427-00L | Signal and Information Processing: Modeling, Filtering, Learning | W | 6 credits | 4G | H.‑A. Loeliger | |

Abstract | Fundamentals in signal processing, detection/estimation, and machine learning. I. Linear signal representation and approximation: Hilbert spaces, LMMSE estimation, regularization and sparsity. II. Learning linear and nonlinear functions and filters: kernel methods, neural networks. III. Structured statistical models: hidden Markov models, factor graphs, Kalman filter, parameter estimation. | |||||

Objective | The course is an introduction to some basic topics in signal processing, detection/estimation theory, and machine learning. | |||||

Content | Part I - Linear Signal Representation and Approximation: Hilbert spaces, least squares and LMMSE estimation, projection and estimation by linear filtering, learning linear functions and filters, L2 regularization, L1 regularization and sparsity, singular-value decomposition and pseudo-inverse, principal-components analysis. Part II - Learning Nonlinear Functions: fundamentals of learning, neural networks, kernel methods. Part III - Structured Statistical Models and Message Passing Algorithms: hidden Markov models, factor graphs, Gaussian message passing, Kalman filter and recursive least squares, Monte Carlo methods, parameter estimation, expectation maximisation, sparse Bayesian learning. | |||||

Lecture notes | Lecture notes. | |||||

Prerequisites / Notice | Prerequisites: - local bachelors: course "Discrete-Time and Statistical Signal Processing" (5. Sem.) - others: solid basics in linear algebra and probability theory | |||||

227-0627-00L | Applied Computer Architecture | W | 6 credits | 4G | A. Gunzinger | |

Abstract | This lecture gives an overview of the requirements and the architecture of parallel computer systems, performance, reliability and costs. | |||||

Objective | Understand the function, the design and the performance modeling of parallel computer systems. | |||||

Content | The lecture "Applied Computer Architecture" gives technical and corporate insights in the innovative Computer Systems/Architectures (CPU, GPU, FPGA, special processors) and their real implementations and applications. Often the designs have to deal with technical limits. Which computer architecture allows the control of the over 1000 magnets at the Swiss Light Source (SLS)? Which architecture is behind the alarm center of the Swiss Railway (SBB)? Which computer architectures are applied for driver assistance systems? Which computer architecture is hidden behind a professional digital audio mixing desk? How can data streams of about 30 TB/s, produced by a protone accelerator, be processed in real time? Can the weather forecast also be processed with GPUs? How can a good computer architecture be found? Which are the driving factors in succesful computer architecture design? | |||||

Lecture notes | Script and exercices sheets. | |||||

Prerequisites / Notice | Prerequisites: Basics of computer architecture. | |||||

252-0237-00L | Concepts of Object-Oriented Programming | W | 6 credits | 3V + 2U | P. Müller | |

Abstract | Course that focuses on an in-depth understanding of object-oriented programming and compares designs of object-oriented programming languages. Topics include different flavors of type systems, inheritance models, encapsulation in the presence of aliasing, object and class initialization, program correctness, reflection | |||||

Objective | After this course, students will: Have a deep understanding of advanced concepts of object-oriented programming and their support through various language features. Be able to understand language concepts on a semantic level and be able to compare and evaluate language designs. Be able to learn new languages more rapidly. Be aware of many subtle problems of object-oriented programming and know how to avoid them. | |||||

Content | The main goal of this course is to convey a deep understanding of the key concepts of sequential object-oriented programming and their support in different programming languages. This is achieved by studying how important challenges are addressed through language features and programming idioms. In particular, the course discusses alternative language designs by contrasting solutions in languages such as C++, C#, Eiffel, Java, Python, and Scala. The course also introduces novel ideas from research languages that may influence the design of future mainstream languages. The topics discussed in the course include among others: The pros and cons of different flavors of type systems (for instance, static vs. dynamic typing, nominal vs. structural, syntactic vs. behavioral typing) The key problems of single and multiple inheritance and how different languages address them Generic type systems, in particular, Java generics, C# generics, and C++ templates The situations in which object-oriented programming does not provide encapsulation, and how to avoid them The pitfalls of object initialization, exemplified by a research type system that prevents null pointer dereferencing How to maintain the consistency of data structures | |||||

Literature | Will be announced in the lecture. | |||||

Prerequisites / Notice | Prerequisites: Mastering at least one object-oriented programming language (this course will NOT provide an introduction to object-oriented programming); programming experience | |||||

252-0417-00L | Randomized Algorithms and Probabilistic Methods | W | 7 credits | 3V + 2U + 1A | A. Steger, E. Welzl | |

Abstract | Las Vegas & Monte Carlo algorithms; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks | |||||

Objective | After this course students will know fundamental techniques from probabilistic combinatorics for designing randomized algorithms and will be able to apply them to solve typical problems in these areas. | |||||

Content | Randomized Algorithms are algorithms that "flip coins" to take certain decisions. This concept extends the classical model of deterministic algorithms and has become very popular and useful within the last twenty years. In many cases, randomized algorithms are faster, simpler or just more elegant than deterministic ones. In the course, we will discuss basic principles and techniques and derive from them a number of randomized methods for problems in different areas. | |||||

Lecture notes | Yes. | |||||

Literature | - Randomized Algorithms, Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press (1995) - Probability and Computing, Michael Mitzenmacher and Eli Upfal, Cambridge University Press (2005) | |||||

252-0546-00L | Physically-Based Simulation in Computer Graphics | W | 4 credits | 2V + 1U | B. Solenthaler, B. Thomaszewski | |

Abstract | This lecture provides an introduction to physically-based animation in computer graphics and gives an overview of fundamental methods and algorithms. The practical exercises include three assignments which are to be solved in small groups. In an addtional course project, topics from the lecture will be implemented into a 3D game or a comparable application. | |||||

Objective | This lecture provides an introduction to physically-based animation in computer graphics and gives an overview of fundamental methods and algorithms. The practical exercises include three assignments which are to be solved in small groups. In an addtional course project, topics from the lecture will be implemented into a 3D game or a comparable application. | |||||

Content | The lecture covers topics in physically-based modeling, such as particle systems, mass-spring models, finite difference and finite element methods. These approaches are used to represent and simulate deformable objects or fluids with applications in animated movies, 3D games and medical systems. Furthermore, the lecture covers topics such as rigid body dynamics, collision detection, and character animation. | |||||

Prerequisites / Notice | Fundamentals of calculus and physics, basic concepts of algorithms and data structures, basic programming skills in C++. Knowledge on numerical mathematics as well as ordinary and partial differential equations is an asset, but not required. | |||||

401-3611-00L | Advanced Topics in Computational StatisticsDoes not take place this semester. | W | 4 credits | 2V | M. H. Maathuis | |

Abstract | This lecture covers selected advanced topics in computational statistics, including various classification methods, the EM algorithm, clustering, handling missing data, and graphical modelling. | |||||

Objective | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||

Content | The course is roughly divided in three parts: (1) Supervised learning via (variations of) nearest neighbor methods, (2) the EM algorithm and clustering, (3) handling missing data and graphical models. | |||||

Lecture notes | Lecture notes. | |||||

Prerequisites / Notice | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||

401-3627-00L | High-Dimensional StatisticsDoes not take place this semester. | W | 4 credits | 2V | P. L. Bühlmann | |

Abstract | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||

Objective | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||

Content | Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling | |||||

Literature | Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2. | |||||

Prerequisites / Notice | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||

401-4623-00L | Time Series Analysis | W | 6 credits | 3G | N. Meinshausen | |

Abstract | Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R. | |||||

Objective | Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R. | |||||

Content | This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R. | |||||

Lecture notes | Not available | |||||

Literature | A list of references will be distributed during the course. | |||||

Prerequisites / Notice | Basic knowledge in probability and statistics | |||||

401-3901-00L | Mathematical Optimization | W | 11 credits | 4V + 2U | R. Weismantel | |

Abstract | Mathematical treatment of diverse optimization techniques. | |||||

Objective | Advanced optimization theory and algorithms. | |||||

Content | 1. 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. | |||||

401-3640-66L | Monte Carlo and Quasi-Monte Carlo Methods: Mathematical and Numerical Analysis Number of participants limited to 6. | W | 4 credits | 2S | C. Schwab | |

Abstract | Introduction and current research topics in the theory and implementation of Monte Carlo and quasi-Monte Carlo methods and applications. | |||||

Objective | ||||||

Prerequisites / Notice | Prerequisites: Completed courses Numerical Analysis of Elliptic/ Parabolic PDEs, or Numerical Analysis of Hyperbolic PDEs, or Numerical Analysis of Stochastic ODEs, and FAI, Probability Theory I. | |||||

402-0777-00L | Particle Accelerator Physics and Modeling I | W | 6 credits | 2V + 1U | A. Adelmann | |

Abstract | This is the first of two courses, introducing particle accelerators from a theoretical point of view and covers state-of-the-art modeling techniques. It emphasizes the multidisciplinary aspect of the field, both in methodology (numerical and computational methods) and with regard to applications such as medical, industrial, material research and particle physics. | |||||

Objective | You understand the building blocks of particle accelerators. Modern analysis tools allows you to model state-of-the art particle accelerators. In some of the exercises you will be confronted with next generation machines. We will develop a Python simulation tool (AcceLEGOrator) that reflects the theory from the lecture. | |||||

Content | Here is the rough plan of the topics, however the actual pace may vary relative to this plan. - Particle Accelerators an Overview - Relativity for Accelerator Physicists - Building Blocks of Particle Accelerators - Lie Algebraic Structure of Classical Mechanics and Applications to Particle Accelerators - Symplectic Maps & Analysis of Maps - Particle Tracking - Linear & Circular Machines - Cyclotrons - Free Electron Lasers - Collective effects in linear approximation - Preview of Particle Accelerator Physics and Modeling II | |||||

Literature | Particle Accelerator Physics, H. Wiedemann, ISBN-13 978-3-540-49043-2, Springer Theory and Design of Charged Particle Beams, M. Reiser, ISBN 0-471-30616-9, Wiley-VCH | |||||

Prerequisites / Notice | Physics, Computational Science (RW) at BSc. Level This lecture is also suited for PhD. students | |||||

227-1033-00L | Neuromorphic Engineering I Registration in this class requires the permission of the instructors. Class size will be limited to available lab spots. Preference is given to students that require this class as part of their major. | W | 6 credits | 2V + 3U | T. Delbrück, G. Indiveri, S.‑C. Liu | |

Abstract | This course covers analog circuits with emphasis on neuromorphic engineering: MOS transistors in CMOS technology, static circuits, dynamic circuits, systems (silicon neuron, silicon retina, silicon cochlea) with an introduction to multi-chip systems. The lectures are accompanied by weekly laboratory sessions. | |||||

Objective | Understanding of the characteristics of neuromorphic circuit elements. | |||||

Content | Neuromorphic circuits are inspired by the organizing principles of biological neural circuits. Their computational primitives are based on physics of semiconductor devices. Neuromorphic architectures often rely on collective computation in parallel networks. Adaptation, learning and memory are implemented locally within the individual computational elements. Transistors are often operated in weak inversion (below threshold), where they exhibit exponential I-V characteristics and low currents. These properties lead to the feasibility of high-density, low-power implementations of functions that are computationally intensive in other paradigms. Application domains of neuromorphic circuits include silicon retinas and cochleas for machine vision and audition, real-time emulations of networks of biological neurons, and the development of autonomous robotic systems. This course covers devices in CMOS technology (MOS transistor below and above threshold, floating-gate MOS transistor, phototransducers), static circuits (differential pair, current mirror, transconductance amplifiers, etc.), dynamic circuits (linear and nonlinear filters, adaptive circuits), systems (silicon neuron, silicon retina and cochlea) and an introduction to multi-chip systems that communicate events analogous to spikes. The lectures are accompanied by weekly laboratory sessions on the characterization of neuromorphic circuits, from elementary devices to systems. | |||||

Literature | S.-C. Liu et al.: Analog VLSI Circuits and Principles; various publications. | |||||

Prerequisites / Notice | Particular: The course is highly recommended for those who intend to take the spring semester course 'Neuromorphic Engineering II', that teaches the conception, simulation, and physical layout of such circuits with chip design tools. Prerequisites: Background in basics of semiconductor physics helpful, but not required. | |||||

227-1037-00L | Introduction to Neuroinformatics | W | 6 credits | 2V + 1U | K. A. Martin, M. Cook, V. Mante, M. Pfeiffer | |

Abstract | The course provides an introduction to the functional properties of neurons. Particularly the description of membrane electrical properties (action potentials, channels), neuronal anatomy, synaptic structures, and neuronal networks. Simple models of computation, learning, and behavior will be explained. Some artificial systems (robot, chip) are presented. | |||||

Objective | Understanding computation by neurons and neuronal circuits is one of the great challenges of science. Many different disciplines can contribute their tools and concepts to solving mysteries of neural computation. The goal of this introductory course is to introduce the monocultures of physics, maths, computer science, engineering, biology, psychology, and even philosophy and history, to discover the enchantments and challenges that we all face in taking on this major 21st century problem and how each discipline can contribute to discovering solutions. | |||||

Content | This course considers the structure and function of biological neural networks at different levels. The function of neural networks lies fundamentally in their wiring and in the electro-chemical properties of nerve cell membranes. Thus, the biological structure of the nerve cell needs to be understood if biologically-realistic models are to be constructed. These simpler models are used to estimate the electrical current flow through dendritic cables and explore how a more complex geometry of neurons influences this current flow. The active properties of nerves are studied to understand both sensory transduction and the generation and transmission of nerve impulses along axons. The concept of local neuronal circuits arises in the context of the rules governing the formation of nerve connections and topographic projections within the nervous system. Communication between neurons in the network can be thought of as information flow across synapses, which can be modified by experience. We need an understanding of the action of inhibitory and excitatory neurotransmitters and neuromodulators, so that the dynamics and logic of synapses can be interpreted. Finally, the neural architectures of feedforward and recurrent networks will be discussed in the context of co-ordination, control, and integration of sensory and motor information in neural networks. | |||||

151-0104-00L | Uncertainty Quantification for Engineering & Life Sciences Does not take place this semester. Number of participants limited to 60. | W | 4 credits | 3G | P. Koumoutsakos | |

Abstract | Quantification of uncertainties in computational models pertaining to applications in engineering and life sciences. Exploitation of massively available data to develop computational models with quantifiable predictive capabilities. Applications of Uncertainty Quantification and Propagation to problems in mechanics, control, systems and cell biology. | |||||

Objective | The course will teach fundamental concept of Uncertainty Quantification and Propagation (UQ+P) for computational models of systems in Engineering and Life Sciences. Emphasis will be placed on practical and computational aspects of UQ+P including the implementation of relevant algorithms in multicore architectures. | |||||

Content | Topics that will be covered include: Uncertainty quantification under parametric and non-parametric modelling uncertainty, Bayesian inference with model class assessment, Markov Chain Monte Carlo simulation, prior and posterior reliability analysis. | |||||

Lecture notes | The class will be largely based on the book: Data Analysis: A Bayesian Tutorial by Devinderjit Sivia as well as on class notes and related literature that will be distributed in class. | |||||

Literature | 1. Data Analysis: A Bayesian Tutorial by Devinderjit Sivia 2. Probability Theory: The Logic of Science by E. T. Jaynes 3. Class Notes | |||||

Prerequisites / Notice | Fundamentals of Probability, Fundamentals of Computational Modeling | |||||

327-1201-00L | Transport Phenomena I | W | 4 credits | 4G | H. C. Öttinger | |

Abstract | Phenomenological approach to "Transport Phenomena" based on balance equations supplemented by thermodynamic considerations to formulate the undetermined fluxes in the local species mass, momentum, and energy balance equations; fundamentals, applications, and simulations | |||||

Objective | The teaching goals of this course are on five different levels: (1) Deep understanding of fundamentals: local balance equations, constitutive equations for fluxes, entropy balance, interfaces, idea of dimensionless numbers, ... (2) Ability to use the fundamental concepts in applications (3) Insight into the role of boundary conditions (4) Knowledge of a number of applications (5) Flavor of numerical techniques: finite elements, finite differences, lattice Boltzmann, Brownian dynamics, ... | |||||

Content | Approach to Transport Phenomena Diffusion Equation Brownian Dynamics Refreshing Topics in Equilibrium Thermodynamics Balance Equations Forces and Fluxes Measuring Transport Coefficients Pressure-Driven Flows Driven Separations Complex Fluids | |||||

Lecture notes | A detailed manuscript is provided; this manuscript will be developed into a book entitled "A Modern Course in Transport Phenomena" by David C. Venerus and Hans Christian Öttinger | |||||

Literature | 1. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd Ed. (Wiley, 2001) 2. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, 2nd Ed. (Dover, 1984) 3. W. M. Deen, Analysis of Transport Phenomena (Oxford University Press, 1998) 4. R. B. Bird, Five Decades of Transport Phenomena (Review Article), AIChE J. 50 (2004) 273-287 | |||||

Prerequisites / Notice | Complex numbers. Vector analysis (integrability; Gauss' divergence theorem). Laplace and Fourier transforms. Ordinary differential equations (basic ideas). Linear algebra (matrices; functions of matrices; eigenvectors and eigenvalues; eigenfunctions). Probability theory (Gaussian distributions; Poisson distributions; averages; moments; variances; random variables). Numerical mathematics (integration). Equilibrium thermodynamics (Gibbs' fundamental equation; thermodynamic potentials; Legendre transforms). Maxwell equations. Programming and simulation techniques (Matlab, Monte Carlo simulations). | |||||

» see also Fields of Specialization | ||||||

Case Studies | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3667-66L | Case Studies Seminar (Autumn Semester 2016) | W | 3 credits | 2S | V. C. Gradinaru, R. Hiptmair, M. Reiher | |

Abstract | In the CSE Case Studies Seminar invited speakers from ETH, from other universities as well as from industry give a talk on an applied topic. Beside of attending the scientific talks students are asked to give short presentations (10 minutes) on a published paper out of a list. | |||||

Objective | ||||||

Semester Paper There are several course units "Semester Paper" that are all equivalent. If, during your studies, you write several semester papers, choose among the different numbers in order to be able to obtain credits again. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3740-01L | Semester Paper No direct enrolment to this course unit in myStudies. Please fill in the online application form. Requirements and application form under www.math.ethz.ch/intranet/students/study-administration/theses.html (Afterwards the enrolment will be done by the Study Administration.) | W | 8 credits | 11A | Professors | |

Abstract | Semester Papers help to deepen the students' knowledge of a specific subject area. Students are offered a selection of topics. These papers serve to develop the students' ability for independent mathematical work as well as to enhance skills in presenting mathematical results in writing. | |||||

Objective | ||||||

Prerequisites / Notice | There are several course units "Semester Paper" that are all equivalent. If, during your studies, you write several semester papers, choose among the different numbers in order to be able to obtain credits again. | |||||

401-3740-02L | Semester Paper No direct enrolment to this course unit in myStudies. Please fill in the online application form. Requirements and application form under www.math.ethz.ch/intranet/students/study-administration/theses.html (Afterwards the enrolment will be done by the Study Administration.) | W | 8 credits | 11A | Professors | |

Abstract | Semester Papers help to deepen the students' knowledge of a specific subject area. Students are offered a selection of topics. These papers serve to develop the students' ability for independent mathematical work as well as to enhance skills in presenting mathematical results in writing. | |||||

Objective | ||||||

Prerequisites / Notice | There are several course units "Semester Paper" that are all equivalent. If, during your studies, you write several semester papers, choose among the different numbers in order to be able to obtain credits again. | |||||

GESS Science in Perspective | ||||||

» see Science in Perspective: Type A: Enhancement of Reflection Capability | ||||||

» see Science in Perspective: Language Courses ETH/UZH | ||||||

» Recommended Science in Perspective (Type B) for D-MATH. | ||||||

Master's Thesis | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-2000-00L | Scientific Works in Mathematics Target audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. Mandatory for all Bachelor and Master students with matriculation in the autumn semester 2014 or later. Directive Link | O | 0 credits | E. Kowalski | ||

Abstract | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | |||||

Objective | Learn the basic standards of scientific works in mathematics. | |||||

Content | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | |||||

Lecture notes | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | |||||

Prerequisites / Notice | This course is completed by the optional course "Recherchieren in der Mathematik" (held in German) by the Mathematics Library. For more details see: http://www.math.ethz.ch/library/services/schulungen | |||||

401-4990-01L | Master's Thesis Only students who fulfil the following criteria are allowed to begin with their master's thesis: a. successful completion of the bachelor programme; b. fulfilling of any additional requirements necessary to gain admission to the master programme. For Programme Regulations 2014 there are additional requirements. No direct enrolment to this course unit in myStudies. Please fill in the online application form. Requirements and application form under www.math.ethz.ch/intranet/students/study-administration/theses.html (Afterwards the enrolment will be done by the Study Administration.) | O | 30 credits | 57D | Professors | |

Abstract | The master's thesis concludes the study programme. Thesis work should prove the students' ability to independent, structured and scientific working. | |||||

Objective | Thesis work should prove the students' ability to independent, structured and scientific working. | |||||

Colloquia | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | E- | 0 credits | 2K | R. Abgrall, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |

Abstract | Research colloquium | |||||

Objective | ||||||

Course Units for Additional Admission Requirements The courses below are only available for MSc students with additional admission requirements. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0122-AAL | Fluid Dynamics for CSEEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 5 credits | 11R | T. Rösgen | |

Abstract | An introduction to the physical and mathematical foundations of fluid dynamics is given. Topics include dimensional analysis, integral and differential conservation laws, inviscid and viscous flows, Navier-Stokes equations, boundary layers, turbulent pipe flow. Elementary solutions and examples are presented. | |||||

Objective | An introduction to the physical and mathematical principles of fluid dynamics. Fundamental terminology/principles and their application to simple problems. | |||||

Content | Phänomene, Anwendungen, Grundfragen Dimensionsanalyse und Ähnlichkeit; Kinematische Beschreibung; Erhaltungssätze (Masse, Impuls, Energie), integrale und differentielle Formulierungen; Reibungsfreie Strömungen: Euler-Gleichungen, Stromfadentheorie, Satz von Bernoulli; Reibungsbehaftete Strömungen: Navier-Stokes-Gleichungen; Grenzschichten; Turbulenz | |||||

Lecture notes | Eine erweiterte Formelsammlung zur Vorlesung wird elektronisch zur Verfügung gestellt. | |||||

Literature | Empfohlenes Buch: Fluid Mechanics, P. Kundu & I. Cohen, Elsevier | |||||

Prerequisites / Notice | Performance Assessment: session examination Allowed aids: Textbook (free selection, list of assignments), list of formulars IFD, 8 Sheets (=4 Pages) own notes, calculator | |||||

406-0353-AAL | Analysis III Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 4 credits | 9R | M. Soner | |

Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | |||||

Objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations. | |||||

Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform | |||||

Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | |||||

Prerequisites / Notice | Up-to-date information about this course can be found at: http://www.math.ethz.ch/education/bachelor/lectures/hs2013/other/analysis3_itet | |||||

406-0603-AAL | Stochastics (Probability and Statistics)Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 4 credits | 9R | M. Kalisch | |

Abstract | Introduction to basic methods and fundamental concepts of statistics and probability theory for non-mathematicians. The concepts are presented on the basis of some descriptive examples. Learning the statistical program R for applying the acquired concepts will be a central theme. | |||||

Objective | The objective of this course is to build a solid fundament in probability and statistics. The student should understand some fundamental concepts and be able to apply these concepts to applications in the real world. Furthermore, the student should have a basic knowledge of the statistical programming language "R". | |||||

Content | From "Statistics for research" (online) Ch 1: The Role of Statistics Ch 2: Populations, Samples, and Probability Distributions Ch 3: Binomial Distributions Ch 6: Sampling Distribution of Averages Ch 7: Normal Distributions Ch 8: Student's t Distribution Ch 9: Distributions of Two Variables From "Introductory Statistics with R (online)" Ch 1: Basics Ch 2: The R Environment Ch 3: Probability and distributions Ch 4: Descriptive statistics and tables Ch 5: One- and two-sample tests Ch 6: Regression and correlation | |||||

Literature | - "Statistics for research" by S. Dowdy et. al. (3rd edition); Print ISBN: 9780471267355; Online ISBN: 9780471477433; DOI: 10.1002/0471477435 From within the ETH, this book is freely available online under: http://onlinelibrary.wiley.com/book/10.1002/0471477435 - "Introductory Statistics with R" by Peter Dalgaard; ISBN 978-0-387-79053-4; DOI: 10.1007/978-0-387-79054-1 From within the ETH, this book is freely available online under: http://www.springerlink.com/content/m17578/ | |||||

406-0663-AAL | Numerical Methods for CSEAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 7 credits | 15R | R. Hiptmair | |

Abstract | he course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The course focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods in C++. | |||||

Objective | * Knowledge of the fundamental algorithms in numerical mathematics * Knowledge of the essential terms in numerical mathematics and the techniques used for the analysis of numerical algorithms * Ability to choose the appropriate numerical method for concrete problems * Ability to interpret numerical results * Ability to implement numerical algorithms afficiently | |||||

Content | 1. Direct Methods for linear systems of equations 2. Least Squares Techniques 3. Data Interpolation and Fitting 4. Filtering Algorithms 8. Approximation of Functions 9. Numerical Quadrature 10. Iterative Methods for non-linear systems of equations 11. Single Step Methods for ODEs 12. Stiff Integrators | |||||

Lecture notes | Lecture materials (PDF documents and codes) will be made available to participants. | |||||

Literature | U. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011. A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000. W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006. M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 | |||||

Prerequisites / Notice | Solid knowledge about fundamental concepts and technques from linear algebra & calculus as taught in the first year of science and engineering curricula. The course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Familiarity with C++, object oriented and generic programming is an advantage. Participants of the course are expected to learn C++ by themselves. | |||||

252-0232-AAL | Software DesignAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 6 credits | 13R | D. Gruntz | |

Abstract | The course Software Design presents and discusses design patterns regularly used to solve problems in object oriented design and object oriented programming. The presented patterns are illustrated with examples from the Java libraries and are applied in a project. | |||||

Objective | The students - know the principles of object oriented programming and can apply these. - know the most important object oriented design patterns. - can apply design patterns to solve design problems. - discover in a given design the use of design patterns. | |||||

529-0483-AAL | Statistical Physics and Computer SimulationAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 4 credits | 9R | M. Reiher | |

Abstract | Principles and applications of statistical mechanics and equilibrium molecular dynamics, Monte Carlo simulation, Stochastic dynamics. Exercises using a MD simulation program to generate ensembles and subsequently calculate ensemble averages. | |||||

Objective | Introduction to statistical mechanics with the aid of computer simulation, development of skills to carry out statistical mechanical calculations using computers and interpret the results. | |||||

Content | Principles and applications of statistical mechanics and equilibrium molecular dynamics, Monte Carlo simulation, Stochastic dynamics. Exercises using a MD simulation program to generate ensembles and subsequently calculate ensemble averages. | |||||

Lecture notes | available | |||||

Literature | see "Course Schedule" | |||||

Prerequisites / Notice | additional information will be provided in the first lecture. |