Suchergebnis: Katalogdaten im Frühjahrssemester 2020
Informatik Bachelor | ||||||
Wahlfächer Es können auch Lehrveranstaltungen aus dem Master-Studiengang in Informatik gewählt werden. Es liegt in der Verantwortung der Studierenden, sicherzustellen, dass sie die Voraussetzungen für diese Lehrveranstaltungen erfüllen. | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|
252-0055-00L | Informationstheorie | W | 4 KP | 2V + 1U | L. Haug, J. M. Buhmann | |
Kurzbeschreibung | Die Vorlesung vermittelt die Grundlagen von Shannons Informations- und Codierungstheorie. Die wichtigsten Themen sind: Entropie, Information, Datenkompression, Kanalcodierung, Codes. | |||||
Lernziel | Ziel der Vorlesung ist es, sowohl mit den theoretischen Grundlagen der Informationstheorie vertraut zu machen, als auch den praktischen Einsatz der Theorie anhand ausgewählter Beispiele aus der Datenkompression und -codierung zu illustrieren. | |||||
Inhalt | Einführung und Motivation, Grundlagen der Wahrscheinlichkeitstheorie, Entropie und Information, Kraft-Ungleichung, Schranken für die erwartete Länge von Quellcodes, Huffman-Codierung, asympotische Äquipartitionseigenschaft und typische Sequenzen, Shannons Quellcodierungstheorem, Kanalkapazität und Kanalcodierung, Shannons Kanalcodierungstheorem, Beispiele | |||||
Literatur | T. Cover, J. Thomas: Elements of Information Theory, John Wiley, 1991. D. MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003. C. Shannon, The Mathematical Theory of Communication, 1948. | |||||
252-0820-00L | Case Studies from Practice | W | 4 KP | 2V + 1U | M. Brandis | |
Kurzbeschreibung | The course is designed to provide students with an understanding of "real-life" computer science challenges in business settings and teach them how to address these. | |||||
Lernziel | By using case studies that are based on actual IT projects, students will learn how to deal with complex, not straightforward problems. It will help them to apply their theoretical Computer Science background in practice and will teach them fundamental principles of IT management and challenges with IT in practice. A particular focus is to make the often imprecise and fuzzy problems in practice accessible to factual analysis and reasoning, and to challenge "common wisdom" and hearsay. | |||||
Inhalt | The course consists of multiple lectures on methods to systematically analyze problems in a business setting and communicate about them as well as about IT management and IT economics, presented by the lecturer, and a number of case studies provided by guest lecturers from either IT companies or IT departments of a diverse range of companies. Students will obtain insights into both established and startup companies, small and big, and different industries. Presenting companies have included avaloq, Accenture, AdNovum, Bank Julius Bär, Credit Suisse, Deloitte, HP, Hotelcard, IBM Research, McKinsey & Company, Open Web Technology, SAP Research, Selfnation, SIX Group, Teralytics, 28msec, Zühlke and dormakaba, and Marc Brandis Strategic Consulting. The participating companies in spring 2019 will be announced at course start. | |||||
Voraussetzungen / Besonderes | Participants should be aware that the provided documents supporting the cases are usually taken directly from the projects and companies being addressed, and thus differ very much in terms of presentation style, terminology, and explicitly provided contextual information. Earlier participants have found it difficult to solve the exercises completely and to fully grasp the contents taught in the cases, if they were not able to attend the case presentation, and were just relying on the provided documents. | |||||
151-0116-10L | High Performance Computing for Science and Engineering (HPCSE) for Engineers II | W | 4 KP | 4G | P. Koumoutsakos, S. M. Martin | |
Kurzbeschreibung | This course focuses on programming methods and tools for parallel computing on multi and many-core architectures. Emphasis will be placed on practical and computational aspects of Uncertainty Quantification and Propagation including the implementation of relevant algorithms on HPC architectures. | |||||
Lernziel | The course will teach - programming models and tools for multi and many-core architectures - fundamental concepts of Uncertainty Quantification and Propagation (UQ+P) for computational models of systems in Engineering and Life Sciences | |||||
Inhalt | High Performance Computing: - Advanced topics in shared-memory programming - Advanced topics in MPI - GPU architectures and CUDA programming Uncertainty Quantification: - Uncertainty quantification under parametric and non-parametric modeling uncertainty - Bayesian inference with model class assessment - Markov Chain Monte Carlo simulation | |||||
Skript | Link Class notes, handouts | |||||
Literatur | - Class notes - Introduction to High Performance Computing for Scientists and Engineers, G. Hager and G. Wellein - CUDA by example, J. Sanders and E. Kandrot - Data Analysis: A Bayesian Tutorial, D. Sivia and J. Skilling - An introduction to Bayesian Analysis - Theory and Methods, J. Gosh, N. Delampady and S. Tapas - Bayesian Data Analysis, A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari and D. Rubin - Machine Learning: A Bayesian and Optimization Perspective, S. Theodorides | |||||
Voraussetzungen / Besonderes | Students must be familiar with the content of High Performance Computing for Science and Engineering I (151-0107-20L) | |||||
401-0674-00L | Numerical Methods for Partial Differential Equations Nicht für Studierende BSc/MSc Mathematik | W | 10 KP | 2G + 2U + 2P + 4A | R. Hiptmair | |
Kurzbeschreibung | Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library. | |||||
Lernziel | Main skills to be acquired in this course: * Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages. | |||||
Inhalt | 1 Second-Order Scalar Elliptic Boundary Value Problems 1.2 Equilibrium Models: Examples 1.3 Sobolev spaces 1.4 Linear Variational Problems 1.5 Equilibrium Models: Boundary Value Problems 1.6 Diffusion Models (Stationary Heat Conduction) 1.7 Boundary Conditions 1.8 Second-Order Elliptic Variational Problems 1.9 Essential and Natural Boundary Conditions 2 Finite Element Methods (FEM) 2.2 Principles of Galerkin Discretization 2.3 Case Study: Linear FEM for Two-Point Boundary Value Problems 2.4 Case Study: Triangular Linear FEM in Two Dimensions 2.5 Building Blocks of General Finite Element Methods 2.6 Lagrangian Finite Element Methods 2.7 Implementation of Finite Element Methods 2.7.1 Mesh Generation and Mesh File Format 2.7.2 Mesh Information and Mesh Data Structures 2.7.2.1 L EHR FEM++ Mesh: Container Layer 2.7.2.2 L EHR FEM++ Mesh: Topology Layer 2.7.2.3 L EHR FEM++ Mesh: Geometry Layer 2.7.3 Vectors and Matrices 2.7.4 Assembly Algorithms 2.7.4.1 Assembly: Localization 2.7.4.2 Assembly: Index Mappings 2.7.4.3 Distribute Assembly Schemes 2.7.4.4 Assembly: Linear Algebra Perspective 2.7.5 Local Computations 2.7.5.1 Analytic Formulas for Entries of Element Matrices 2.7.5.2 Local Quadrature 2.7.6 Treatment of Essential Boundary Conditions 2.8 Parametric Finite Element Methods 3 FEM: Convergence and Accuracy 3.1 Abstract Galerkin Error Estimates 3.2 Empirical (Asymptotic) Convergence of Lagrangian FEM 3.3 A Priori (Asymptotic) Finite Element Error Estimates 3.4 Elliptic Regularity Theory 3.5 Variational Crimes 3.6 FEM: Duality Techniques for Error Estimation 3.7 Discrete Maximum Principle 3.8 Validation and Debugging of Finite Element Codes 4 Beyond FEM: Alternative Discretizations [dropped] 5 Non-Linear Elliptic Boundary Value Problems [dropped] 6 Second-Order Linear Evolution Problems 6.1 Time-Dependent Boundary Value Problems 6.2 Parabolic Initial-Boundary Value Problems 6.3 Linear Wave Equations 7 Convection-Diffusion Problems [dropped] 8 Numerical Methods for Conservation Laws 8.1 Conservation Laws: Examples 8.2 Scalar Conservation Laws in 1D 8.3 Conservative Finite Volume (FV) Discretization 8.4 Timestepping for Finite-Volume Methods 8.5 Higher-Order Conservative Finite-Volume Schemes | |||||
Skript | The lecture will be taught in flipped classroom format: - Video tutorials for all thematic units will be published online. - Tablet notes accompanying the videos will be made available to the audience as PDF. - A comprehensive lecture document will cover all aspects of the course. | |||||
Literatur | Chapters of the following books provide supplementary reading (detailed references in course material): * D. Braess: Finite Elemente, Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online). * S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online). * A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004. * Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007. * W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992. * P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002. However, study of supplementary literature is not important for for following the course. | |||||
Voraussetzungen / Besonderes | Mastery of basic calculus and linear algebra is taken for granted. Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential. Important: Coding skills and experience in C++ are essential. Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks. |
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