# Search result: Catalogue data in Spring Semester 2017

Mathematics Master | ||||||

Additional Courses | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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402-0101-00L | The Zurich Physics Colloquium | E- | 0 credits | 1K | R. Renner, G. Aeppli, C. Anastasiou, N. Beisert, G. Blatter, S. Cantalupo, M. Carollo, C. Degen, G. Dissertori, K. Ensslin, T. Esslinger, J. Faist, M. Gaberdiel, G. M. Graf, R. Grange, J. Home, S. Huber, A. Imamoglu, P. Jetzer, S. Johnson, U. Keller, K. S. Kirch, S. Lilly, L. M. Mayer, J. Mesot, B. Moore, D. Pescia, A. Refregier, A. Rubbia, K. Schawinski, T. C. Schulthess, M. Sigrist, A. Vaterlaus, R. Wallny, A. Wallraff, W. Wegscheider, A. Zheludev, O. Zilberberg | |

Abstract | Research colloquium | |||||

Objective | ||||||

Prerequisites / Notice | Occasionally, talks may be delivered in German. | |||||

251-0100-00L | Computer Science Colloquium | E- | 0 credits | 2K | Lecturers | |

Abstract | Invited talks on the entire spectrum of Computer Science. External guests are welcome. A detailed program is published at the beginning of every semester. | |||||

Objective | ||||||

Content | Eingeladene Vorträge aus dem gesamten Bereich der Informatik, zu denen auch Auswärtige kostenlos eingeladen sind. Zu Semesterbeginn erscheint jeweils ein ausführliches Programm. | |||||

252-4202-00L | Seminar in Theoretical Computer Science | E- | 2 credits | 2S | E. Welzl, B. Gärtner, M. Hoffmann, J. Lengler, A. Steger, B. Sudakov | |

Abstract | Presentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates. | |||||

Objective | To get an overview of current research in the areas covered by the involved research groups. To present results from the literature. | |||||

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 | |

406-2004-AAL | Algebra IIEnrolment 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 | L. Halbeisen | |

Abstract | Galois theory and Representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | |||||

Objective | Introduction to fundamentals of Galois theory, and representation theory of finite groups and algebras | |||||

Content | Fundamentals of Galois theory Representation theory of finite groups and algebras | |||||

Literature | S. Lang, Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag I.R. Shafarevich, Basic notions of algebra, Springer verlag G. Mislin: Algebra I, vdf Hochschulverlag U. Stammbach: Algebra, in der Polybuchhandlung erhältlich I. Stewart: Galois Theory, Chapman Hall (2008) G. Wüstholz, Algebra, vieweg-Verlag, 2004 J-P. Serre, Linear representations of finite groups, Springer Verlag | |||||

Prerequisites / Notice | Algebra I | |||||

406-2005-AAL | Algebra I and IIEnrolment 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- | 12 credits | 26R | L. Halbeisen | |

Abstract | Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras. The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | |||||

Objective | ||||||

Content | Basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Group actions and applications Basic notions and examples of rings; Ring Homomorphisms, ideals, and quotient rings, rings of fractions Euclidean domains, Principal ideal domains, Unique factorization domains Basic notions and examples of fields; Field extensions, Algebraic extensions, Classical straight edge and compass constructions Fundamentals of Galois theory Representation theory of finite groups and algebras | |||||

Literature | S. Lang, Algebra, Springer Verlag B.L. van der Waerden: Algebra I und II, Springer Verlag I.R. Shafarevich, Basic notions of algebra, Springer verlag G. Mislin: Algebra I, vdf Hochschulverlag U. Stammbach: Algebra, in der Polybuchhandlung erhältlich I. Stewart: Galois Theory, Chapman Hall (2008) G. Wüstholz, Algebra, vieweg-Verlag, 2004 J-P. Serre, Linear representations of finite groups, Springer Verlag | |||||

406-2284-AAL | Measure and IntegrationEnrolment 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- | 6 credits | 13R | M. Schweizer | |

Abstract | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Objective | Basic acquaintance with the abstract theory of measure and integration | |||||

Content | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Lecture notes | no lecture notes | |||||

Literature | 1. P.R. Halmos, "Measure Theory", Springer 2. Extra material: Lecture Notes by Emmanuel Kowalski and Josef Teichmann from spring semester 2012, http://www.math.ethz.ch/~jteichma/measure-integral_120615.pdf 3. Extra material: P. Cannarsa & T. D'Aprile, "Lecture Notes on Measure Theory and Functional Analysis", http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf | |||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | |||||

406-2303-AAL | Complex AnalysisAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 6 credits | 13R | R. Pandharipande | |

Abstract | Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem. | |||||

Objective | ||||||

Literature | L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co. B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. R.Remmert: Theory of Complex Functions.. Springer Verlag E.Hille: Analytic Function Theory. AMS Chelsea Publication | |||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | |||||

406-2554-AAL | TopologyAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 6 credits | 13R | W. Werner | |

Abstract | Topological and metric spaces, continuity, connectedness, compactness, product and quotient spaces, separation axioms, quotient spaces, Baire category, homotopy, fundamental group, covering spaces. | |||||

Objective | Cover the basic notions of set-theoretic topology. | |||||

Lecture notes | See lecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-2554-00L/ | |||||

Literature | Klaus Jänich: Topologie (Springer) http://link.springer.com/book/10.1007/978-3-662-10575-7 Boto von Querenburg: Mengentheoretische Topologie (Springer) http://link.springer.com/book/10.1007/978-3-642-56860-2 Lynn Arthur Steen, J. Arthur Seebach Jr.: Counterexamples in Topology (Springer) http://link.springer.com/book/10.1007/978-1-4612-6290-9 Nicolas Bourbaki: Topologie Générale, chapitres 1 à 10 (Hermann, Paris) oder General Topology (Chapters 1-10) (Springer) Ryszard Engelking: General topology. Heldermann Verlag, Berlin, 1989. | |||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. | |||||

406-2604-AAL | Probability and StatisticsAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 7 credits | 15R | S. van de Geer | |

Abstract | Introduction to probability and statistics with many examples, based on chapters from the books "Probability and Random Processes" by G. Grimmett and D. Stirzaker and "Mathematical Statistics and Data Analysis" by J. Rice. | |||||

Objective | The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. In addition to a mathematically rigorous treatment, also an intuitive understanding and familiarity with the ideas behind the definitions are emphasized. Measure theory is not used systematically, but it should become clear why and where measure theory is needed. | |||||

Content | Probability: Chapters 1-5 (Probabilities and events, Discrete and continuous random variables, Generating functions) and Sections 7.1-7.5 (Convergence of random variables) from the book "Probability and Random Processes". Most of this material is also covered in Chap. 1-5 of "Mathematical Statistics and Data Analysis", on a slightly easier level. Statistics: Sections 8.1 - 8.5 (Estimation of parameters), 9.1 - 9.4 (Testing Hypotheses), 11.1 - 11.3 (Comparing two samples) from "Mathematical Statistics and Data Analysis". | |||||

Literature | Geoffrey Grimmett and David Stirzaker, Probability and Random Processes. 3rd Edition. Oxford University Press, 2001. John A. Rice, Mathematical Statistics and Data Analysis, 3rd edition. Duxbury Press, 2006. | |||||

406-3461-AAL | Functional Analysis IAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 10 credits | 21R | M. Struwe | |

Abstract | Baire category; Banach spaces and linear operators; Fundamental theorems: Open Mapping Theorem, Closed Range Theorem, Uniform Boundedness Principle, Hahn-Banach Theorem; Convexity; reflexive spaces; Spectral theory. | |||||

Objective | ||||||

Prerequisites / Notice | ||||||

406-3621-AAL | Fundamentals of Mathematical StatisticsAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 10 credits | 21R | F. Balabdaoui | |

Abstract | The course covers the basics of inferential statistics. | |||||

Objective |

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