Search result: Catalogue data in Spring Semester 2017
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Course units
Mathematics Master
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
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.
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.
406-2004-AAL Algebra II
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- 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 II
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.
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
Basic notions and examples of fields;
Field extensions, Algebraic extensions, Classical straight edge and compass constructions
Fundamentals of Galois theory
406-2284-AAL Measure and Integration
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 Analysis
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.
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
406-2554-AAL Topology
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)
Lynn Arthur Steen, J. Arthur Seebach Jr.: Counterexamples in Topology (Springer)
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.
406-2604-AAL Probability and Statistics
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.
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 I
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.
406-3621-AAL Fundamentals of Mathematical Statistics
E- 10 credits 21R F. Balabdaoui
Abstract The course covers the basics of inferential statistics.