Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

Search result: Catalogue data in Spring Semester 2017

Mathematics Master Information
Additional Courses
NumberTitleTypeECTSHoursLecturers
402-0101-00LThe Zurich Physics Colloquium Information E-0 credits1KR. 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
AbstractResearch colloquium
Objective
Prerequisites / NoticeOccasionally, talks may be delivered in German.
251-0100-00LComputer Science Colloquium Information E-0 credits2KLecturers
AbstractInvited talks on the entire spectrum of Computer Science. External guests are welcome. A detailed program is published at the beginning of every semester.
Objective
ContentEingeladene Vorträge aus dem gesamten Bereich der Informatik, zu denen auch Auswärtige kostenlos eingeladen sind. Zu Semesterbeginn erscheint jeweils ein ausführliches Programm.
252-4202-00LSeminar in Theoretical Computer Science Information E-2 credits2SE. Welzl, B. Gärtner, M. Hoffmann, J. Lengler, A. Steger, B. Sudakov
AbstractPresentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates.
ObjectiveTo 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.
NumberTitleTypeECTSHoursLecturers
406-2004-AALAlgebra 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 credits11RL. Halbeisen
AbstractGalois 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.
ObjectiveIntroduction to fundamentals of Galois theory, and representation theory of finite groups and algebras
ContentFundamentals of Galois theory
Representation theory of finite groups and algebras
LiteratureS. 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 / NoticeAlgebra I
406-2005-AALAlgebra I and 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-12 credits26RL. Halbeisen
AbstractIntroduction 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
ContentBasic 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
LiteratureS. 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-AALMeasure and Integration
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-6 credits13RM. Schweizer
AbstractIntroduction 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
ObjectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction 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 notesno lecture notes
Literature1. 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 / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-2303-AALComplex Analysis
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-6 credits13RR. Pandharipande
AbstractComplex 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
LiteratureL. 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 / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-2554-AALTopology
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-6 credits13RW. Werner
AbstractTopological and metric spaces, continuity, connectedness, compactness, product and quotient spaces, separation axioms, quotient spaces, Baire category, homotopy, fundamental group, covering spaces.
ObjectiveCover the basic notions of set-theoretic topology.
Lecture notesSee lecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-2554-00L/
LiteratureKlaus 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 / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-2604-AALProbability 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-7 credits15RS. van de Geer
AbstractIntroduction 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.
ObjectiveThe 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.
ContentProbability:
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".
LiteratureGeoffrey 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-AALFunctional Analysis I
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-10 credits21RM. Struwe
AbstractBaire 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 / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-3621-AALFundamentals of Mathematical 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-10 credits21RF. Balabdaoui
AbstractThe course covers the basics of inferential statistics.
Objective
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