Search result: Catalogue data in Autumn Semester 2018

Number	Title	Type	ECTS	Hours	Lecturers
Mathematics Master
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	M. Burger
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.
Learning 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
Lecture notes	For a summary of the content and exercises with solutions of my lecture course in FS2016 see: https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/
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 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 credits	26R	M. Burger, E. Kowalski
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.
Learning 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
Lecture notes	For a summary of the content and exercises with solutions of my lecture courses in HS2015 and FS2016 see: Link https://www2.math.ethz.ch/education/bachelor/lectures/fs2016/math/algebra2/
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
406-2303-AAL	Complex 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 credits	13R	M. Struwe
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.
Learning 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
406-2284-AAL	Measure 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 credits	13R	U. Lang
Abstract	Introduction to the abstract measure theory and integration, including the following topics: Lebesgue measure and Lebesgue integral, Lp-spaces, convergence theorems, differentiation of measures, product measures (Fubini's theorem), abstract measures, Radon-Nikodym theorem, probabilistic language.
Learning objective	Basic acquaintance with the theory of measure and integration, in particular, Lebesgue's measure and integral.
Literature	1. Lecture notes by Professor Michael Struwe (http://www.math.ethz.ch/~struwe/Skripten/AnalysisIII-SS2007-18-4-08.pdf) 2. L. Evans and R.F. Gariepy "Measure theory and fine properties of functions" 3. Walter Rudin "Real and complex analysis" 4. R. Bartle The elements of Integration and Lebesgue Measure 5. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis. http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf
406-2554-AAL	Topology 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 credits	13R	A. Sisto
Abstract	Topological spaces, continuous maps, connectedness, compactness, separation axioms, metric spaces, quotient spaces, homotopy, fundamental group and covering spaces, van Kampen Theorem, surfaces and manifolds.
Learning objective
Literature	Klaus Jänich: Topologie (Springer-Verlag) Link James Munkres: Topology (Prentice Hall) William Massey: Algebraic Topology: an Introduction (Springer-Verlag) Alan Hatcher: Algebraic Topology (Cambridge University Press) http://www.math.cornell.edu/~hatcher/AT/ATpage.html
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 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 credits	15R	J. Teichmann
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.
Learning 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 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 credits	21R	M. Einsiedler
Abstract	Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
Learning objective	Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Literature	We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
406-3621-AAL	Fundamentals 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 credits	21R	S. van de Geer
Abstract	The course covers the basics of inferential statistics.
Learning objective

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