Suchergebnis: Katalogdaten im Herbstsemester 2016
Mathematik Bachelor | ||||||
Bachelor-Studium (Studienreglement 2010) | ||||||
Kernfächer | ||||||
Kernfächer aus Bereichen der angewandten Mathematik ... vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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401-3601-00L | Probability Theory Das Bachelor-Kernfach 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist für Studierende mit einem ETH Zürich Bachelor-Abschluss in Mathematik für den Master-Studiengang Mathematik anrechenbar, falls sie im vorangegangenen Bachelor-Studium keine der drei Lerneinheiten 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory, 401-3642-00L Brownian Motion and Stochastic Calculus bzw. 401-3602-00L Applied Stochastic Processes für den Bachelor-Abschluss anrechnen liessen. Ausserdem ist höchstens eines der drei Fächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory im Master-Studiengang Mathematik anrechenbar. | W | 10 KP | 4V + 1U | A.‑S. Sznitman | |
Kurzbeschreibung | Basics of probability theory and the theory of stochastic processes in discrete time | |||||
Lernziel | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||
Inhalt | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||
Skript | available, will be sold in the course | |||||
Literatur | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 | |||||
401-3621-00L | Fundamentals of Mathematical Statistics | W | 10 KP | 4V + 1U | F. Balabdaoui | |
Kurzbeschreibung | The course covers the basics of inferential statistics. | |||||
Lernziel | ||||||
252-0057-00L | Theoretische Informatik | W | 8 KP | 4V + 2U + 1A | J. Hromkovic | |
Kurzbeschreibung | Konzepte zur Beantwortung grundlegender Fragen wie: a) Was ist völlig automatisiert machbar (algorithmisch lösbar) b) Wie kann man die Schwierigkeit von Aufgaben (Problemen) messen? c) Was ist Zufall und wie kann er nützlich sein? d) Was ist Nichtdeterminisus und welche Rolle spielt er in der Informatik? e) Wie kann man unendliche Objekte durch Automaten und Grammatiken endlich darstellen? | |||||
Lernziel | Vermittlung der grundlegenden Konzepte der Informatik in ihrer geschichtlichen Entwicklung | |||||
Inhalt | Die Veranstaltung ist eine Einführung in die Theoretische Informatik, die die grundlegenden Konzepte und Methoden der Informatik in ihrem geschichtlichen Zusammenhang vorstellt. Wir präsentieren Informatik als eine interdisziplinäre Wissenschaft, die auf einer Seite die Grenzen zwischen Möglichem und Unmöglichem und die quantitativen Gesetze der Informationsverarbeitung erforscht und auf der anderen Seite Systeme entwirft, analysiert, verifiziert und implementiert. Die Hauptthemen der Vorlesung sind: - Alphabete, Wörter, Sprachen, Messung der Informationsgehalte von Wörtern, Darstellung von algorithmischen Aufgaben - endliche Automaten, reguläre und kontextfreie Grammatiken - Turingmaschinen und Berechenbarkeit - Komplexitätstheorie und NP-Vollständigkeit - Algorithmenentwurf für schwere Probleme | |||||
Skript | Die Vorlesung ist detailliert durch das Lehrbuch "Theoretische Informatik" bedeckt. | |||||
Literatur | Basisliteratur: 1. J. Hromkovic: Theoretische Informatik. 5. Auflage, Springer Vieweg 2014. 2. J. Hromkovic: Theoretical Computer Science. Springer 2004. Weiterführende Literatur: 3. M. Sipser: Introduction to the Theory of Computation, PWS Publ. Comp.1997 4. J.E. Hopcroft, R. Motwani, J.D. Ullman: Einführung in die Automatentheorie, Formale Sprachen und Komplexitätstheorie. Pearson 2002. 5. I. Wegener: Theoretische Informatik. Teubner Weitere Übungen und Beispiele: 6. A. Asteroth, Ch. Baier: Theoretische Informatik | |||||
Voraussetzungen / Besonderes | Während des Semesters werden zwei freiwillige Probeklausuren gestellt. | |||||
252-0209-00L | Algorithms, Probability, and Computing | W | 8 KP | 4V + 2U + 1A | E. Welzl, M. Ghaffari, A. Steger, P. Widmayer | |
Kurzbeschreibung | Advanced design and analysis methods for algorithms and data structures: Random(ized) Search Trees, Point Location, Minimum Cut, Linear Programming, Randomized Algebraic Algorithms (matchings), Probabilistically Checkable Proofs (introduction). | |||||
Lernziel | Studying and understanding of fundamental advanced concepts in algorithms, data structures and complexity theory. | |||||
Skript | Will be handed out. | |||||
Literatur | Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest; Randomized Algorithms by R. Motwani und P. Raghavan; Computational Geometry - Algorithms and Applications by M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf. | |||||
» Kernfächer aus Bereichen der angewandten Mathematik ... (Mathematik Master) | ||||||
Kernfächer aus weiteren anwendungsorientierten Gebieten 402-0205-00L Quantenmechanik I ist als angewandtes Kernfach anrechenbar, aber nur unter der Bedingung, dass 402-0224-00L Theoretische Physik (letztmals im FS 2016 angeboten) nicht angerechnet wird (weder im Bachelor- noch im Master-Studiengang). Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link). | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
402-0205-00L | Quantenmechanik I | W | 10 KP | 3V + 2U | T. K. Gehrmann | |
Kurzbeschreibung | Einführung in die nicht-relativistische Einteilchen-Quantenmechanik. Diskussion grundlegender Ideen der Quantenmechanik, insbesondere Quantisierung klassischer Systeme, Wellenfunktionen und die Beschreibung von Observablen durch Operatoren auf einem Hilbertraum, und die Analyse von Symmetrien. Grundlegende Phänomene werden analysiert und durch generische Beispiele illustriert. | |||||
Lernziel | Einführung in die Einteilchen Quantenmechanik. Beherrschung grundlegender Ideen (Quantisierung, Operatorformalismus, Symmetrien, Störungstheorie) und generischer Beispiele und Anwendungen (gebunden Zustände, Tunneleffekt, Streutheorie in ein- und dreidimensionalen Problemen). Fähigkeit zur Lösung einfacher Probleme. | |||||
Inhalt | Stichworte: Schrödinger-Gleichung, Formalismus der Quantenmechanik (Zustände, Operatoren, Kommutatoren, Messprozess), Symmetrien (Translation, Rotationen), Quantenmechanik in einer Dimension, Zentralkraftprobleme, Potentialstreuung, Störungstheorie, Variations-Verfahren, Drehimpuls, Spin, Drehimpulsaddition, Relation QM und klassische Physik. | |||||
Literatur | F. Schwabl: Quantenmechanik J.J. Sakurai: Modern Quantum Mechanics W. Nolting: Quantenmechanik (Theoretische Physik 5.1, 5.2) C. Cohen-Tannoudji: Quantenmechanik I | |||||
Wahlfächer | ||||||
Auswahl: Algebra, Topologie, diskrete Mathematik, Logik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3117-66L | Introduction to the Circle Method | W | 6 KP | 2V + 1U | E. Kowalski | |
Kurzbeschreibung | The circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large. | |||||
Lernziel | ||||||
Inhalt | The circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large. The lecture will present an introduction to this method. In particular, it will present the solution of Waring's Problem concerning the representability of integers as sums of a bounded numbers of (fixed) powers of integers. | |||||
Literatur | H. Davenport, "Analytic methods for Diophantine equations and Diophatine inequalities", Cambridge H. Iwaniec and E. Kowalski, "Analytic number theory", chapter 20; AMS R. Vaughan, "The Hardy-Littlewood method", Cambridge | |||||
401-4209-66L | Group and Representation Theory: Beyond an Introduction | W | 8 KP | 3V + 1U | T. H. Willwacher | |
Kurzbeschreibung | The goal of the course is to study several classical and important (and beautiful!) topics in group and representation theory, that are otherwise often overlooked in a standard curriculum. In particular, we plan to study reflection and Coxeter groups, classical invariant theory, and the theory of real semi simple Lie algebras and their representations. | |||||
Lernziel | Despite the title, the course will begin by a recollection of basic concepts of group and representation theory, in particular that of finite groups and Lie groups. Hence the course should be accessible also for students who only had a brief exposure to representation theory, as for example in the MMP course. | |||||
401-3059-00L | Kombinatorik II Findet dieses Semester nicht statt. | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Der Kurs Kombinatorik I und II ist eine Einfuehrung in die abzaehlende Kombinatorik. | |||||
Lernziel | Die Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden. | |||||
Inhalt | Inhalt der Vorlesungen Kombinatorik I und II: Kongruenztransformationen der Ebene, Symmetriegruppen von geometrischen Figuren, Eulersche Funktion, Cayley-Graphen, formale Potenzreihen, Permutationsgruppen, Zyklen, Lemma von Burnside, Zyklenzeiger, Saetze von Polya, Anwendung auf die Graphentheorie und isomere Molekuele. | |||||
Auswahl: Geometrie | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3057-00L | Endliche Geometrien II | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Endliche Geometrien I, II: Endliche Geometrien verbinden Aspekte der Geometrie mit solchen der diskreten Mathematik und der Algebra endlicher Körper. Inbesondere werden Modelle der Inzidenzaxiome konstruiert und Schliessungssätze der Geometrie untersucht. Anwendungen liegen im Bereich der Statistik, der Theorie der Blockpläne und der Konstruktion orthogonaler lateinischer Quadrate. | |||||
Lernziel | Endliche Geometrien I, II: Die Studierenden sind in der Lage, Modelle endlicher Geometrien zu konstruieren und zu analysieren. Sie kennen die Schliessungssätze der Inzidenzgeometrie und können mit Hilfe der Theorie statistische Tests entwerfen sowie orthogonale lateinische Quadrate konstruieren. Sie sind vertraut mit Elementen der Theorie der Blockpläne. | |||||
Inhalt | Endliche Geometrien I, II: Endliche Körper, Polynomringe, endliche affine Ebenen, Axiome der Inzidenzgeometrie, Eulersches Offiziersproblem, statistische Versuchsplanung, orthogonale lateinische Quadrate, Transformationen endlicher Ebenen, Schliessungsfiguren von Desargues und Pappus-Pascal, Hierarchie der Schliessungsfiguren, endliche Koordinatenebenen, Schiefkörper, endliche projektive Ebenen, Dualitätsprinzip, endliche Möbiusebenen, selbstkorrigierende Codes, Blockpläne | |||||
Literatur | - Max Jeger, Endliche Geometrien, ETH Skript 1988 - Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983 - Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press - Dembowski: Finite Geometries. | |||||
401-3309-66L | Riemann Surfaces (Part 2) | W | 4 KP | 2V | A. Buryak | |
Kurzbeschreibung | The program will be the following: * Proof of the Serre duality; * Riemann-Hurwitz formula; * Functions and differential forms on a compact Riemann surface with prescribed principal parts; * Weierstrass points on a compact Riemann surface; * The Jacobian and the Picard group of a compact Riemann surface; * Holomorphic vector bundles; * Non-compact Riemann surfaces. | |||||
Lernziel | ||||||
Literatur | O. Forster. Lectures on Riemann Surfaces. | |||||
Voraussetzungen / Besonderes | This is a continuation of 401-3308-16L Riemann Surfaces that was taught in the spring semester (FS 2016), see Link for the lecture notes. The students are also assumed to be familiar with what would generally be covered in one semester courses on general topology and on algebra. | |||||
Auswahl: Analysis | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3303-00L | Ausgewählte Themen der Funktionentheorie | W | 6 KP | 3V | H. Knörrer | |
Kurzbeschreibung | Hypergeometrische Funktionen, Randwerte holomorpher Funktionen, Nevanlinna Theorie und andere spezielle Themen | |||||
Lernziel | Fortgeschrittene Methoden der Funktionentheorie | |||||
Literatur | R. Remmert: Funktionentheorie II. Springer Verlag E.Titchmarsh: The Theory of Functions. Oxford University Press C.Caratheodory: Funktionentheorie. Birkhaeuser E.Hille: Analytic Function Theory. AMS Chelsea Publishing A.Gogolin:Komplexe Integration. Springer | |||||
Voraussetzungen / Besonderes | Funktionentheorie | |||||
Auswahl: Numerische Mathematik kein Angebot | ||||||
Auswahl: Wahrscheinlichkeitstheorie, Statistik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3604-66L | Special Topics in Probability | W | 4 KP | 2V | P. Nolin | |
Kurzbeschreibung | The goal of this course is to present recent developments in Percolation Theory | |||||
Lernziel | The goal of this course is to present recent developments in Percolation Theory | |||||
Inhalt | Independent percolation is obtained by deleting randomly (and independently) the edges of a lattice, each with a given probability p between 0 and 1. One is then interested in the connectivity properties of the random subgraph so-obtained. It is arguably the simplest model from statistical mechanics that displays a phase transition, a drastic change of behavior as the parameter p varies. We will first present classical tools and properties of percolation theory: in particular correlation inequalities, exponential decay of connection probabilities, and uniqueness of the infinite connected component. We will then discuss recent developments: for example percolation on Cayley graphs, and continuum limits in two dimensions. | |||||
Literatur | B. Bollobas, O. Riordan: Percolation, CUP 2006 G. Grimmett: Percolation 2ed, Springer 1999 | |||||
Voraussetzungen / Besonderes | Prerequisites: 401-2604-00L Probability and Statistics (mandatory) 401-3601-00L Probability Theory (recommended) | |||||
401-3627-00L | High-Dimensional Statistics Findet dieses Semester nicht statt. | W | 4 KP | 2V | P. L. Bühlmann | |
Kurzbeschreibung | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||
Lernziel | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||
Inhalt | Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling | |||||
Literatur | Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2. | |||||
Voraussetzungen / Besonderes | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||
401-4623-00L | Time Series Analysis | W | 6 KP | 3G | N. Meinshausen | |
Kurzbeschreibung | Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R. | |||||
Lernziel | Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R. | |||||
Inhalt | This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R. | |||||
Skript | Not available | |||||
Literatur | A list of references will be distributed during the course. | |||||
Voraussetzungen / Besonderes | Basic knowledge in probability and statistics | |||||
401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 KP | 2V + 1U | L. Meier | |
Kurzbeschreibung | Principles of experimental design. One-way analysis of variance. Multi-factor experiments and analysis of variance. Block designs. Latin square designs. Split-plot and strip-plot designs. Random effects and mixed effects models. Full factorials and fractional designs. | |||||
Lernziel | Participants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R. | |||||
Inhalt | Principles of experimental design. One-way analysis of variance. Multi-factor experiments and analysis of variance. Block designs. Latin square designs. Split-plot and strip-plot designs. Random effects and mixed effects models. Full factorials and fractional designs. | |||||
Literatur | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||
Voraussetzungen / Besonderes | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held. | |||||
401-3611-00L | Advanced Topics in Computational Statistics Findet dieses Semester nicht statt. | W | 4 KP | 2V | M. H. Maathuis | |
Kurzbeschreibung | This lecture covers selected advanced topics in computational statistics, including various classification methods, the EM algorithm, clustering, handling missing data, and graphical modelling. | |||||
Lernziel | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||
Inhalt | The course is roughly divided in three parts: (1) Supervised learning via (variations of) nearest neighbor methods, (2) the EM algorithm and clustering, (3) handling missing data and graphical models. | |||||
Skript | Lecture notes. | |||||
Voraussetzungen / Besonderes | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||
401-0649-00L | Applied Statistical Regression | W | 5 KP | 2V + 1U | M. Dettling | |
Kurzbeschreibung | This course offers a practically oriented introduction into regression modeling methods. The basic concepts and some mathematical background are included, with the emphasis lying in learning "good practice" that can be applied in every student's own projects and daily work life. A special focus will be laid in the use of the statistical software package R for regression analysis. | |||||
Lernziel | The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling. | |||||
Inhalt | The course starts with the basics of linear modeling, and then proceeds to parameter estimation, tests, confidence intervals, residual analysis, model choice, and prediction. More rarely touched but practically relevant topics that will be covered include variable transformations, multicollinearity problems and model interpretation, as well as general modeling strategies. The last third of the course is dedicated to an introduction to generalized linear models: this includes the generalized additive model, logistic regression for binary response variables, binomial regression for grouped data and poisson regression for count data. | |||||
Skript | A script will be available. | |||||
Literatur | Faraway (2005): Linear Models with R Faraway (2006): Extending the Linear Model with R Draper & Smith (1998): Applied Regression Analysis Fox (2008): Applied Regression Analysis and GLMs Montgomery et al. (2006): Introduction to Linear Regression Analysis | |||||
Voraussetzungen / Besonderes | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software package R, for which an introduction will be held. In the Mathematics Bachelor and Master programmes, the two course units 401-0649-00L "Applied Statistical Regression" and 401-3622-00L "Regression" are mutually exclusive. Registration for the examination of one of these two course units is only allowed if you have not registered for the examination of the other course unit. | |||||
Auswahl: Finanz- und Versicherungsmathematik Im Bachelor-Studiengang Mathematik ist auch 401-3913-01L Mathematical Foundations for Finance als Wahlfach anrechenbar, aber nur unter der Bedingung, dass 401-3888-00L Introduction to Mathematical Finance nicht angerechnet wird (weder im Bachelor- noch im Master-Studiengang). Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link). | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3925-00L | Non-Life Insurance: Mathematics and Statistics | W | 6 KP | 4G | M. V. Wüthrich | |
Kurzbeschreibung | The lecture aims at providing a basis in non-life insurance mathematics which forms a core subject of actuarial sciences. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models, credibility theory, claims reserving and solvency. | |||||
Lernziel | The student is familiar with the basics in non-life insurance mathematics and statistics. This includes the basic mathematical models for insurance liability modeling, pricing concepts, stochastic claims reserving models and ruin and solvency considerations. | |||||
Inhalt | The following topics are treated: Collective Risk Modeling Individual Claim Size Modeling Approximations for Compound Distributions Ruin Theory in Discrete Time Premium Calculation Principles Tariffication and Generalized Linear Models Bayesian Models and Credibility Theory Claims Reserving Solvency Considerations | |||||
Skript | M. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics Link | |||||
Voraussetzungen / Besonderes | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link. Prerequisites: knowledge of probability theory, statistics and applied stochastic processes. | |||||
401-3922-00L | Life Insurance Mathematics | W | 4 KP | 2V | M. Koller | |
Kurzbeschreibung | The classical life insurance model is presented together with the important insurance types (insurance on one and two lives, term and endowment insurance and disability). Besides that the most important terms such as mathematical reserves are introduced and calculated. The profit and loss account and the balance sheet of a life insurance company is explained and illustrated. | |||||
Lernziel |
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