# Search result: Catalogue data in Spring Semester 2020

Mathematics Bachelor | ||||||

Core Courses | ||||||

Core Courses: Applied Mathematics and Further Appl.-Oriented Fields ¬ | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3632-00L | Computational Statistics | W | 8 credits | 3V + 1U | M. H. Maathuis | |

Abstract | We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R. | |||||

Objective | The student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R. | |||||

Content | See the class website | |||||

Prerequisites / Notice | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||

401-3602-00L | Applied Stochastic Processes Does not take place this semester. | W | 8 credits | 3V + 1U | not available | |

Abstract | Poisson processes; renewal processes; Markov chains in discrete and in continuous time; some applications. | |||||

Objective | Stochastic processes are a way to describe and study the behaviour of systems that evolve in some random way. In this course, the evolution will be with respect to a scalar parameter interpreted as time, so that we discuss the temporal evolution of the system. We present several classes of stochastic processes, analyse their properties and behaviour and show by some examples how they can be used. The main emphasis is on theory; in that sense, "applied" should be understood to mean "applicable". | |||||

Literature | R. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online: http://epubs.siam.org/doi/book/10.1137/1.9780898718997 R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online: http://link.springer.com/book/10.1007/978-1-4614-3615-7/page/1 M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online: http://link.springer.com/book/10.1007/978-0-387-48976-6/page/1 S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005) | |||||

Prerequisites / Notice | Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L). | |||||

401-3652-00L | Numerical Methods for Hyperbolic Partial Differential Equations (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: MAT827 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/mobilitaet.html | W | 10 credits | 4V + 2U | University lecturers | |

Abstract | This course treats numerical methods for hyperbolic initial-boundary value problems, ranging from wave equations to the equations of gas dynamics. The principal methods discussed in the course are finite volume methods, including TVD, ENO and WENO schemes. Exercises involve implementation of numerical methods in MATLAB. | |||||

Objective | The goal of this course is familiarity with the fundamental ideas and mathematical consideration underlying modern numerical methods for conservation laws and wave equations. | |||||

Content | * Introduction to hyperbolic problems: Conservation, flux modeling, examples and significance in physics and engineering. * Linear Advection equations in one dimension: Characteristics, energy estimates, upwind schemes. * Scalar conservation laws: shocks, rarefactions, solutions of the Riemann problem, weak and entropy solutions, some existence and uniqueness results, finite volume schemes of the Godunov, Engquist-Osher and Lax-Friedrichs type. Convergence for monotone methods and E-schemes. * Second-order schemes: Lax-Wendroff, TVD schemes, limiters, strong stability preserving Runge-Kutta methods. * Linear systems: explicit solutions, energy estimates, first- and high-order finite volume schemes. * Non-linear Systems: Hugoniot Locus and integral curves, explicit Riemann solutions of shallow-water and Euler equations. Review of available theory. | |||||

Lecture notes | Lecture slides will be made available to participants. However, additional material might be covered in the course. | |||||

Literature | H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, Springer 2011. Available online. R. J. LeVeque, Finite Volume methods for hyperbolic problems, Cambridge university Press, 2002. Available online. E. Godlewski and P. A. Raviart, Hyperbolic systems of conservation laws, Ellipses, Paris, 1991. | |||||

Prerequisites / Notice | Having attended the course on the numerical treatment of elliptic and parabolic problems is no prerequisite. Programming exercises in MATLAB Former course title: "Numerical Solution of Hyperbolic Partial Differential Equations" | |||||

» Core Courses: Applied Mathematics and Further Appl.-Oriented Fields (Mathematics Master) | ||||||

Core Courses: Further Application-Oriented Fields 402-0204-00L Electrodynamics is eligible in the Bachelor's programme in Mathematics as an applied core course, but only if 402-0224-00L Theoretical Physics (offered for the last time in FS 2016) isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

402-0204-00L | Electrodynamics | W | 7 credits | 4V + 2U | R. Renner | |

Abstract | Derivation and discussion of Maxwell's equations, from the static limit to the full dynamical case. Wave equation, waveguides, cavities. Generation of electromagnetic radiation, scattering and diffraction of light. Structure of Maxwell's equations, relativity theory and covariance, Lagrangian formulation. Dynamics of relativistic particles in the presence of fields and radiation properties. | |||||

Objective | Develop a physical understanding for static and dynamic phenomena related to (moving) charged objects and understand the structure of the classical field theory of electrodynamics (transverse versus longitudinal physics, invariances (Lorentz-, gauge-)). Appreciate the interrelation between electric, magnetic, and optical phenomena and the influence of media. Understand a set of classic electrodynamical phenomena and develop the ability to solve simple problems independently. Apply previously learned mathematical concepts (vector analysis, complete systems of functions, Green's functions, co- and contravariant coordinates, etc.). Prepare for quantum mechanics (eigenvalue problems, wave guides and cavities). | |||||

Content | Classical field theory of electrodynamics: Derivation and discussion of Maxwell equations, starting from the static limit (electrostatics, magnetostatics, boundary value problems) in the vacuum and in media and subsequent generalization to the full dynamical case (Faraday's law, Ampere/Maxwell law; potentials and gauge invariance). Wave equation and solutions in full space, half-space (Snell's law), waveguides, cavities, generation of electromagnetic radiation, scattering and diffraction of light (optics). Application to various specific examples. Discussion of the structure of Maxwell's equations, Lorentz invariance, relativity theory and covariance, Lagrangian formulation. Dynamics of relativistic particles in the presence of fields and their radiation properties (synchrotron). | |||||

Literature | J.D. Jackson, Classical Electrodynamics W.K.H Panovsky and M. Phillis, Classical electricity and magnetism L.D. Landau, E.M. Lifshitz, and L.P. Pitaevskii, Electrodynamics of continuus media A. Sommerfeld, Electrodynamics / Optics (Lectures on Theoretical Physics) M. Born and E. Wolf, Principles of optics R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures of Physics, Vol II W. Nolting, Elektrodynamik (Grundkurs Theoretische Physik 3) | |||||

Electives | ||||||

Selection: Algebra, Number Thy, Topology, Discrete Mathematics, Logic | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3201-00L | Algebraic Groups | W | 8 credits | 4G | P. D. Nelson | |

Abstract | Introduction to the theory of linear algebraic groups. Lie algebras, the Jordan Chevalley decomposition, semisimple and reductive groups, root systems, Borel subgroups, classification of reductive groups and their representations. | |||||

Objective | ||||||

Literature | A. L. Onishchik and E.B. Vinberg, Lie Groups and Algebraic Groups | |||||

Prerequisites / Notice | Abstract algebra: groups, rings, fields, tensor product, etc. Some familiarity with the basics of Lie groups and their Lie algebras would be helpful, but is not absolutely necessary. We will develop what we need from algebraic geometry, without assuming prior knowledge. | |||||

401-3109-65L | Probabilistic Number Theory Does not take place this semester. | W | 8 credits | 4G | E. Kowalski | |

Abstract | The course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums. | |||||

Objective | The goal of the course is to present some results of probabilistic number theory in a unified manner. | |||||

Content | The main concepts will be presented in parallel with the proof of a few main theorems: (1) the Erdős-Wintner and Erdős-Kac theorems concerning the distribution of values of arithmetic functions; (2) the distribution of values of the Riemann zeta function, including Selberg's central limit theorem for the Riemann zeta function on the critical line; (3) the Chebychev bias for primes in arithmetic progressions; (4) functional limit theorems for the paths of partial sums of families of exponential sums. | |||||

Lecture notes | The lecture notes for the class are available at https://www.math.ethz.ch/~kowalski/probabilistic-number-theory.pdf | |||||

Prerequisites / Notice | Prerequisites: Complex analysis, measure and integral; some probability theory is useful but the main concepts needed will be recalled. Some knowledge of number theory is useful but the main results will be summarized. | |||||

401-3202-09L | The Representation Theory of the Finite Symmetric Groups NOTICE: No physical class for the next few weeks until further notice. Instead a video recording will be offered. | W | 4 credits | 2V | L. Wu | |

Abstract | This course is an Introduction to the Representation Theory of the Groups. | |||||

Objective | Our goal is to give an introduction of the Representation Theory using the examples of the Finite Symmetry Groups. | |||||

Literature | * Jean-Pierre Serre: Linear Representations of Finite Groups, Graduate Texts in Mathematics, Springer. * William Fulton and Joe Harris: Representation Theory A First Course, Graduate Texts in Mathematics, Springer. * G. D. James: The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics, Springer. * Bruce E. Sagan: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Graduate Texts in Mathematics, Springer. | |||||

Prerequisites / Notice | Some basic knowledge of the Group Theory and Linear Algebra. | |||||

401-8112-20L | Geometry of Numbers (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: MAT548 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/mobilitaet.html | W | 9 credits | 4V + 1U | University lecturers | |

Abstract | The Geometry of Numbers studies distribution of lattice points in the n dimensional space, for instance, existence of lattice points in various domains and existence of integral solutions of polynomial inequalities. This subject is also closely related to the Theory of Diophantine Approximation, which seeks good rational approximations for real vectors. | |||||

Objective | Learn basic techniques in the Geometry of Numbers | |||||

Literature | 1. Cassels, An introduction to Diophantine Approximation 2. Cassels, An introduction to the Geometry of Numbers 3. Schmidt, Diophantine approximation 4. Siegel, Lectures on the Geometry of Numbers | |||||

401-3058-00L | Combinatorics IDoes not take place this semester. | W | 4 credits | 2G | N. Hungerbühler | |

Abstract | The course Combinatorics I and II is an introduction into the field of enumerative combinatorics. | |||||

Objective | Upon completion of the course, students are able to classify combinatorial problems and to apply adequate techniques to solve them. | |||||

Content | Contents of the lectures Combinatorics I and II: congruence transformation of the plane, symmetry groups of geometric figures, Euler's function, Cayley graphs, formal power series, permutation groups, cycles, Bunside's lemma, cycle index, Polya's theorems, applications to graph theory and isomers. | |||||

Prerequisites / Notice | Recognition of credits as an elective course in the Mathematics Bachelor's or Master's Programmes is only possible if you have not received credits for the course unit 401-3052-00L Combinatorics (which was for the last time taught in the spring semester 2008). | |||||

Selection: Geometry | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3056-00L | Finite Geometries I | W | 4 credits | 2G | N. Hungerbühler | |

Abstract | Finite geometries I, II: Finite geometries combine aspects of geometry, discrete mathematics and the algebra of finite fields. In particular, we will construct models of axioms of incidence and investigate closing theorems. Applications include test design in statistics, block design, and the construction of orthogonal Latin squares. | |||||

Objective | Finite geometries I, II: Students will be able to construct and analyse models of finite geometries. They are familiar with closing theorems of the axioms of incidence and are able to design statistical tests by using the theory of finite geometries. They are able to construct orthogonal Latin squares and know the basic elements of the theory of block design. | |||||

Content | Finite geometries I, II: finite fields, rings of polynomials, finite affine planes, axioms of incidence, Euler's thirty-six officers problem, design of statistical tests, orthogonal Latin squares, transformation of finite planes, closing theorems of Desargues and Pappus-Pascal, hierarchy of closing theorems, finite coordinate planes, division rings, finite projective planes, duality principle, finite Moebius planes, error correcting codes, block design | |||||

Literature | - 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. | |||||

401-3556-20L | Topics in Symplectic Topology | W | 6 credits | 3V | P. Biran | |

Abstract | This will be an introductory course in symplectic geometry and topology. We will cover the simplest instances of symplectic rigidity phenomena, and techniques to detect and study them. The last part of the course will be devoted to more advanced techniques such as Floer theory. | |||||

Objective | Get acquainted with the basics of symplectic topology and phenomena of symplectic rigidity. | |||||

Literature | 1) Book: "Introduction to Symplectic Topology", 3'rd edition, by McDuff and Salamon. Oxford Graduate Texts in Mathematics 2) Some published articles that will be announced during the semester. | |||||

401-3574-61L | Introduction to Knot Theory Does not take place this semester. | W | 6 credits | 3G | ||

Abstract | Introduction to the mathematical theory of knots. We will discuss some elementary topics in knot theory and we will repeatedly centre on how this knowledge can be used in secondary school. | |||||

Objective | The aim of this lecture course is to give an introduction to knot theory. In the course we will discuss the definition of a knot and what is meant by equivalence. The focus of the course will be on knot invariants. We will consider various knot invariants amongst which we will also find the so called knot polynomials. In doing so we will again and again show how this knowledge can be transferred down to secondary school. | |||||

Content | Definition of a knot and of equivalent knots. Definition of a knot invariant and some elementary examples. Various operations on knots. Knot polynomials (Jones, ev. Alexander.....) | |||||

Literature | An extensive bibliography will be handed out in the course. | |||||

Prerequisites / Notice | Prerequisites are some elementary knowledge of algebra and topology. | |||||

Selection: Analysis No offering in this semester yet | ||||||

Selection: Numerical Analysis No offering in this semester yet | ||||||

Selection: Probability Theory, Statistics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-6102-00L | Multivariate StatisticsDoes not take place this semester. | W | 4 credits | 2G | not available | |

Abstract | Multivariate Statistics deals with joint distributions of several random variables. This course introduces the basic concepts and provides an overview over classical and modern methods of multivariate statistics. We will consider the theory behind the methods as well as their applications. | |||||

Objective | After the course, you should be able to: - describe the various methods and the concepts and theory behind them - identify adequate methods for a given statistical problem - use the statistical software "R" to efficiently apply these methods - interpret the output of these methods | |||||

Content | Visualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis | |||||

Lecture notes | None | |||||

Literature | The course will be based on class notes and books that are available electronically via the ETH library. | |||||

Prerequisites / Notice | Target audience: This course is the more theoretical version of "Applied Multivariate Statistics" (401-0102-00L) and is targeted at students with a math background. Prerequisite: A basic course in probability and statistics. Note: The courses 401-0102-00L and 401-6102-00L are mutually exclusive. You may register for at most one of these two course units. | |||||

401-4626-00L | Advanced Statistical Modelling: Mixed Models | W | 4 credits | 2V | M. Mächler | |

Abstract | Mixed Models = (*| generalized| non-) linear Mixed-effects Models, extend traditional regression models by adding "random effect" terms. In applications, such models are called "hierarchical models", "repeated measures" or "split plot designs". Mixed models are widely used and appropriate in an aera of complex data measured from living creatures from biology to human sciences. | |||||

Objective | - Becoming aware how mixed models are more realistic and more powerful in many cases than traditional ("fixed-effects only") regression models. - Learning to fit such models to data correctly, critically interpreting results for such model fits, and hence learning to work the creative cycle of responsible statistical data analysis: "fit -> interpret & diagnose -> modify the fit -> interpret & ...." - Becoming aware of computational and methodological limitations of these models, even when using state-of-the art software. | |||||

Content | The lecture will build on various examples, use R and notably the `lme4` package, to illustrate concepts. The relevant R scripts are made available online. Inference (significance of factors, confidence intervals) will focus on the more realistic *un*balanced situation where classical (ANOVA, sum of squares etc) methods are known to be deficient. Hence, Maximum Likelihood (ML) and its variant, "REML", will be used for estimation and inference. | |||||

Lecture notes | We will work with an unfinished book proposal from Prof Douglas Bates, Wisconsin, USA which itself is a mixture of theory and worked R code examples. These lecture notes and all R scripts are made available from https://github.com/mmaechler/MEMo | |||||

Literature | (see web page and lecture notes) | |||||

Prerequisites / Notice | - We assume a good working knowledge about multiple linear regression ("the general linear model') and an intermediate (not beginner's) knowledge about model based statistics (estimation, confidence intervals,..). Typically this means at least two classes of (math based) statistics, say 1. Intro to probability and statistics 2. (Applied) regression including Matrix-Vector notation Y = X b + E - Basic (1 semester) "Matrix calculus" / linear algebra is also assumed. - If familiarity with [R](https://www.r-project.org/) is not given, it should be acquired during the course (by the student on own initiative). | |||||

401-4627-00L | Empirical Process Theory and Applications | W | 4 credits | 2V | S. van de Geer | |

Abstract | Empirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc. | |||||

Objective | ||||||

Content | In this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection. | |||||

Selection: Financial and Insurance Mathematics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3888-00L | Introduction to Mathematical Finance A related course is 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS credits). Although both courses can be taken independently of each other, only one will be recognised for credits in the Bachelor and Master degree. In other words, it is not allowed to earn credit points with one for the Bachelor and with the other for the Master degree. | W | 10 credits | 4V + 1U | C. Czichowsky | |

Abstract | This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization. | |||||

Objective | This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation, and maybe other topics. We prove the fundamental theorem of asset pricing and the hedging duality theorems in discrete time, and also study convex duality in utility maximization. | |||||

Content | This course focuses on discrete-time financial markets. It presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course is offered every year in the Spring semester. This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II. For an overview of courses offered in the area of mathematical finance, see Link. | |||||

Lecture notes | The course is based on different parts from different textbooks as well as on original research literature. Lecture notes will not be available. | |||||

Literature | Literature: Michael U. Dothan, "Prices in Financial Markets", Oxford University Press Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter Marek Capinski and Ekkehard Kopp, "Discrete Models of Financial Markets", Cambridge University Press Robert J. Elliott and P. Ekkehard Kopp, "Mathematics of Financial Markets", Springer | |||||

Prerequisites / Notice | A related course is "Mathematical Foundations for Finance" (MFF), 401-3913-01. Although both courses can be taken independently of each other, only one will be given credit points for the Bachelor and the Master degree. In other words, it is also not possible to earn credit points with one for the Bachelor and with the other for the Master degree. This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II. For an overview of courses offered in the area of mathematical finance, see Link. | |||||

401-3629-00L | Quantitative Risk Management | W | 4 credits | 2V + 1U | P. Cheridito | |

Abstract | This course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas, dependence structures and operational risk. | |||||

Objective | The goal is to learn the most important methods from probability theory and statistics used in financial risk modeling. | |||||

Content | 1. Introduction 2. Basic Concepts in Risk Management 3. Empirical Properties of Financial Data 4. Financial Time Series 5. Extreme Value Theory 6. Multivariate Models 7. Copulas and Dependence 8. Operational Risk | |||||

Lecture notes | Course material is available on https://people.math.ethz.ch/~patrickc/qrm | |||||

Literature | Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) http://press.princeton.edu/titles/10496.html | |||||

Prerequisites / Notice | The course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance. | |||||

401-3923-00L | Selected Topics in Life Insurance Mathematics | W | 4 credits | 2V | M. Koller | |

Abstract | Stochastic Models for Life insurance 1) Markov chains 2) Stochastic Processes for demography and interest rates 3) Cash flow streams and reserves 4) Mathematical Reserves and Thiele's differential equation 5) Theorem of Hattendorff 6) Unit linked policies | |||||

Objective | ||||||

401-3917-00L | Stochastic Loss Reserving Methods | W | 4 credits | 2V | R. Dahms | |

Abstract | Loss Reserving is one of the central topics in non-life insurance. Mathematicians and actuaries need to estimate adequate reserves for liabilities caused by claims. These claims reserves have influence all financial statements, future premiums and solvency margins. We present the stochastics behind various methods that are used in practice to calculate those loss reserves. | |||||

Objective | Our goal is to present the stochastics behind various methods that are used in prctice to estimate claim reserves. These methods enable us to set adequate reserves for liabilities caused by claims and to determine prediction errors of these predictions. | |||||

Content | We will present the following stochastic claims reserving methods/models: - Stochastic Chain-Ladder Method - Bayesian Methods, Bornhuetter-Ferguson Method, Credibility Methods - Distributional Models - Linear Stochastic Reserving Models, with and without inflation - Bootstrap Methods - Claims Development Result (solvency view) - Coupling of portfolios | |||||

Literature | M. V. Wüthrich, M. Merz, Stochastic Claims Reserving Methods in Insurance, Wiley 2008. | |||||

Prerequisites / Notice | The exams ONLY take place during the official ETH examination periods. This course will be held in English and counts towards the diploma "Aktuar SAV". For the latter, see details under www.actuaries.ch. Basic knowledge in probability theory is assumed, in particular conditional expectations. |

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