# Search result: Catalogue data in Autumn Semester 2018

Mathematics Master | ||||||

Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Electives: Pure Mathematics | ||||||

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

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3113-68L | Exponential Sums over Finite Fields | W | 8 credits | 4G | E. Kowalski | |

Abstract | Exponential sums over finite fields arise in many problems of number theory. We will discuss the elementary aspects of the theory (centered on the Riemann Hypothesis for curves, following Stepanov's method) and survey the formalism arising from Deligne's general form of the Riemann Hypothesis over finite fields. We will then discuss various applications, especially in analytic number theory. | |||||

Objective | The goal is to understand both the basic results on exponential sums in one variable, and the general formalism of Deligne and Katz that underlies estimates for much more general types of exponential sums, including the "trace functions" over finite fields. | |||||

Content | Examples of elementary exponential sums The Riemann Hypothesis for curves and its applications Definition of trace functions over finite fields The formalism of the Riemann Hypothesis of Deligne Selected applications | |||||

Lecture notes | Lectures notes from various sources will be provided | |||||

Literature | Kowalski, "Exponential sums over finite fields, I: elementary methods: Iwaniec-Kowalski, "Analytic number theory", chapter 11 Fouvry, Kowalski and Michel, "Trace functions over finite fields and their applications" | |||||

401-3100-68L | Introduction to Analytic Number Theory | W | 8 credits | 4G | I. N. Petrow | |

Abstract | This course is an introduction to classical multiplicative analytic number theory. The main object of study is the distribution of the prime numbers in the integers. We will study arithmetic functions and learn the basic tools for manipulating and calculating their averages. We will make use of generating series and tools from complex analysis. | |||||

Objective | The main goal for the course is to prove the prime number theorem in arithmetic progressions: If gcd(a,q)=1, then the number of primes p = a mod q with p<x is approximately (1/phi(q))*(x/log x), as x tends to infinity, where phi(q) is the Euler totient function. | |||||

Content | Developing the necessary techniques and theory to prove the prime number theorem in arithmetic progressions will lead us to the study of prime numbers by Chebyshev's method, to study techniques for summing arithmetic functions by Dirichlet series, multiplicative functions, L-series, characters of a finite abelian group, theory of integral functions, and a detailed study of the Riemann zeta function and Dirichlet's L-functions. | |||||

Lecture notes | Lecture notes will be provided for the course. | |||||

Literature | Multiplicative Number Theory by Harold Davenport Multiplicative Number Theory I. Classical Theory by Hugh L. Montgomery and Robert C. Vaughan Analytic Number Theory by Henryk Iwaniec and Emmanuel Kowalski | |||||

Prerequisites / Notice | Complex analysis Group theory Linear algebra Familiarity with the Fourier transform and Fourier series preferable but not required. | |||||

401-3059-00L | Combinatorics IIDoes 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. | |||||

Selection: Geometry | ||||||

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

401-3057-00L | Finite Geometries II | 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. | |||||

401-3111-68L | Elliptic Curves and Cryptography | W | 8 credits | 3V + 1U | L. Halbeisen | |

Abstract | Im ersten Teil der Vorlesung wird die algebraische Struktur von elliptischen Kurven behandelt. Insbesondere wird der Satz von Mordell bewiesen. Im zweiten Teil der Vorlesung werden dann Anwendungen elliptischer Kurven in der Kryptographie gezeigt, wie z.B. der Diffie-Hellman-Schluesselaustausch. | |||||

Objective | Rationale Punkte auf elliptischen Kurven, insbesondere Arithmetik auf elliptischen Kurven, Satz von Mordell, Kongruente Zahlen Anwendungen der elliptischen Kurven in der Kryptographie, wie zum Beispiel Diffie-Hellman-Schluesselaustausch, Pollard-Rho-Methode | |||||

Content | Im ersten Teil der Vorlesung wird die algebraische Struktur von elliptischen Kurven behandelt und die Menge der rationalen Punkte auf elliptischen Kurven untersucht. Insbesondere wird mit Hilfe von Saetzen aus der Algebra wie auch aus der projektiven Geometrie gezeigt, dass die Menge der rationalen Punkte auf einer elliptischen Kurven unter einer bestimmten Operation eine endlich erzeugte abelsche Gruppe bildet. Zudem werden elliptische Kurven untersucht, welche mit rationalen, rechtwinkligen Dreiecken mit ganzzahligem Flaecheninhalt zusammenhaengen. Im zweiten Teil der Vorlesung werden dann Anwendungen elliptischer Kurven in der Kryptographie gezeigt. Solche Anwendungen sind zum Beispiel ein auf elliptischen Kurven basierendes Kryptosystem oder ein Algorithmus zur Faktorisierung grosser Zahlen. | |||||

Literature | Joseph Silverman, John Tate: "Rational Points on Elliptic Curves", Undergraduate Texts in Mathematics, Springer-Verlag (1992) Ian Blake, Gadiel Seroussi, Nigel Smart: "Elliptic Curves in Cryptography", Lecture Notes Series 265, Cambridge University Press (2004) | |||||

Prerequisites / Notice | Voraussgesetzt werden Algebra I und Grundbegriffe der projektiven Geometrie. | |||||

Selection: Analysis | ||||||

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

401-4115-00L | Introduction to Geometric Measure Theory | W | 6 credits | 3V | U. Lang | |

Abstract | Introduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications. | |||||

Objective | ||||||

Content | Extendability and differentiability of Lipschitz maps, metric differentiability, rectifiable sets, approximate tangent spaces, area and coarea formula, brief survey of the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, currents with finite mass and normal currents, relation to BV functions, rectifiable and integral currents, slicing, compactness theorem for integral currents and applications. | |||||

Literature | - Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995 - Herbert Federer, Geometric Measure Theory, 1969 - Leon Simon, Introduction to Geometric Measure Theory, 2014, Link - Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta math. 185 (2000), 1-80 - Urs Lang, Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683-742 | |||||

401-4463-62L | Fourier Analysis in Function Space Theory | W | 4 credits | 2V | T. Rivière | |

Abstract | In the most important part of the course, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators. | |||||

Objective | ||||||

Content | During the first lectures we will review the theory of tempered distributions and their Fourier transforms. We will go in particular through the notion of Fréchet spaces, Banach-Steinhaus for Fréchet spaces etc. We will then apply this theory to the Fourier characterization of Hilbert-Sobolev spaces. In the second part of the course we will study fundamental properties of the Hardy-Littlewood Maximal Function in relation with L^p spaces. We will then make a digression through the notion of Marcinkiewicz weak L^p spaces and Lorentz spaces. At this occasion we shall give in particular a proof of Aoki-Rolewicz theorem on the metrisability of quasi-normed spaces. We will introduce the preduals to the weak L^p spaces, the Lorentz L^{p',1} spaces as well as the general L^{p,q} spaces and show some applications of these dualities such as the improved Sobolev embeddings. In the third part of the course, the most important one, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators. This theory will naturally bring us, via the so called Littlewood-Paley decomposition, to the Fourier characterization of classical Hilbert and non Hilbert Function spaces which is one of the main goals of this course. If time permits we shall present the notion of Paraproduct, Paracompositions and the use of Littlewood-Paley decomposition for estimating products and general non-linearities. We also hope to cover fundamental notions from integrability by compensation theory such as Coifman-Rochberg-Weiss commutator estimates and some of its applications to the analysis of PDE. | |||||

Literature | 1) Elias M. Stein, "Singular Integrals and Differentiability Properties of Functions" (PMS-30) Princeton University Press. 2) Javier Duoandikoetxea, "Fourier Analysis" AMS. 3) Loukas Grafakos, "Classical Fourier Analysis" GTM 249 Springer. 4) Loukas Grafakos, "Modern Fourier Analysis" GTM 250 Springer. | |||||

Prerequisites / Notice | Notions from ETH courses in Measure Theory, Functional Analysis I and II (Fundamental results in Banach and Hilbert Space theory, Fourier transform of L^2 Functions) | |||||

Selection: Further Realms | ||||||

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

401-3502-68L | Reading Course THE ENROLMENT IS DONE BY THE STUDY ADMINISTRATION. Please send an email to Studiensekretariat D-MATH <Link> including the following pieces of information: 1) which Reading Course (60, 90, 120 hours of work, corresponding to 2, 3, 4 ECTS credits) you wish to register; 2) in which semester; 3) for which degree programme; 4) your name and first name; 5) your student number; 6) the name and first name of the supervisor of the Reading Course. | W | 2 credits | 4A | Professors | |

Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||

Objective | ||||||

401-3503-68L | Reading Course THE ENROLMENT IS DONE BY THE STUDY ADMINISTRATION. Please send an email to Studiensekretariat D-MATH <Link> including the following pieces of information: 1) which Reading Course (60, 90, 120 hours of work, corresponding to 2, 3, 4 ECTS credits) you wish to register; 2) in which semester; 3) for which degree programme; 4) your name and first name; 5) your student number; 6) the name and first name of the supervisor of the Reading Course. | W | 3 credits | 6A | Professors | |

Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||

Objective | ||||||

401-3504-68L | Reading Course THE ENROLMENT IS DONE BY THE STUDY ADMINISTRATION. Please send an email to Studiensekretariat D-MATH <Link> including the following pieces of information: 1) which Reading Course (60, 90, 120 hours of work, corresponding to 2, 3, 4 ECTS credits) you wish to register; 2) in which semester; 3) for which degree programme; 4) your name and first name; 5) your student number; 6) the name and first name of the supervisor of the Reading Course. | W | 4 credits | 9A | Professors | |

Abstract | For this Reading Course proactive students make an individual agreement with a lecturer to acquire knowledge through independent literature study. | |||||

Objective | ||||||

401-0000-00L | Communication in Mathematics | W | 1 credit | 1V | W. Merry | |

Abstract | Don't hide your Next Great Theorem behind bad writing. This course teaches fundamental communication skills in mathematics: how to write clearly and how to structure mathematical content for different audiences, from theses, to preprints, to personal statements in applications. | |||||

Objective | Knowing how to present written mathematics in a structured and clear manner. | |||||

Content | Topics covered include: - How to write a thesis (more generally, a mathematics paper). - Elementary LaTeX skills and language conventions. - How to write a personal statement for Masters and PhD applications. | |||||

Lecture notes | Full lecture notes will be made available on my website: Link | |||||

Prerequisites / Notice | There are no formal mathematical prerequisites. | |||||

Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||

Selection: Numerical Analysis | ||||||

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

401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 credits | 3V + 1U | A. Jentzen, L. Yaroslavtseva | |

Abstract | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | |||||

Objective | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||

Content | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Applications to computational finance: Option valuation | |||||

Lecture notes | Lecture notes are available as a PDF file: see Learning materials. | |||||

Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | |||||

Prerequisites / Notice | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 19, 2018. Date of the End-of-Semester examination: Wednesday, December 19, 2018, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19. Room for the End-of-Semester examination: ETH HG E 19. Exam inspection: Tuesday, February 26, 2019, 12:00-13:00 at HG D 7.2. Please bring your legi. | |||||

401-4785-00L | Mathematical and Computational Methods in Photonics | W | 8 credits | 4G | H. Ammari | |

Abstract | The aim of this course is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods used to address challenging problems in nanophotonics. The emphasis will be on analyzing plasmon resonant nanoparticles, super-focusing & super-resolution of electromagnetic waves, photonic crystals, electromagnetic cloaking, metamaterials, and metasurfaces | |||||

Objective | The field of photonics encompasses the fundamental science of light propagation and interactions in complex structures, and its technological applications. The recent advances in nanoscience present great challenges for the applied and computational mathematics community. In nanophotonics, the aim is to control, manipulate, reshape, guide, and focus electromagnetic waves at nanometer length scales, beyond the resolution limit. In particular, one wants to break the resolution limit by reducing the focal spot and confine light to length scales that are significantly smaller than half the wavelength. Interactions between the field of photonics and mathematics has led to the emergence of a multitude of new and unique solutions in which today's conventional technologies are approaching their limits in terms of speed, capacity and accuracy. Light can be used for detection and measurement in a fast, sensitive and accurate manner, and thus photonics possesses a unique potential to revolutionize healthcare. Light-based technologies can be used effectively for the very early detection of diseases, with non-invasive imaging techniques or point-of-care applications. They are also instrumental in the analysis of processes at the molecular level, giving a greater understanding of the origin of diseases, and hence allowing prevention along with new treatments. Photonic technologies also play a major role in addressing the needs of our ageing society: from pace-makers to synthetic bones, and from endoscopes to the micro-cameras used in in-vivo processes. Furthermore, photonics are also used in advanced lighting technology, and in improving energy efficiency and quality. By using photonic media to control waves across a wide band of wavelengths, we have an unprecedented ability to fabricate new materials with specific microstructures. The main objective in this course is to report on the use of sophisticated mathematics in diffractive optics, plasmonics, super-resolution, photonic crystals, and metamaterials for electromagnetic invisibility and cloaking. The book merges highly nontrivial multi-mathematics in order to make a breakthrough in the field of mathematical modelling, imaging, and optimal design of optical nanodevices and nanostructures capable of light enhancement, and of the focusing and guiding of light at a subwavelength scale. We demonstrate the power of layer potential techniques in solving challenging problems in photonics, when they are combined with asymptotic analysis and the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. In this course we shall consider both analytical and computational matters in photonics. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, spectral analysis, mathematical imaging, optimal design, stochastic modelling, and analysis of wave propagation phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in photonics, requires a deep understanding of the different scales in the wave propagation problem, an accurate mathematical modelling of the nanodevices, and fine analysis of complex wave propagation phenomena. An emphasis is put on mathematically analyzing plasmon resonant nanoparticles, diffractive optics, photonic crystals, super-resolution, and metamaterials. | |||||

401-4357-68L | On Deep Artificial Neural Networks and Partial Differential Equations | W | 4 credits | 2G | A. Jentzen | |

Abstract | In this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs). | |||||

Objective | The aim of this course is to teach the students a decent knowledge on deep artificial neural networks and their approximation capacities. | |||||

Content | In recent years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a series of computational problems ranging from computer vision, image classification, speech recognition, and natural language processing to computational advertisement. Such numerical simulations indicate that deep artificial neural networks seem to admit the fundamental power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named applications. In this lecture we rigorously analyse approximation capacities of deep artificial neural networks and prove that deep artificial neural networks do overcome the curse of dimensionality in the numerical approximation of solutions of partial differential equations (PDEs). In particular, this course includes (i) a rigorous mathematical introduction to artificial neural networks, (ii) an introduction to some partial differential equations, and (iii) results on approximation capacities of deep artificial neural networks. | |||||

Lecture notes | Lecture notes will be available as a PDF file. | |||||

Literature | Related literature: * Arnulf Jentzen, Diyora Salimova, and Timo Welti, A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients. arXiv:1809.07321 (2018), 48 pages. Available online at [Link]. * Philipp Grohs, Fabian Hornung, Arnulf Jentzen, and Philippe von Wurstemberger, A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. arXiv:1809.02362 (2018), 124 pages. Available online at [Link]. * Andrew R. Barron, Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 (1993), no. 3, 930--945. | |||||

Prerequisites / Notice | Prerequisites: Analysis I and II, Elementary Probability Theory, and Measure Theory | |||||

401-4503-68L | Reading Course: Reduced Basis Methods | W | 4 credits | 2G | R. Hiptmair | |

Abstract | Reduced Basis Methods (RBM) allow the efficient repeated numerical soluton of parameter depedent differential equations, which arise, e.g., in PDE-constrained optimization, optimal control, inverse problems, and uncertainty quantification. This course introduces the mathematical foundations of RBM and discusses algorithmic and implementation aspects. | |||||

Objective | * Knowledge about the main principles underlying RBMs * Familiarity with algorithms for the construction of reduced bases * Knowledge about the role of and techniques for a posteriori error estimation. * Familiarity with some applications of RBMs. | |||||

Literature | Main reference: Hesthaven, Jan S.; Rozza, Gianluigi; Stamm, Benjamin, Certified reduced basis methods for parametrized partial differential equations. SpringerBriefs in Mathematics, 2016 Supplementary reference: Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico, Reduced basis methods for partial differential equations. An introduction. Unitext 92, Springer, Cham, 2016. | |||||

Prerequisites / Notice | This is a reading course, which will closely follow the book by J. Hesthaven, G. Rozza and B. Stamm. Participants are expected to study particular sections of the book every week, which will then be discussed during the course sessions. | |||||

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

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

401-4607-68L | Topics on the Gaussian Free Field | W | 4 credits | 2V | W. Werner | |

Abstract | We will discuss various aspects and properties of the Gaussian Free Field. | |||||

Objective | ||||||

Content | Topics discussed will include: - Discrete and continuous Gaussian Free Field - Local sets. - Relation to loop-soups. - Uniform spanning trees. | |||||

401-4611-68L | Regularity Structures | W | 6 credits | 3V | J. Teichmann | |

Abstract | We develop the main tools of Martin Hairer's theory of regularity structures to solve singular stochastic partial differential equations in a pathwise way or addtionally by re-normalization techniques. | |||||

Objective | ||||||

401-4619-67L | Advanced Topics in Computational StatisticsDoes not take place this semester. | W | 4 credits | 2V | N. Meinshausen | |

Abstract | This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling. | |||||

Objective | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||

Content | The main focus will be on graphical models in various forms: Markov properties of undirected graphs; Belief propagation; Hidden Markov Models; Structure estimation and parameter estimation; inference for high-dimensional data; causal graphical models | |||||

Prerequisites / Notice | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||

401-3628-14L | Bayesian StatisticsDoes not take place this semester. | W | 4 credits | 2V | ||

Abstract | Introduction to the Bayesian approach to statistics: Decision theory, prior distributions, hierarchical Bayes models, Bayesian tests and model selection, empirical Bayes, computational methods, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods. | |||||

Objective | Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis. | |||||

Content | Topics that we will discuss are: Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, Jeffreys priors), tests and model selection (Bayes factors, hyper-g priors in regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods) | |||||

Lecture notes | A script will be available in English. | |||||

Literature | Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007. A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013). Additional references will be given in the course. | |||||

Prerequisites / Notice | Familiarity with basic concepts of frequentist statistics and with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||

401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 credits | 2V + 1U | L. Meier | |

Abstract | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Objective | 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. | |||||

Content | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Literature | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||

Prerequisites / Notice | 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. |

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