# Search result: Catalogue data in Spring Semester 2020

Statistics Master The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible. | ||||||

Core Courses In each subject area, the core courses offered are normally mathematical as well as application-oriented in content. For each subject area, only one of these is recognised for the Master degree. | ||||||

Regression No offering in this semester (401-3622-00L Statistical Modelling is offered in the autumn semester). | ||||||

Analysis of Variance and Design of Experiments No offering in this semester | ||||||

Multivariate 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. | |||||

401-0102-00L | Applied Multivariate Statistics | W | 5 credits | 2V + 1U | F. Sigrist | |

Abstract | Multivariate statistics analyzes data on several random variables simultaneously. This course introduces the basic concepts and provides an overview of classical and modern methods of multivariate statistics including visualization, dimension reduction, supervised and unsupervised learning for multivariate data. An emphasis is on applications and solving problems with the statistical software R. | |||||

Objective | After the course, you are able to: - describe the various methods and the concepts 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, multivariate outliers, the multivariate normal distribution, dimension reduction, principal component analysis, multidimensional scaling, factor analysis, cluster analysis, classification, multivariate tests and multiple testing | |||||

Lecture notes | None | |||||

Literature | 1) "An Introduction to Applied Multivariate Analysis with R" (2011) by Everitt and Hothorn 2) "An Introduction to Statistical Learning: With Applications in R" (2013) by Gareth, Witten, Hastie and Tibshirani Electronic versions (pdf) of both books can be downloaded for free from the ETH library. | |||||

Prerequisites / Notice | This course is targeted at students with a non-math background. Requirements: ========== 1) Introductory course in statistics (min: t-test, regression; ideal: conditional probability, multiple regression) 2) Good understanding of R (if you don't know R, it is recommended that you study chapters 1,2,3,4, and 5 of "Introductory Statistics with R" from Peter Dalgaard, which is freely available online from the ETH library) An alternative course with more emphasis on theory is 401-6102-00L "Multivariate Statistics" (only every second year). 401-0102-00L and 401-6102-00L are mutually exclusive. You can register for only one of these two courses. | |||||

Time Series and Stochastic Processes | ||||||

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

401-6624-11L | Applied Time Series | W | 5 credits | 2V + 1U | M. Dettling | |

Abstract | The course starts with an introduction to time series analysis (examples, goal, mathematical notation). In the following, descriptive techniques, modeling and prediction as well as advanced topics will be covered. | |||||

Objective | Getting to know the mathematical properties of time series, as well as the requirements, descriptive techniques, models, advanced methods and software that are necessary such that the student can independently run an applied time series analysis. | |||||

Content | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. | |||||

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

Prerequisites / Notice | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. | |||||

Mathematical Statistics No offering in this semester | ||||||

Specialization Areas and Electives | ||||||

Statistical and Mathematical Courses | ||||||

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

401-4632-15L | Causality | W | 4 credits | 2G | C. Heinze-Deml | |

Abstract | In statistics, we are used to search for the best predictors of some random variable. In many situations, however, we are interested in predicting a system's behavior under manipulations. For such an analysis, we require knowledge about the underlying causal structure of the system. In this course, we study concepts and theory behind causal inference. | |||||

Objective | After this course, you should be able to - understand the language and concepts of causal inference - know the assumptions under which one can infer causal relations from observational and/or interventional data - describe and apply different methods for causal structure learning - given data and a causal structure, derive causal effects and predictions of interventional experiments | |||||

Prerequisites / Notice | Prerequisites: basic knowledge of probability theory and regression | |||||

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. | |||||

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). | |||||

401-3642-00L | Brownian Motion and Stochastic Calculus | W | 10 credits | 4V + 1U | W. Werner | |

Abstract | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||

Objective | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||

Lecture notes | Lecture notes will be distributed in class. | |||||

Literature | - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). - D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). | |||||

Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). | |||||

401-6228-00L | Programming with R for Reproducible Research | W | 1 credit | 1G | M. Mächler | |

Abstract | Deeper understanding of R: Function calls, rather than "commands". Reproducible research and data analysis via Sweave and Rmarkdown. Limits of floating point arithmetic. Understanding how functions work. Environments, packages, namespaces. Closures, i.e., Functions returning functions. Lists and [mc]lapply() for easy parallelization. Performance measurement and improvements. | |||||

Objective | Learn to understand R as a (very versatile and flexible) programming language and learn about some of its lower level functionalities which are needed to understand *why* R works the way it does. | |||||

Content | See "Skript": https://github.com/mmaechler/ProgRRR/tree/master/ETH | |||||

Lecture notes | Material available from Github https://github.com/mmaechler/ProgRRR/tree/master/ETH (typically will be updated during course) | |||||

Literature | Norman Matloff (2011) The Art of R Programming - A tour of statistical software design. no starch press, San Francisco. on stock at Polybuchhandlung (CHF 42.-). More material, notably H.Wickam's "Advanced R" : see my ProgRRR github page. | |||||

Prerequisites / Notice | R Knowledge on the same level as after *both* parts of the ETH lecture 401-6217-00L Using R for Data Analysis and Graphics Link An interest to dig deeper than average R users do. Bring your own laptop with a recent version of R installed | |||||

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. | |||||

401-4658-00L | Computational Methods for Quantitative Finance: PDE Methods | W | 6 credits | 3V + 1U | C. Schwab | |

Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming and knowledge of numerical mathematics at ETH BSc level. | |||||

Objective | Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation. | |||||

Content | 1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques. | |||||

Lecture notes | There will be english, typed lecture notes as well as MATLAB software for registered participants in the course. | |||||

Literature | R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000. N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. | |||||

401-2284-00L | Measure and Integration | W | 6 credits | 3V + 2U | F. Da Lio | |

Abstract | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Objective | Basic acquaintance with the abstract theory of measure and integration | |||||

Content | Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces | |||||

Lecture notes | New lecture notes in English will be made available during the course | |||||

Literature | 1. L. Evans and R.F. Gariepy " Measure theory and fine properties of functions" 2. Walter Rudin "Real and complex analysis" 3. R. Bartle The elements of Integration and Lebesgue Measure 4. The notes by Prof. Michael Struwe Springsemester 2013, https://people.math.ethz.ch/~struwe/Skripten/AnalysisIII-FS2013-12-9-13.pdf. 5. The notes by Prof. UrsLang Springsemester 2019. https://people.math.ethz.ch/~lang/mi.pdf 6. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis: http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf . | |||||

401-3903-11L | Geometric Integer Programming | W | 6 credits | 2V + 1U | J. Paat | |

Abstract | Integer programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems. | |||||

Objective | The purpose of the lecture is to provide a geometric treatment of the theory of integer optimization. | |||||

Content | Key topics are: - Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension. - Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems - Duality theory for integer optimization problems from the vantage point of lattice free sets. | |||||

Lecture notes | not available, blackboard presentation | |||||

Literature | Lecture notes will be provided. Other helpful materials include Bertsimas, Weismantel: Optimization over Integers, 2005 and Schrijver: Theory of linear and integer programming, 1986. | |||||

Prerequisites / Notice | "Mathematical Optimization" (401-3901-00L) | |||||

401-4944-20L | Mathematics of Data Science | W | 8 credits | 4G | A. Bandeira | |

Abstract | Mostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data. | |||||

Objective | Introduction to various mathematical aspects of Data Science. | |||||

Content | These topics lie in overlaps of (Applied) Mathematics with: Computer Science, Electrical Engineering, Statistics, and/or Operations Research. Each lecture will feature a couple of Mathematical Open Problem(s) related to Data Science. The main mathematical tools used will be Probability and Linear Algebra, and a basic familiarity with these subjects is required. There will also be some (although knowledge of these tools is not assumed) Graph Theory, Representation Theory, Applied Harmonic Analysis, among others. The topics treated will include Dimension reduction, Manifold learning, Sparse recovery, Random Matrices, Approximation Algorithms, Community detection in graphs, and several others. | |||||

Lecture notes | https://people.math.ethz.ch/~abandeira/TenLecturesFortyTwoProblems.pdf | |||||

Prerequisites / Notice | The main mathematical tools used will be Probability, Linear Algebra (and real analysis), and a working knowledge of these subjects is required. In addition to these prerequisites, this class requires a certain degree of mathematical maturity--including abstract thinking and the ability to understand and write proofs. We encourage students who are interested in mathematical data science to take both this course and ``227-0434-10L Mathematics of Information'' taught by Prof. H. Bölcskei. The two courses are designed to be complementary. A. Bandeira and H. Bölcskei | |||||

227-0434-10L | Mathematics of Information | W | 8 credits | 3V + 2U + 2A | H. Bölcskei | |

Abstract | The class focuses on mathematical aspects of 1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction 2. Learning theory: Approximation theory, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension | |||||

Objective | The aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture, exercise sessions with homework problems, and of a research project, which can be carried out either individually or in groups. The research project consists of either 1. software development for the solution of a practical signal processing or machine learning problem or 2. the analysis of a research paper or 3. a theoretical research problem of suitable complexity. Students are welcome to propose their own project at the beginning of the semester. The outcomes of all projects have to be presented to the entire class at the end of the semester. | |||||

Content | Mathematics of Information 1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems 2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, matching pursuits, super-resolution, spectrum-blind sampling, subspace algorithms (MUSIC, ESPRIT, matrix pencil), estimation in the high-dimensional noisy case, Lasso 3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma Mathematics of Learning 4. Approximation theory: Nonlinear approximation theory, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes, recovery from incomplete data, information-based complexity, curse of dimensionality 5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination, blessings of dimensionality | |||||

Lecture notes | Detailed lecture notes will be provided at the beginning of the semester and as we go along. | |||||

Prerequisites / Notice | This course is aimed at students with a background in basic linear algebra, analysis, statistics, and probability. We encourage students who are interested in mathematical data science to take both this course and "401-4944-20L Mathematics of Data Science" by Prof. A. Bandeira. The two courses are designed to be complementary. H. Bölcskei and A. Bandeira | |||||

261-5110-00L | Optimization for Data Science | W | 8 credits | 3V + 2U + 2A | B. Gärtner, D. Steurer | |

Abstract | This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in data science. | |||||

Objective | Understanding the theoretical guarantees (and their limits) of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science. | |||||

Content | This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in machine learning and data science. In the first part of the course, we will first give a brief introduction to convex optimization, with some basic motivating examples from machine learning. Then we will analyse classical and more recent first and second order methods for convex optimization: gradient descent, projected gradient descent, subgradient descent, stochastic gradient descent, Nesterov's accelerated method, Newton's method, and Quasi-Newton methods. The emphasis will be on analysis techniques that occur repeatedly in convergence analyses for various classes of convex functions. We will also discuss some classical and recent theoretical results for nonconvex optimization. In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation. | |||||

Prerequisites / Notice | As background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary. | |||||

252-0220-00L | Introduction to Machine Learning Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact studiensekretariat@inf.ethz.ch | W | 8 credits | 4V + 2U + 1A | A. Krause | |

Abstract | The course introduces the foundations of learning and making predictions based on data. | |||||

Objective | The course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project. | |||||

Content | - Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent) - Linear classification: Logistic regression (feature selection, sparsity, multi-class) - Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor - Neural networks (backpropagation, regularization, convolutional neural networks) - Unsupervised learning (k-means, PCA, neural network autoencoders) - The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference) - Statistical decision theory (decision making based on statistical models and utility functions) - Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions) - Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE) - Bayesian approaches to unsupervised learning (Gaussian mixtures, EM) | |||||

Literature | Textbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press | |||||

Prerequisites / Notice | Designed to provide a basis for following courses: - Advanced Machine Learning - Deep Learning - Probabilistic Artificial Intelligence - Seminar "Advanced Topics in Machine Learning" | |||||

252-0526-00L | Statistical Learning Theory | W | 7 credits | 3V + 2U + 1A | J. M. Buhmann, C. Cotrini Jimenez | |

Abstract | The course covers advanced methods of statistical learning: - Variational methods and optimization. - Deterministic annealing. - Clustering for diverse types of data. - Model validation by information theory. | |||||

Objective | The course surveys recent methods of statistical learning. The fundamentals of machine learning, as presented in the courses "Introduction to Machine Learning" and "Advanced Machine Learning", are expanded from the perspective of statistical learning. | |||||

Content | - Variational methods and optimization. We consider optimization approaches for problems where the optimizer is a probability distribution. We will discuss concepts like maximum entropy, information bottleneck, and deterministic annealing. - Clustering. This is the problem of sorting data into groups without using training samples. We discuss alternative notions of "similarity" between data points and adequate optimization procedures. - Model selection and validation. This refers to the question of how complex the chosen model should be. In particular, we present an information theoretic approach for model validation. - Statistical physics models. We discuss approaches for approximately optimizing large systems, which originate in statistical physics (free energy minimization applied to spin glasses and other models). We also study sampling methods based on these models. | |||||

Lecture notes | A draft of a script will be provided. Lecture slides will be made available. | |||||

Literature | Hastie, Tibshirani, Friedman: The Elements of Statistical Learning, Springer, 2001. L. Devroye, L. Gyorfi, and G. Lugosi: A probabilistic theory of pattern recognition. Springer, New York, 1996 | |||||

Prerequisites / Notice | Knowledge of machine learning (introduction to machine learning and/or advanced machine learning) Basic knowledge of statistics. | |||||

252-3900-00L | Big Data for Engineers This course is not intended for Computer Science and Data Science MSc students! | W | 6 credits | 2V + 2U + 1A | G. Fourny | |

Abstract | This course is part of the series of database lectures offered to all ETH departments, together with Information Systems for Engineers. It introduces the most recent advances in the database field: how do we scale storage and querying to Petabytes of data, with trillions of records? How do we deal with heterogeneous data sets? How do we deal with alternate data shapes like trees and graphs? | |||||

Objective | This lesson is complementary with Information Systems for Engineers as they cover different time periods of database history and practices -- you can even take both lectures at the same time. The key challenge of the information society is to turn data into information, information into knowledge, knowledge into value. This has become increasingly complex. Data comes in larger volumes, diverse shapes, from different sources. Data is more heterogeneous and less structured than forty years ago. Nevertheless, it still needs to be processed fast, with support for complex operations. This combination of requirements, together with the technologies that have emerged in order to address them, is typically referred to as "Big Data." This revolution has led to a completely new way to do business, e.g., develop new products and business models, but also to do science -- which is sometimes referred to as data-driven science or the "fourth paradigm". Unfortunately, the quantity of data produced and available -- now in the Zettabyte range (that's 21 zeros) per year -- keeps growing faster than our ability to process it. Hence, new architectures and approaches for processing it were and are still needed. Harnessing them must involve a deep understanding of data not only in the large, but also in the small. The field of databases evolves at a fast pace. In order to be prepared, to the extent possible, to the (r)evolutions that will take place in the next few decades, the emphasis of the lecture will be on the paradigms and core design ideas, while today's technologies will serve as supporting illustrations thereof. After visiting this lecture, you should have gained an overview and understanding of the Big Data landscape, which is the basis on which one can make informed decisions, i.e., pick and orchestrate the relevant technologies together for addressing each business use case efficiently and consistently. | |||||

Content | This course gives an overview of database technologies and of the most important database design principles that lay the foundations of the Big Data universe. It targets specifically students with a scientific or Engineering, but not Computer Science, background. We take the monolithic, one-machine relational stack from the 1970s, smash it down and rebuild it on top of large clusters: starting with distributed storage, and all the way up to syntax, models, validation, processing, indexing, and querying. A broad range of aspects is covered with a focus on how they fit all together in the big picture of the Big Data ecosystem. No data is harmed during this course, however, please be psychologically prepared that our data may not always be in normal form. - physical storage: distributed file systems (HDFS), object storage(S3), key-value stores - logical storage: document stores (MongoDB), column stores (HBase) - data formats and syntaxes (XML, JSON, RDF, CSV, YAML, protocol buffers, Avro) - data shapes and models (tables, trees) - type systems and schemas: atomic types, structured types (arrays, maps), set-based type systems (?, *, +) - an overview of functional, declarative programming languages across data shapes (SQL, JSONiq) - the most important query paradigms (selection, projection, joining, grouping, ordering, windowing) - paradigms for parallel processing, two-stage (MapReduce) and DAG-based (Spark) - resource management (YARN) - what a data center is made of and why it matters (racks, nodes, ...) - underlying architectures (internal machinery of HDFS, HBase, Spark) - optimization techniques (functional and declarative paradigms, query plans, rewrites, indexing) - applications. Large scale analytics and machine learning are outside of the scope of this course. | |||||

Literature | Papers from scientific conferences and journals. References will be given as part of the course material during the semester. | |||||

Prerequisites / Notice | This course is not intended for Computer Science and Data Science students. Computer Science and Data Science students interested in Big Data MUST attend the Master's level Big Data lecture, offered in Fall. Requirements: programming knowledge (Java, C++, Python, PHP, ...) as well as basic knowledge on databases (SQL). If you have already built your own website with a backend SQL database, this is perfect. Attendance is especially recommended to those who attended Information Systems for Engineers last Fall, which introduced the "good old databases of the 1970s" (SQL, tables and cubes). However, this is not a strict requirement, and it is also possible to take the lectures in reverse order. | |||||

263-5300-00L | Guarantees for Machine Learning | W | 5 credits | 2V + 2A | F. Yang | |

Abstract | This course teaches classical and recent methods in statistics and optimization commonly used to prove theoretical guarantees for machine learning algorithms. The knowledge is then applied in project work that focuses on understanding phenomena in modern machine learning. | |||||

Objective | This course is aimed at advanced master and doctorate students who want to understand and/or conduct independent research on theory for modern machine learning. For this purpose, students will learn common mathematical techniques from statistical learning theory. In independent project work, they then apply their knowledge and go through the process of critically questioning recently published work, finding relevant research questions and learning how to effectively present research ideas to a professional audience. | |||||

Content | This course teaches some classical and recent methods in statistical learning theory aimed at proving theoretical guarantees for machine learning algorithms, including topics in - concentration bounds, uniform convergence - high-dimensional statistics (e.g. Lasso) - prediction error bounds for non-parametric statistics (e.g. in kernel spaces) - minimax lower bounds - regularization via optimization The project work focuses on active theoretical ML research that aims to understand modern phenomena in machine learning, including but not limited to - how overparameterization could help generalization ( interpolating models, linearized NN ) - how overparameterization could help optimization ( non-convex optimization, loss landscape ) - complexity measures and approximation theoretic properties of randomly initialized and trained NN - generalization of robust learning ( adversarial robustness, standard and robust error tradeoff ) - prediction with calibrated confidence ( conformal prediction, calibration ) | |||||

Prerequisites / Notice | It’s absolutely necessary for students to have a strong mathematical background (basic real analysis, probability theory, linear algebra) and good knowledge of core concepts in machine learning taught in courses such as “Introduction to Machine Learning”, “Regression”/ “Statistical Modelling”. It's also helpful to have heard an optimization course or approximation theoretic course. In addition to these prerequisites, this class requires a certain degree of mathematical maturity—including abstract thinking and the ability to understand and write proofs. | |||||

636-0702-00L | Statistical Models in Computational Biology | W | 6 credits | 2V + 1U + 2A | N. Beerenwinkel | |

Abstract | The course offers an introduction to graphical models and their application to complex biological systems. Graphical models combine a statistical methodology with efficient algorithms for inference in settings of high dimension and uncertainty. The unifying graphical model framework is developed and used to examine several classical and topical computational biology methods. | |||||

Objective | The goal of this course is to establish the common language of graphical models for applications in computational biology and to see this methodology at work for several real-world data sets. | |||||

Content | Graphical models are a marriage between probability theory and graph theory. They combine the notion of probabilities with efficient algorithms for inference among many random variables. Graphical models play an important role in computational biology, because they explicitly address two features that are inherent to biological systems: complexity and uncertainty. We will develop the basic theory and the common underlying formalism of graphical models and discuss several computational biology applications. Topics covered include conditional independence, Bayesian networks, Markov random fields, Gaussian graphical models, EM algorithm, junction tree algorithm, model selection, Dirichlet process mixture, causality, the pair hidden Markov model for sequence alignment, probabilistic phylogenetic models, phylo-HMMs, microarray experiments and gene regulatory networks, protein interaction networks, learning from perturbation experiments, time series data and dynamic Bayesian networks. Some of the biological applications will be explored in small data analysis problems as part of the exercises. | |||||

Lecture notes | no | |||||

Literature | - Airoldi EM (2007) Getting started in probabilistic graphical models. PLoS Comput Biol 3(12): e252. doi:10.1371/journal.pcbi.0030252 - Bishop CM. Pattern Recognition and Machine Learning. Springer, 2007. - Durbin R, Eddy S, Krogh A, Mitchinson G. Biological Sequence Analysis. Cambridge university Press, 2004 | |||||

701-0104-00L | Statistical Modelling of Spatial Data | W | 3 credits | 2G | A. J. Papritz | |

Abstract | In environmental sciences one often deals with spatial data. When analysing such data the focus is either on exploring their structure (dependence on explanatory variables, autocorrelation) and/or on spatial prediction. The course provides an introduction to geostatistical methods that are useful for such analyses. | |||||

Objective | The course will provide an overview of the basic concepts and stochastic models that are used to model spatial data. In addition, participants will learn a number of geostatistical techniques and acquire familiarity with R software that is useful for analyzing spatial data. | |||||

Content | After an introductory discussion of the types of problems and the kind of data that arise in environmental research, an introduction into linear geostatistics (models: stationary and intrinsic random processes, modelling large-scale spatial patterns by linear regression, modelling autocorrelation by variogram; kriging: mean square prediction of spatial data) will be taught. The lectures will be complemented by data analyses that the participants have to do themselves. | |||||

Lecture notes | Slides, descriptions of the problems for the data analyses and solutions to them will be provided. | |||||

Literature | P.J. Diggle & P.J. Ribeiro Jr. 2007. Model-based Geostatistics. Springer. Bivand, R. S., Pebesma, E. J. & Gómez-Rubio, V. 2013. Applied Spatial Data Analysis with R. Springer. | |||||

Prerequisites / Notice | Familiarity with linear regression analysis (e.g. equivalent to the first part of the course 401-0649-00L Applied Statistical Regression) and with the software R (e.g. 401-6215-00L Using R for Data Analysis and Graphics (Part I), 401-6217-00L Using R for Data Analysis and Graphics (Part II)) are required for attending the course. | |||||

401-6222-00L | Robust and Nonlinear Regression | W | 2 credits | 1V + 1U | A. F. Ruckstuhl | |

Abstract | In a first part, the basic ideas of robust fitting techniques are explained theoretically and practically using regression models and explorative multivariate analysis. The second part addresses the challenges of fitting nonlinear regression functions and finding reliable confidence intervals. | |||||

Objective | Participants are familiar with common robust fitting methods for the linear regression models as well as for exploratory multivariate analysis and are able to assess their suitability for the data at hand. They know the challenges that arise in fitting of nonlinear regression functions, and know the difference between classical and profile based methods to determine confidence intervals. They can apply the discussed methods in practise by using the statistics software R. | |||||

Content | Robust fitting: influence function, breakdown point, regression M-estimation, regression MM-estimation, robust inference, covariance estimation with high breakdown point, application in principal component analysis and linear discriminant analysis. Nonlinear regression: the nonlinear regression model, estimation methods, approximate tests and confidence intervals, estimation methods, profile t plot, profile traces, parameter transformation, prediction and calibration | |||||

Lecture notes | Lecture notes are available | |||||

Prerequisites / Notice | It is a block course on three Mondays in June | |||||

401-8618-00L | Statistical Methods in Epidemiology (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: STA408 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/mobilitaet.html | W | 5 credits | 3G | University lecturers | |

Abstract | Analysis of case-control and cohort studies. The most relevant measures of effect (odds and rate ratios) are introduced, and methods for adjusting for confounders (Mantel-Haenszel, regression) are thoroughly discussed. Advanced topics such as measurement error and propensity score adjustments are also covered. We will outline statistical methods for case-crossover and case series studies etc. | |||||

Objective | ||||||

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). | |||||

447-6236-00L | Statistics for Survival Data | W | 2 credits | 1V + 1U | A. Hauser | |

Abstract | The primary purpose of a survival analysis is to model and analyze time-to-event data; that is, data that have as a principal endpoint the length of time for an event to occur. This block course introduces the field of survival analysis without getting too embroiled in the theoretical technicalities. | |||||

Objective | Presented here are some frequently used parametric models and methods, including accelerated failure time models; and the newer nonparametric procedures which include the Kaplan-Meier estimate of survival and the Cox proportional hazards regression model. The statistical tools treated are applicable to data from medical clinical trials, public health, epidemiology, engineering, economics, psychology, and demography as well. | |||||

Content | The primary purpose of a survival analysis is to model and analyze time-to-event data; that is, data that have as a principal endpoint the length of time for an event to occur. Such events are generally referred to as "failures." Some examples are time until an electrical component fails, time to first recurrence of a tumor (i.e., length of remission) after initial treatment, time to death, time to the learning of a skill, and promotion times for employees. In these examples we can see that it is possible that a "failure" time will not be observed either by deliberate design or due to random censoring. This occurs, for example, if a patient is still alive at the end of a clinical trial period or has moved away. The necessity of obtaining methods of analysis that accommodate censoring is the primary reason for developing specialized models and procedures for failure time data. Survival analysis is the modern name given to the collection of statistical procedures which accommodate time-to-event censored data. Prior to these new procedures, incomplete data were treated as missing data and omitted from the analysis. This resulted in the loss of the partial information obtained and in introducing serious systematic error (bias) in estimated quantities. This, of course, lowers the efficacy of the study. The procedures discussed here avoid bias and are more powerful as they utilize the partial information available on a subject or item. This block course introduces the field of survival analysis without getting too embroiled in the theoretical technicalities. Models for failure times describe either the survivor function or hazard rate and their dependence on explanatory variables. Presented here are some frequently used parametric models and methods, including accelerated failure time models; and the newer nonparametric procedures which include the Kaplan-Meier estimate of survival and the Cox proportional hazards regression model. The statistical tools treated are applicable to data from medical clinical trials, public health, epidemiology, engineering, economics, psychology, and demography as well. | |||||

401-8628-00L | Survival Analysis (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: STA425 Mind the enrolment deadlines at UZH: http://www.uzh.ch/studies/application/mobilitaet_en.html | W | 3 credits | 1.5G | University lecturers | |

Abstract | The analysis of survival times, or in more general terms, the analysis of time to event variables is concerned with models for censored observations. Because we cannot always wait until the event of interest actually happens, the methods discussed here are required for an appropriate handling of incomplete observations where we only know that the event of interest did not happen within ... | |||||

Objective | ||||||

Content | During the course, we will study the most important methods and models for censored data, including - general concepts of censoring, - simple summary statistics, - estimation of survival curves, - frequentist inference for two and more groups, and - regression models for censored observations | |||||

Application Areas Students select one area of application and look for suitable courses in which quantitative methods and modeling play a role. They need the consent by the Advisor (http://stat.ethz.ch/~kalisch/) that the chosen courses are eligible in the category "Application Areas". For the category assignment of eligible courses keep the choice "no category" and take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat/staff/ekuenti) after having received the credits. The Study Administration Office needs the Advisor's consent. | ||||||

Seminar or Semester Paper | ||||||

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

401-4620-00L | Statistics Lab Number of participants limited to 27. | W | 6 credits | 2S | M. Kalisch, M. H. Maathuis, M. Mächler, L. Meier, N. Meinshausen | |

Abstract | "Statistics Lab" is an Applied Statistics Workshop in Data Analysis. It provides a learning environment in a realistic setting. Students lead a regular consulting session at the Seminar für Statistik (SfS). After the session, the statistical data analysis is carried out and a written report and results are presented to the client. The project is also presented in the course's seminar. | |||||

Objective | - gain initial experience in the consultancy process - carry out a consultancy session and produce a report - apply theoretical knowledge to an applied problem After the course, students will have practical knowledge about statistical consulting. They will have determined the scientific problem and its context, enquired the design of the experiment or data collection, and selected the appropriate methods to tackle the problem. They will have deepened their statistical knowledge, and applied their theoretical knowledge to the problem. They will have gathered experience in explaining the relevant mathematical and software issues to a client. They will have performed a statistical analysis using R (or SPSS). They improve their skills in writing a report and presenting statistical issues in a talk. | |||||

Content | Students participate in consulting meetings at the SfS. Several consulting dates are available for student participation. These are arranged individually. -During the first meeting the student mainly observes and participates in the discussion. During the second meeting (with a different client), the student leads the meeting. The member of the consulting team is overseeing (and contributing to) the meeting. -After the meeting, the student performs the recommended analysis, produces a report and presents the results to the client. -Finally, the student presents the case in the weekly course seminar in a talk. All students are required to attend the seminar regularly. | |||||

Lecture notes | n/a | |||||

Literature | The required literature will depend on the specific statistical problem under investigation. Some introductory material can be found below. | |||||

Prerequisites / Notice | Prerequisites: Sound knowledge in basic statistical methods, especially regression and, if possible, analysis of variance. Basic experience in Data Analysis with R. | |||||

401-3630-04L | Semester Paper Successful participation in the course unit 401-2000-00L Scientific Works in Mathematics is required. For more information, see www.math.ethz.ch/intranet/students/study-administration/theses.html | W | 4 credits | 6A | Supervisors | |

Abstract | Semester papers serve to delve into a problem in statistics and to study it with the appropriate methods or to compile and clearly exhibit a case study of a statistical evaluation. | |||||

Objective | ||||||

401-3630-94L | Semester Paper Successful participation in the course unit 401-2000-00L Scientific Works in Mathematics is required. For more information, see www.math.ethz.ch/intranet/students/study-administration/theses.html | W | 4 credits | 6A | Supervisors | |

Abstract | Semester papers serve to delve into a problem in statistics and to study it with the appropriate methods or to compile and clearly exhibit a case study of a statistical evaluation. | |||||

Objective | ||||||

401-3630-06L | Semester Paper Successful participation in the course unit 401-2000-00L Scientific Works in Mathematics is required. For more information, see www.math.ethz.ch/intranet/students/study-administration/theses.html | W | 6 credits | 9A | Supervisors | |

Abstract | Semester papers serve to delve into a problem in statistics and to study it with the appropriate methods or to compile and clearly exhibit a case study of a statistical evaluation. | |||||

Objective | ||||||

401-3620-20L | Student Seminar in Statistics: Inference in Non-Classical Regression Models Number of participants limited to 24. Mainly for students from the Mathematics Bachelor and Master Programmes who, in addition to the introductory course unit 401-2604-00L Probability and Statistics, have heard at least one core or elective course in statistics. Also offered in the Master Programmes Statistics resp. Data Science. | W | 4 credits | 2S | F. Balabdaoui | |

Abstract | Review of some non-standard regression models and the statistical properties of estimation methods in such models. | |||||

Objective | The main goal is the students get to discover some less known regression models which either generalize the well-known linear model (for example monotone regression) or violate some of the most fundamental assumptions (as in shuffled or unlinked regression models). | |||||

Content | Linear regression is one of the most used models for prediction and hence one of the most understood in statistical literature. However, linearity might too simplistic to capture the actual relationship between some response and given covariates. Also, there are many real data problems where linearity is plausible but the actual pairing between the observed covariates and responses is completely lost or at partially. In this seminar, we review some of the non-classical regression models and the statistical properties of the estimation methods considered by well-known statisticians and machine learners. This will encompass: 1. Monotone regression 2. Single index model 3. Unlinked regression 4. Partially unlinked regression | |||||

Lecture notes | No script is necessary for this seminar | |||||

Literature | In the following is the material that will read and studied by each pair of students (all the items listed below are available through the ETH electronic library or arXiv): 1. Chapter 2 from the book "Nonparametric estimation under shape constraints" by P. Groeneboom and G. Jongbloed, 2014, Cambridge University Press 2. "Nonparametric shape-restricted regression" by A. Guntuoyina and B. Sen, 2018, Statistical Science, Volume 33, 568-594 3. "Asymptotic distributions for two estimators of the single index model" by Y. Xia, 2006, Econometric Theory, Volume 22, 1112-1137 4. "Least squares estimation in the monotone single index model" by F. Balabdaoui, C. Durot and H. K. Jankowski, Journal of Bernoulli, 2019, Volume 4B, 3276-3310 5. "Least angle regression" by B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, 2004, Annals of Statsitics, Volume 32, 407-499. 6. "Sharp thresholds for high dimensional and noisy sparsity recovery using l1-constrained quadratic programming (Lasso)" by M. Wainwright, 2009, IEEE transactions in Information Theory, Volume 55, 1-19 7."Denoising linear models with permuted data" by A. Pananjady, M. Wainwright and T. A. Courtade and , 2017, IEEE International Symposium on Information Theory, 446-450. 8. "Linear regression with shuffled data: statistical and computation limits of permutation recovery" by A. Pananjady, M. Wainwright and T. A. Courtade , 2018, IEEE transactions in Information Theory, Volume 64, 3286-3300 9. "Linear regression without correspondence" by D. Hsu, K. Shi and X. Sun, 2017, NIPS 10. "A pseudo-likelihood approach to linear regression with partially shuffled data" by M. Slawski, G. Diao, E. Ben-David, 2019, arXiv. 11. "Uncoupled isotonic regression via minimum Wasserstein deconvolution" by P. Rigollet and J. Weed, 2019, Information and Inference, Volume 00, 1-27 | |||||

401-3940-20L | Student Seminar in Mathematics and Data: Optimization of Random Functions Number of participants limited to 12. | W | 4 credits | 2S | A. Bandeira | |

Abstract | More information at course webpage: https://people.math.ethz.ch/~abandeira/Spring2020.StudentSeminar.html | |||||

Objective | ||||||

363-1100-00L | Risk Case Study Challenge Does not take place this semester. | W | 3 credits | 2S | A. Bommier, S. Feuerriegel | |

Abstract | This seminar provides master students at ETH with the challenging opportunity of working on a real risk modelling and risk management case in close collaboration with a Risk Center Partner Company. For the Spring 2019 Edition the Partner will be Zurich Insurance Group. | |||||

Objective | Students work on a real risk-related case of a business relevant topic provided by experts from Risk Center partners. While gaining substantial insights into the risk modeling and management of the industry, students explore the case or problem on their own, working in teams, and develop possible solutions. The cases allow students to use logical problem solving skills with emphasis on evidence and application and involve the integration of scientific knowledge. Typically, the risk-related cases can be complex, cover ambiguities, and may be addressed in more than one way. During the seminar students visit the partners’ headquarters, conduct interviews with members of the management team as well as internal and external experts, and present their results. | |||||

Content | Get a basic understanding of o The insurance and reinsurance business o Risk management and risk modelling o The role of operational risk management Get in contact with industry experts and conduct interviews on the topic. Conduct a small empirical study and present findings to the company | |||||

Prerequisites / Notice | Please apply for this course via the official website (www.riskcenter.ethz.ch/education/lectures/risk-case-study-challenge-.html). Apply no later than February 15, 2019. The number of participants is limited to 14. | |||||

GESS Science in Perspective Two credits are needed from the "Science in Perspective" programme with language courses excluded if three credits from language courses have already been recognised for the Bachelor's degree. see Link (Eight credits must be acquired in this category: normally six during the Bachelor’s degree programme, and two during the Master’s degree programme. A maximum of three credits from language courses from the range of the Language Center of the University of Zurich and ETH Zurich may be recognised. In addition, only advanced courses (level B2 upwards) in the European languages English, French, Italian and Spanish are recognised. German language courses are recognised from level C2 upwards.) | ||||||

» see Science in Perspective: Type A: Enhancement of Reflection Capability | ||||||

» Recommended Science in Perspective (Type B) for D-MATH | ||||||

» see Science in Perspective: Language Courses ETH/UZH | ||||||

Master's Thesis | ||||||

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

401-2000-00L | Scientific Works in MathematicsTarget audience: Third year Bachelor students; Master students who cannot document to have received an adequate training in working scientifically. | O | 0 credits | Ö. Imamoglu, E. Kowalski | ||

Abstract | Introduction to scientific writing for students with focus on publication standards and ethical issues, especially in the case of citations (references to works of others.) | |||||

Objective | Learn the basic standards of scientific works in mathematics. | |||||

Content | - Types of mathematical works - Publication standards in pure and applied mathematics - Data handling - Ethical issues - Citation guidelines | |||||

Lecture notes | Moodle of the Mathematics Library: https://moodle-app2.let.ethz.ch/course/view.php?id=519 | |||||

Prerequisites / Notice | Directive Link | |||||

401-2000-01L | Lunch Sessions – Thesis Basics for Mathematics StudentsDetails and registration for the optional MathBib training course: https://www.math.ethz.ch/mathbib-schulungen | Z | 0 credits | Speakers | ||

Abstract | Optional course "Recherchieren in der Mathematik" (held in German) by the Mathematics Library. | |||||

Objective | ||||||

401-4990-02L | Master's Thesis Only students who fulfil the following criteria are allowed to begin with their Master's thesis: a. successful completion of the Bachelor's programme; b. fulfilling of any additional requirements necessary to gain admission to the Master's programme; c. They have acquired at least 16 credits in the category ‘Core courses‘. Successful participation in the course unit 401-2000-00L Scientific Works in Mathematics is required. For more information, see www.math.ethz.ch/intranet/students/study-administration/theses.html | O | 30 credits | 57D | Supervisors | |

Abstract | The master's thesis concludes the study programme. Thesis work should prove the students' ability to independent, structured and scientific working. | |||||

Objective | Die Studierenden sollen mit der Master-Arbeit, die den Abschluss des Studiengangs bildet, ihre Fähigkeit zu selbständiger, strukturierter und wissenschaftlicher Tätigkeit unter Beweis stellen. | |||||

Course Units for Additional Admission Requirements The courses below are only available for MSc students with additional admission requirements. | ||||||

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

406-0173-AAL | Linear Algebra I and IIEnrolment 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 | N. Hungerbühler | |

Abstract | Linear algebra is an indispensable tool of engineering mathematics. The course is an introduction to basic methods and fundamental concepts of linear algebra and its applications to engineering sciences. | |||||

Objective | After completion of this course, students are able to recognize linear structures and to apply adequate tools from linear algebra in order to solve corresponding problems from theory and applications. In addition, students have a basic knowledge of the software package Matlab. | |||||

Content | Systems of linear equations, Gaussian elimination, solution space, matrices, LR decomposition, determinants, structure of linear spaces, normed vector spaces, inner products, method of least squares, QR decomposition, introduction to MATLAB, applications. Linear maps, kernel and image, coordinates and matrices, coordinate transformations, norm of a matrix, orthogonal matrices, eigenvalues and eigenvectors, algebraic and geometric multiplicity, eigenbasis, diagonalizable matrices, symmetric matrices, orthonormal basis, condition number, linear differential equations, Jordan decomposition, singular value decomposition, examples in MATLAB, applications. Reading: Gilbert Strang "Introduction to linear algebra", Wellesley-Cambridge Press: Chapters 1-6, 7.1-7.3, 8.1, 8.2, 8.6 A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf | |||||

Literature | - Gilbert Strang: Introduction to linear algebra. Wellesley-Cambridge Press - A Practical Introduction to MATLAB: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/intro.pdf - Matlab Primer: http://www.math.ethz.ch/~grsam/Numerik_MAVT_WS0203/docs/primer.pdf - K. Nipp / D. Stoffer, Lineare Algebra, vdf Hochschulverlag, 5. Auflage 2002 - K. Meyberg / P. Vachenauer, Höhere Mathematik 1, Springer 2003 | |||||

406-0243-AAL | Analysis 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- | 14 credits | 30R | M. Akveld | |

Abstract | Mathematical tools for the engineer | |||||

Objective | Mathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers. | |||||

Content | Short introduction to mathematical logic. Complex numbers. Calculus for functions of one variable with applications. Simple types of ordinary differential equations. Simple Mathematical models in engineering. Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. | |||||

Literature | Textbooks in English: - J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6 - J. Stewart: Multivariable Calculus, Thomson Brooks/Cole (e.g. Appendix G on complex numbers) - V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus - W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education Textbooks in German: - M. Akveld, R. Sperb: Analysis I, vdf - M. Akveld, R. Sperb: Analysis II, vdf - L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag - L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag | |||||

406-0603-AAL | Stochastics (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- | 4 credits | 9R | M. Kalisch | |

Abstract | Introduction to basic methods and fundamental concepts of statistics and probability theory for non-mathematicians. The concepts are presented on the basis of some descriptive examples. The course will be based on the book "Statistics for research" by S. Dowdy et.al. and on the book "Introductory Statistics with R" by P. Dalgaard. | |||||

Objective | The objective of this course is to build a solid fundament in probability and statistics. The student should understand some fundamental concepts and be able to apply these concepts to applications in the real world. Furthermore, the student should have a basic knowledge of the statistical programming language "R". The main topics of the course are: - Introduction to probability - Common distributions - Binomialtest - z-Test, t-Test - Regression | |||||

Content | From "Statistics for research": Ch 1: The Role of Statistics Ch 2: Populations, Samples, and Probability Distributions Ch 3: Binomial Distributions Ch 6: Sampling Distribution of Averages Ch 7: Normal Distributions Ch 8: Student's t Distribution Ch 9: Distributions of Two Variables [Regression] From "Introductory Statistics with R": Ch 1: Basics Ch 2: Probability and distributions Ch 3: Descriptive statistics and tables Ch 4: One- and two-sample tests Ch 5: Regression and correlation | |||||

Literature | "Statistics for research" by S. Dowdy et. al. (3rd edition); Print ISBN: 9780471267355; Online ISBN: 9780471477433; DOI: 10.1002/0471477435; From within the ETH, this book is freely available online under: http://onlinelibrary.wiley.com/book/10.1002/0471477435 "Introductory Statistics with R" by Peter Dalgaard; ISBN 978-0-387-79053-4; DOI: 10.1007/978-0-387-79054-1 From within the ETH, this book is freely available online under: http://www.springerlink.com/content/m17578/ | |||||

406-2604-AAL | Probability and StatisticsAny other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | E- | 7 credits | 15R | M. Schweizer | |

Abstract | - Discrete probability spaces - Continuous models - Limit theorems - Introduction to statistics | |||||

Objective | The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. This includes a mathematically rigorous treatment as well as intuition and getting acquainted with the ideas behind the definitions. The course does not use measure theory systematically, but does point out where this is required and what the connections are. | |||||

Content | - Probability: Chapters 1-12 from the book by DasGupta - Statistics: Chapters 8-11 from the book by Rice | |||||

Lecture notes | There will be lecture notes (in German) that are continuously updated during the semester. | |||||

Literature | A. DasGupta, Fundamentals of Probability: A First Course, Springer (2010) J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, second edition (1995) | |||||

Prerequisites / Notice | Some of the exercise classes associated to the original course (which is in German) will be offered in English. |