# Search result: Catalogue data in Autumn Semester 2017

Mathematics Bachelor | ||||||

Seminars Early enrolments for seminars in myStudies are encouraged, so that we will recognize need for additional seminars in a timely manner. Some seminars have waiting lists. Nevertheless, register for at most two mathematics seminars. In this case, you express a stronger preference for the seminar for which you register earlier. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3680-67L | Persistent Homology and Topological Data Analysis Number of participants limited to 8. | W | 4 credits | 2S | P. S. Jossen | |

Abstract | We study the fundamental tools of topological data analysis: Persistent homology, persistence modules and barcodes. Our goal is to read and understand parts of the paper "Principal Component Analysis of Persistent Homology..." by Vanessa Robins and Kate Turner (ArXiV 1507.01454v1). | |||||

Objective | To get familiar with the basic concepts of topological data analysis and see some applications thereof. | |||||

Literature | Herbert Edelsbrunner and John L. Harer: Computational Topology, An Introduction. AMS 2010 | |||||

Prerequisites / Notice | Participants are supposed to be familiar with singular homology. | |||||

401-3180-67L | Algebraic K-theory Number of participants limited to 26. | W | 4 credits | 2S | C. Busch | |

Abstract | The "algebraic K-theory" describes a branch of algebra which centers about two functors which assign to each associative ring R an abelian group. | |||||

Objective | We will introduce the functors K0 and K1 and consider the further development of K-theory. | |||||

Literature | John Milnor, Introduction to algebraic K-theory, Annals of Mathematics Studies 72, Princeton University Press and University of Tokyo Press (1971). | |||||

Prerequisites / Notice | Basic knowledge of Algebra as taught in a course Algebra I + II. Every week two students will give a talk and deliver a summary containing the main results of their subject. The weekly attendance of the seminar is mandatory. | |||||

401-3370-67L | Seminar on Homogeneous Dynamics and Applications Number of participants limited to 12. | W | 4 credits | 2S | M. Einsiedler, M. Akka Ginosar, Ç. Sert | |

Abstract | This seminar is offered to students taking the course Homogeneous Dynamics and Applications. It will give some more details and fill in some of the background of the material in the course. Exercises will also be an integral part of the seminar. | |||||

Objective | ||||||

Content | Seminar website: Link | |||||

Prerequisites / Notice | The seminar is restricted to 12 students, registration will be finalised in the first week of the semester. | |||||

401-3650-67L | Numerical Analysis Seminar: Tensor Numerics and Deep Neural Networks Number of participants limited to 10. | W | 4 credits | 2S | C. Schwab | |

Abstract | The seminar addresses recently discovered _mathematical_ connections between Deep Learning and Tensor-formatted numerical analysis, with particular attention to the numerical solution of partial differential equations, with random input data. | |||||

Objective | The aim of the seminar is to review recent [2015-] research work and results, together with recently published software such as the TT-Toolbox, and Google's TENSORFLOW. The focus is on the mathematical analysis and interpretation of current learning approaches and related mathematical and technical fields, e.g. high-dimensional approximation, tensor structured numerical methods for the numerical solution of highdimensional PDEs, with applications in computational UQ. For theory, we refer to the references in the survey Link Numerical experiments will be done with TENSORFLOW and with the TT toolbox at Link | |||||

Lecture notes | The seminar will study a set of 10 orginial papers from 2015 to today. | |||||

Literature | Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen Optimal Approximation with Sparsely Connected Deep Neural Networks arXiv:1705.01714 N. Cohen, O. Sharir, Y. Levine, R. Tamari, D. Yakira and A. Shashua (May 2017): Analysis and design of convolutional networks via hierarchical tensor decompositions, arXiv:1705.02302v3. N. Cohen and A. Shashua (March 2016), Convolutional rectifier networks as generalized tensor decompositions, Technical report, arXiv:1603.00162. Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016. N. Cohen, O. Sharir and A. Shashua (Sept. 2015), On the expressive power of deep learning: A tensor analysis, Technical report, arXiv:1509.05009. Journal-ref: 29th Annual Conference on Learning Theory, pp. 698-728, 2016. | |||||

Prerequisites / Notice | Completed BSc MATH exam. | |||||

401-3620-67L | Student Seminar in Statistics: Computer Age Statistical Inference 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. | W | 4 credits | 2S | M. H. Maathuis, P. L. Bühlmann, N. Meinshausen, S. van de Geer | |

Abstract | We study selected chapters from the book "Computer Age Statistical Inference: Algorithms, Evidence and Data Science" by Bradley Efron and Trevor Hastie. | |||||

Objective | During this seminar, we will study roughly one chapter per week from the book "Computer Age Statistical Inference: Algorithms, Evidence and Data Science" by Bradley Efron and Trevor Hastie. You will obtain a good overview of the field of modern statistics. Moreover, you will practice your self-studying and presentation skills. | |||||

Content | In the words of Efron and Hastie: "The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. “Big data,” “data science,” and “machine learning” have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on a journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories – Bayesian, frequentist, Fisherian – individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The book integrates methodology and algorithms with statistical inference, and ends with speculation on the future direction of statistics and data science." | |||||

Literature | Bradley Efron and Trevor Hastie (2016). Computer Age Statistical Inference: Algorithms, Evidence and Data Science. Cambridge University Press, New York. ISBN: 9781107149892. | |||||

Prerequisites / Notice | We require at least one course in statistics in addition to the 4th semester course Introduction to Probability and Statistics, as well as some experience with the statistical software R. Topics will be assigned during the first meeting. | |||||

401-3920-67L | Optimal Stopping Number of participants limited to 26. | W | 4 credits | 2S | P. Cheridito | |

Abstract | In this seminar different methods to solve optimal stopping problems are studied and various applications are discussed. | |||||

Objective | The goal is to learn different methods that can be used to solve optimal stopping problems in discrete and continuous time. | |||||

Content | Methods of optimal stopping theory in both discrete and continuous time using both martingale and Markovian approaches. Various concrete problems from the theory of probability, mathematical statistics and mathematical finance that can be reformulated as problems of optimal stopping of stochastic processes. | |||||

Literature | Optimal Stopping and Free-Boundary Problems. G. Peskir and A. Shiryaev. 2006 Springer. | |||||

Prerequisites / Notice | Probability theory, stochastic processes, martingales, Brownian motion, stochastic calculus | |||||

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