# Search result: Catalogue data in Autumn Semester 2017

Mathematics Bachelor | ||||||

Core Courses | ||||||

Core Courses: Applied Mathematics and Further Appl.-Oriented Fields vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3651-00L | Numerical Methods for Elliptic and Parabolic Partial Differential Equations (University of Zurich)Course audience at ETH: 3rd year ETH BSc Mathematics and MSc Mathematics and MSc Applied Mathematics students. Other ETH-students are advised to attend the course "Numerical Methods for Partial Differential Equations" (401-0674-00L) in the CSE curriculum during the spring semester. No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH. UZH Module Code: MAT802 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/mobilitaet.html | W | 10 credits | 4V + 1U + 1P | S. Sauter | |

Abstract | This course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods. Practical exercises include MATLAB implementations of finite element methods. | |||||

Objective | Participants of the course should become familiar with * concepts underlying the discretization of elliptic and parabolic boundary value problems * analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems * methods for the efficient solution of discrete boundary value problems * implementational aspects of the finite element method | |||||

Content | A selection of the following topics will be covered: * Elliptic boundary value problems * Galerkin discretization of linear variational problems * The primal finite element method * Mixed finite element methods * Discontinuous Galerkin Methods * Boundary element methods * Spectral methods * Adaptive finite element schemes * Singularly perturbed problems * Sparse grids * Galerkin discretization of elliptic eigenproblems * Non-linear elliptic boundary value problems * Discretization of parabolic initial boundary value problems | |||||

Lecture notes | Course slides will be made available to the audience. | |||||

Literature | n.a. | |||||

Prerequisites / Notice | Practical exercises based on MATLAB | |||||

401-3601-00L | Probability TheoryAt most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. | W | 10 credits | 4V + 1U | A.‑S. Sznitman | |

Abstract | Basics of probability theory and the theory of stochastic processes in discrete time | |||||

Objective | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Content | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Lecture notes | available, will be sold in the course | |||||

Literature | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 | |||||

401-3621-00L | Fundamentals of Mathematical Statistics | W | 10 credits | 4V + 1U | S. van de Geer | |

Abstract | The course covers the basics of inferential statistics. | |||||

Objective | ||||||

401-3901-00L | Mathematical Optimization | W | 11 credits | 4V + 2U | R. Weismantel | |

Abstract | Mathematical treatment of diverse optimization techniques. | |||||

Objective | Advanced optimization theory and algorithms. | |||||

Content | 1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming. 2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization. 3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory. 4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems. | |||||

Literature | 1) D. Bertsimas & R. Weismantel, "Optimization over Integers". Dynamic Ideas, 2005. 2) A. Schrijver, "Theory of Linear and Integer Programming". John Wiley, 1986. 3) D. Bertsimas & J.N. Tsitsiklis, "Introduction to Linear Optimization". Athena Scientific, 1997. 4) Y. Nesterov, "Introductory Lectures on Convex Optimization: a Basic Course". Kluwer Academic Publishers, 2003. 5) C.H. Papadimitriou, "Combinatorial Optimization". Prentice-Hall Inc., 1982. | |||||

Prerequisites / Notice | Linear algebra. | |||||

252-0057-00L | Theoretical Computer Science Remark: Students, who already took the course 252-0065-00 Theoretische Informatik (8 KP) are not allowed to register for 252-0057-00 Theoretische Informatik (7 KP). | W | 7 credits | 4V + 2U | J. Hromkovic | |

Abstract | Concepts to cope with: a) what can be accomplished in a fully automated fashion (algorithmically solvable) b) How to measure the inherent difficulty of tasks (problems) c) What is randomness and how can it be useful? d) What is nondeterminism and what role does it play in CS? e) How to represent infinite objects by finite automata and grammars? | |||||

Objective | Learning the basic concepts of computer science along their historical development | |||||

Content | This lecture gives an introduction to theoretical computer science, presenting the basic concepts and methods of computer science in its historical context. We present computer science as an interdisciplinary science which, on the one hand, investigates the border between the possible and the impossible and the quantitative laws of information processing, and, on the other hand, designs, analyzes, verifies, and implements computer systems. The main topics of the lecture are: - alphabets, words, languages, measuring the information content of words, representation of algorithmic tasks - finite automata, regular and context-free grammars - Turing machines and computability - complexity theory and NP-completeness - design of algorithms for hard problems | |||||

Lecture notes | The lecture is covered in detail by the textbook "Theoretical Computer Science". | |||||

Literature | Basic literature: 1. J. Hromkovic: Theoretische Informatik. 5th edition, Springer Vieweg 2014. 2. J. Hromkovic: Theoretical Computer Science. Springer 2004. Further reading: 3. M. Sipser: Introduction to the Theory of Computation, PWS Publ. Comp.1997 4. J.E. Hopcroft, R. Motwani, J.D. Ullman: Introduction to Automata Theory, Languages, and Computation (3rd Edition), Addison-Wesley 2006. 5. I. Wegener: Theoretische Informatik. Teubner. More exercises and examples in: 6. A. Asteroth, Ch. Baier: Theoretische Informatik | |||||

Prerequisites / Notice | During the semester, two non-obligatory test exams will be offered. | |||||

252-0209-00L | Algorithms, Probability, and Computing | W | 8 credits | 4V + 2U + 1A | E. Welzl, M. Ghaffari, A. Steger, D. Steurer, P. Widmayer | |

Abstract | Advanced design and analysis methods for algorithms and data structures: Random(ized) Search Trees, Point Location, Minimum Cut, Linear Programming, Randomized Algebraic Algorithms (matchings), Probabilistically Checkable Proofs (introduction). | |||||

Objective | Studying and understanding of fundamental advanced concepts in algorithms, data structures and complexity theory. | |||||

Lecture notes | Will be handed out. | |||||

Literature | Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest; Randomized Algorithms by R. Motwani und P. Raghavan; Computational Geometry - Algorithms and Applications by M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf. | |||||

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

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