Suchergebnis: Katalogdaten im Herbstsemester 2017

Mathematik Master Information
Wahlfächer
Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.
Wahlfächer aus Bereichen der angewandten Mathematik ...
vollständiger Titel:
Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten
Auswahl: Theoretische Informatik, diskrete Mathematik
NummerTitelTypECTSUmfangDozierende
263-4500-00LAdvanced Algorithms Information W6 KP2V + 2U + 1AM. Ghaffari
KurzbeschreibungThis is an advanced course on the design and analysis of algorithms, covering a range of topics and techniques not studied in typical introductory courses on algorithms.
LernzielThis course is intended to familiarize students with (some of) the main tools and techniques developed over the last 15-20 years in algorithm design, which are by now among the key ingredients used in developing efficient algorithms.
Inhaltthe lectures will cover a range of topics, including the following: graph sparsifications while preserving cuts or distances, various approximation algorithms techniques and concepts, metric embeddings and probabilistic tree embeddings, online algorithms, multiplicative weight updates, streaming algorithms, sketching algorithms, and a bried glance at MapReduce algorithms.
Voraussetzungen / BesonderesThis course is designed for masters and doctoral students and it especially targets those interested in theoretical computer science, but it should also be accessible to last-year bachelor students.

Sufficient comfort with both (A) Algorithm Design & Analysis and (B) Probability & Concentrations. E.g., having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, though not required formally. If you are not sure whether you're ready for this class or not, please consulte the instructor.
252-1425-00LGeometry: Combinatorics and Algorithms Information W6 KP2V + 2U + 1AE. Welzl, L. F. Barba Flores, M. Hoffmann, A. Pilz
KurzbeschreibungGeometric structures are useful in many areas, and there is a need to understand their structural properties, and to work with them algorithmically. The lecture addresses theoretical foundations concerning geometric structures. Central objects of interest are triangulations. We study combinatorial (Does a certain object exist?) and algorithmic questions (Can we find a certain object efficiently?)
LernzielThe goal is to make students familiar with fundamental concepts, techniques and results in combinatorial and computational geometry, so as to enable them to model, analyze, and solve theoretical and practical problems in the area and in various application domains.
In particular, we want to prepare students for conducting independent research, for instance, within the scope of a thesis project.
InhaltPlanar and geometric graphs, embeddings and their representation (Whitney's Theorem, canonical orderings, DCEL), polygon triangulations and the art gallery theorem, convexity in R^d, planar convex hull algorithms (Jarvis Wrap, Graham Scan, Chan's Algorithm), point set triangulations, Delaunay triangulations (Lawson flips, lifting map, randomized incremental construction), Voronoi diagrams, the Crossing Lemma and incidence bounds, line arrangements (duality, Zone Theorem, ham-sandwich cuts), 3-SUM hardness, counting planar triangulations.
Skriptyes
LiteraturMark de Berg, Marc van Kreveld, Mark Overmars, Otfried Cheong, Computational Geometry: Algorithms and Applications, Springer, 3rd ed., 2008.
Satyan Devadoss, Joseph O'Rourke, Discrete and Computational Geometry, Princeton University Press, 2011.
Stefan Felsner, Geometric Graphs and Arrangements: Some Chapters from Combinatorial Geometry, Teubner, 2004.
Jiri Matousek, Lectures on Discrete Geometry, Springer, 2002.
Takao Nishizeki, Md. Saidur Rahman, Planar Graph Drawing, World Scientific, 2004.
Voraussetzungen / BesonderesPrerequisites: The course assumes basic knowledge of discrete mathematics and algorithms, as supplied in the first semesters of Bachelor Studies at ETH.
Outlook: In the following spring semester there is a seminar "Geometry: Combinatorics and Algorithms" that builds on this course. There are ample possibilities for Semester-, Bachelor- and Master Thesis projects in the area.
252-1407-00LAlgorithmic Game Theory Information W7 KP3V + 2U + 1AP. Penna
KurzbeschreibungGame theory provides a formal model to study the behavior and interaction of self-interested users and programs in large-scale distributed computer systems without central control. The course discusses algorithmic aspects of game theory.
LernzielLearning the basic concepts of game theory and mechanism design, acquiring the computational paradigm of self-interested agents, and using these concepts in the computational and algorithmic setting.
InhaltThe Internet is a typical example of a large-scale distributed computer system without central control, with users that are typically only interested in their own good. For instance, they are interested in getting high bandwidth for themselves, but don't care about others, and the same is true for computational load or download rates. Game theory provides a particularly well-suited model for the behavior and interaction of such selfish users and programs. Classic game theory dates back to the 1930s and typically does not consider algorithmic aspects at all. Only a few years back, algorithms and game theory have been considered together, in an attempt to reconcile selfish behavior of independent agents with the common good.

This course discusses algorithmic aspects of game-theoretic models, with a focus on recent algorithmic and mathematical developments. Rather than giving an overview of such developments, the course aims to study selected important topics in depth.

Outline:
- Introduction to classic game-theoretic concepts.
- Existence of stable solutions (equilibria), algorithms for computing equilibria, computational complexity.
- Speed of convergence of natural game playing dynamics such as best-response dynamics or regret minimization.
- Techniques for bounding the quality-loss due to selfish behavior versus optimal outcomes under central control (a.k.a. the 'Price of Anarchy').
- Design and analysis of mechanisms that induce truthful behavior or near-optimal outcomes at equilibrium.
- Selected current research topics, such as Google's Sponsored Search Auction, the U.S. FCC Spectrum Auction, Kidney Exchange.
SkriptLecture notes will be usually posted on the website shortly after each lecture.
Literatur"Algorithmic Game Theory", edited by N. Nisan, T. Roughgarden, E. Tardos, and V. Vazirani, Cambridge University Press, 2008;

"Game Theory and Strategy", Philip D. Straffin, The Mathematical Association of America, 5th printing, 2004

Several copies of both books are available in the Computer Science library.
Voraussetzungen / BesonderesAudience: Although this is a Computer Science course, we encourage the participation from all students who are interested in this topic.

Requirements: You should enjoy precise mathematical reasoning. You need to have passed a course on algorithms and complexity. No knowledge of game theory is required.
252-0417-00LRandomized Algorithms and Probabilistic MethodsW8 KP3V + 2U + 2AA. Steger, E. Welzl
KurzbeschreibungLas Vegas & Monte Carlo algorithms; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks
LernzielAfter this course students will know fundamental techniques from probabilistic combinatorics for designing randomized algorithms and will be able to apply them to solve typical problems in these areas.
InhaltRandomized Algorithms are algorithms that "flip coins" to take certain decisions. This concept extends the classical model of deterministic algorithms and has become very popular and useful within the last twenty years. In many cases, randomized algorithms are faster, simpler or just more elegant than deterministic ones. In the course, we will discuss basic principles and techniques and derive from them a number of randomized methods for problems in different areas.
SkriptYes.
Literatur- Randomized Algorithms, Rajeev Motwani and Prabhakar Raghavan, Cambridge University Press (1995)
- Probability and Computing, Michael Mitzenmacher and Eli Upfal, Cambridge University Press (2005)
  •  Seite  1  von  1