Suchergebnis: Katalogdaten im Herbstsemester 2015
Mathematik Master | ||||||
Kernfächer 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. | ||||||
Kernfächer aus Bereichen der reinen Mathematik (auch Bachelor-)Kernfächer (Link) sind unter gewissen Bedingungen anrechenbar. | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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401-3225-00L | Introduction to Lie Groups | W | 8 KP | 4G | M. Einsiedler | |
Kurzbeschreibung | Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups. | |||||
Lernziel | The goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it. | |||||
Literatur | A. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser) A.Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73) F.Warner: "Foundations of differentiable manifolds and Lie groups" (Springer) H. Samelson: "Notes on Lie algebras" (Springer, '90) S.Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78) A.Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press) | |||||
Voraussetzungen / Besonderes | Topology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester. Course webpage: Link | |||||
401-3118-09L | Modular Forms | W | 8 KP | 3V + 1U | Ö. Imamoglu | |
Kurzbeschreibung | This is a introductory course on automorphic forms covering its basic properties with emphasis on connections with number theory. | |||||
Lernziel | The aim of the course is to cover the classical theory of modular forms. | |||||
Inhalt | Basic definitions and properties of SL(2,Z), its subgroups and modular forms for SL(2,Z). Eisenstein and Poincare series. L-functions of modular forms. Hecke operators. Theta functions. Possibly Maass forms. Possibly automorphic forms for more general groups. | |||||
Literatur | J.P. Serre, A Course in Arithmetic; N. Koblitz, Introduction to Elliptic Curves and Modular Forms; D. Zagier, The 1-2-3 of Modular Forms; H. Iwaniec, Topics in Classical Automorphic Forms. | |||||
Kernfächer aus Bereichen der angewandten Mathematik ... vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten (auch Bachelor-)Kernfächer (Link) sind unter gewissen Bedingungen anrechenbar. | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3651-00L | Numerical Methods for Elliptic and Parabolic Partial Differential Equations 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. | W | 10 KP | 4V + 1U | C. Schwab | |
Kurzbeschreibung | 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. | |||||
Lernziel | 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 | |||||
Inhalt | 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 | |||||
Skript | Course slides will be made available to the audience. | |||||
Literatur | S. C. Brenner and L. Ridgway Scott: The mathematical theory of Finite Element Methods. New York, Berlin [etc]: Springer-Verl, cop.1994. A. Ern and J.L. Guermond: Theory and Practice of Finite Element Methods, Springer Applied Mathematical Sciences Vol. 159, Springer, 2004. V. Thomee: Galerkin Finite Element Methods for Parabolic Problems, SECOND Ed., Springer Verlag (2006). Additional Literature: D. Braess: Finite Elements, THIRD Ed., Cambridge Univ. Press, (2007). (Also available in German.) D. A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69 SMAI Mathématiques et Applications, Springer, 2012 [DOI: 10.1007/978-3-642-22980-0] R. Verfürth: A Posteriori Error Estimation Techniques for Finite Element Methods, Oxford University Press, 2013 | |||||
Voraussetzungen / Besonderes | Practical exercises based on MATLAB | |||||
401-3621-00L | Fundamentals of Mathematical Statistics | W | 10 KP | 4V + 1U | S. van de Geer | |
Kurzbeschreibung | The course covers the basics of inferential statistics. | |||||
Lernziel | ||||||
401-3901-00L | Mathematical Optimization | W | 11 KP | 4V + 2U | R. Weismantel | |
Kurzbeschreibung | Mathematical treatment of diverse optimization techniques. | |||||
Lernziel | Advanced optimization theory and algorithms. | |||||
Inhalt | 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. | |||||
(auch Bachelor-)Kernfächer aus Bereichen der reinen Mathematik Die Anrechnung von 401-3531-00L Differentialgeometrie I / Differential Geometry I im Master-Studiengang ist nur dann zulässig, wenn 401-3532-00L Differentialgeometrie II / Differential Geometry II nicht für den Bachelor-Studiengang angerechnet wurde. Ebenso für: 401-3461-00L Funktionalanalysis I / Functional Analysis I - 401-3462-00L Funktionalanalysis II / Functional Analysis II 401-3001-61L Algebraische Topologie I / Algebraic Topology I - 401-3002-12L Algebraische Topologie II / Algebraic Topology II 401-3132-00L Kommutative Algebra / Commutative Algebra - 401-3146-12L Algebraische Geometrie / Algebraic Geometry 401-3371-00L Dynamische Systeme I / Dynamical Systems I - 401-3372-00L Dynamische Systeme II / Dynamical Systems II Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link). | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3531-00L | Differential Geometry I | W | 10 KP | 4V + 1U | M. Burger | |
Kurzbeschreibung | This course is an introduction to differential and riemannian geometry. | |||||
Lernziel | The aim is to lead students from a reasonable knowledge of advanced calculus, basic knowledge of general topology and solid knowledge of linear algebra to fundamental knowledge of differentiable manifolds and their basic tools. Riemannian geometry, some basic Lie theory, and de Rham cohomology will be developed as applications. | |||||
Literatur | W.Boothby "An introduction to differentiable manifolds and Riemannian geometry" J.M.Lee "Introduction to smooth manifolds" M.P. Do Carmo "Riemannian Geometry" | |||||
401-3461-00L | Functional Analysis I | W | 10 KP | 4V + 1U | D. A. Salamon | |
Kurzbeschreibung | Baire category; Banach and Hilbert spaces, bounded linear operators; Three Fundamental Principles: Uniform Boundedness, Open Mapping/Closed Graph, Hahn-Banach; Convexity; Dual Spaces: weak and weak* topologies, Banach-Alaoglu, reflexive spaces; Ergodic Theorem; compact operators and Fredholm theory, Closed Image Theorem; Spectral theory, self-adjoint operators. | |||||
Lernziel | ||||||
Skript | Lecture Notes on "Functional Analysis" by D.A. Salamon | |||||
401-3001-61L | Algebraic Topology I | W | 8 KP | 4G | P. Biran | |
Kurzbeschreibung | This is an introductory course in algebraic topology. The course will cover the following main topics: introduction to homotopy theory, homology and cohomology of spaces. | |||||
Lernziel | ||||||
Literatur | 1) G. Bredon, "Topology and geometry", Graduate Texts in Mathematics, 139. Springer-Verlag, 1997. 2) A. Hatcher, "Algebraic topology", Cambridge University Press, Cambridge, 2002. Book can be downloaded for free at: Link See also: Link 3) E. Spanier, "Algebraic topology", Springer-Verlag | |||||
Voraussetzungen / Besonderes | General topology, linear algebra. Some knowledge of differential geometry and differential topology is useful but not absolutely necessary. | |||||
401-3132-00L | Commutative Algebra | W | 10 KP | 4V + 1U | P. D. Nelson | |
Kurzbeschreibung | This course is meant to provide an introduction to commutative algebra that equips the student to start studying the basics of algebraic geometry. | |||||
Lernziel | About the course: We shall closely follow the text "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald. Wherever possible, there will be extra focus on exercises that lead towards the basics of Algebraic Geometry. Topics include * Basics about rings, ideals and modules * Localisation * Primary decomposition * Integral dependence and valuations * Noetherian rings * Completions * Basic dimension theory | |||||
Literatur | References: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) 2. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) | |||||
Voraussetzungen / Besonderes | Prerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory). | |||||
401-3371-00L | Dynamical Systems I | W | 10 KP | 4V + 1U | W. Merry | |
Kurzbeschreibung | This course is a Part I of a broad introduction to dynamical systems. Topic covered include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics. In Part II (FS 2016), we will cover low-dimensional dynamics, complex dynamics, measure-theoretic entropy and Hamiltonian dynamics. | |||||
Lernziel | Mastery of the basic methods and principal themes of dynamical systems. | |||||
Inhalt | The course introduces the principal themes of modern dynamical systems. Topics covered include: 1. Topological dynamics (transitivity, attractors, chaos, structural stability) 2. Symbolic dynamics (Perron-Frobenius theorem, zeta functions) 3. Ergodic theory (Poincare recurrence theorem, Birkhoff ergodic theorem, existence of invariant measures) 4. Hyperbolic dynamics (Grobman-Hartman theorem, Shadowing lemma, Closing lemma and applications) | |||||
Literatur | The most relevant textbook for this course is Introduction to Dynamical Systems, Brin and Stuck, CUP, 2002. Another excellent book (which will be relevant also for Dynamical Systems II) is Lectures on Dynamical Systems, Zehnder, EMS 2010. A more advanced textbook which covers everything in both Dynamical Systems I and II (and much more!) is Introduction to the Modern Theory of Dynamical Systems, Katok and Hasselblatt, CUP, 1995. | |||||
Voraussetzungen / Besonderes | The material of the basic courses of the first two years of the program at ETH is assumed. Some basic differential geometry and functional analysis would be useful but not essential. | |||||
(auch Bachelor-)Kernfächer aus Bereichen der angewandten Mathematik Die Anrechnung von 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory im Master-Studiengang ist nur dann zulässig, wenn weder 401-3642-00L Brownian Motion and Stochastic Calculus noch 401-3602-00L Applied Stochastic Processes für den Bachelor-Studiengang angerechnet wurde. Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link). | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3601-00L | Probability Theory | W | 10 KP | 4V + 1U | A.‑S. Sznitman | |
Kurzbeschreibung | Basics of probability theory and the theory of stochastic processes in discrete time | |||||
Lernziel | 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. | |||||
Inhalt | 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. | |||||
Skript | available, will be sold in the course | |||||
Literatur | 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 | |||||
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 reinen Mathematik | ||||||
Auswahl: Algebra, Topologie, diskrete Mathematik, Logik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3035-00L | Forcing: Einführung in Unabhängigkeitsbeweise | W | 8 KP | 3V + 1U | L. Halbeisen | |
Kurzbeschreibung | Mit Hilfe der Forcing-Technik werden verschiedene Unabhaengigkeitsbeweise gefuehrt. Insbesondere wird gezeigt, dass die Kontinuumshypothese von den Axiomen der Mengenlehre unabhaengig ist. | |||||
Lernziel | Die Forcing-Technik kennenlernen und verschiedene Unabhaengigkeitsbeweise fuehren koennen. | |||||
Inhalt | Mit Hilfe der sogenannten Forcing-Technik, welche anfangs der 1960er Jahre von Paul Cohen entwickelt wurde, werden verschiedene Unabhaengigkeitsbeweise gefuehrt. Insbesondere wird gezeigt, dass die Kontinuumshypothese CH von den Axiomen der Mengenlehre ZFC unabhaengig ist. Weiter wird in Modellen von ZFC, in denen CH nicht gilt, die Groesse verschiedener Kardinalzahlcharakteristiken untersucht. Zum Schluss der Vorlesung wird ein Modell von ZFC konstruiert, in dem es (bis auf Isomorphie) genau n Ramsey-Ultrafilter gibt, wobei n fuer irgend eine nicht-negative ganze Zahl steht. | |||||
Skript | Ich werde mich weitgehend an mein Buch "Combinatorial Set Theory" halten, aus dem einige Kapitel aus Part II & III behandelt werden. | |||||
Literatur | "Combinatorial Set Theory: with a gentle introduction to forcing" (Springer-Verlag 2012) Link | |||||
Voraussetzungen / Besonderes | Voraussetzung ist die Vorlesung "Axiomatische Mengenlehre" (Fruehlingssemester 2015) bzw. die entsprechenden Kapitel aus meinem Buch. | |||||
401-3109-65L | Probabilistic Number Theory | W | 6 KP | 2V + 1U | E. Kowalski | |
Kurzbeschreibung | The course presents some aspects of probabilistic number theory, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums. | |||||
Lernziel | ||||||
Inhalt | The goal of the course is to present some results of probabilistic number theory in a unified manner. The main concepts will be presented in parallel with the proof of three main theorems: (1) the Erdös-Kac theorem and its variants concerning the number of prime divisors of integers in various sequences; (2) the distribution of values of the Riemann zeta function, including Selberg's central limit theorem for the Riemann zeta function on the critical line; (3) functional limit theorems for the paths of partial sums of families of exponential sums such as Kloosterman sums. | |||||
Literatur | H. Iwaniec and E. Kowalski: "Analytic number theory", and additional lecture notes will be prepared. | |||||
Voraussetzungen / Besonderes | Prerequisites: Complex analysis, measure and integral; some probability theory is useful but the main concepts needed will be recalled. Some knowledge of number theory is useful but the main results will be summarized. | |||||
401-3149-65L | Elliptic Curves | W | 4 KP | 2V | E. Viada | |
Kurzbeschreibung | We will study elliptic curves from different point of view: as varieties, as equations, as quotients. We will then study some properties of algebraic points on an elliptic curve. We will finally describe special subset of the rational points of curves that are embedded in products of elliptic curves. | |||||
Lernziel | The aim of this course is to get used to geometric objects and algebraic tools, such as elliptic curves, curves, heights and degree. | |||||
Inhalt | We will first study the properties of elliptic curves. We prove that an elliptic curve can be described as the quotient of the complex numbers by a lattice and equivalently as the zero set of an equation of degree 3. We will introduce the notion of height and degree of algebraic points and describe subsets of algebraic points of bounded height and degree. Finally, We will study some properties of algebraic points on curves embedded in products of elliptic curves. | |||||
Literatur | J. Silverman "The arithmetic of Elliptic Curves" J. Silverman " Advanced Topics in the arithmetic of Elliptic Curves" E. Bombieri & W. Gubler " Heights in Diophantine Geometry" | |||||
Voraussetzungen / Besonderes | Algebra and Linear Algebra, Topology, Geometry, some basic Algebraic Geometry. | |||||
401-3059-00L | Kombinatorik II | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Der Kurs Kombinatorik I und II ist eine Einfuehrung in die abzaehlende Kombinatorik. | |||||
Lernziel | Die Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden. | |||||
Inhalt | Inhalt der Vorlesungen Kombinatorik I und II: Kongruenztransformationen der Ebene, Symmetriegruppen von geometrischen Figuren, Eulersche Funktion, Cayley-Graphen, formale Potenzreihen, Permutationsgruppen, Zyklen, Lemma von Burnside, Zyklenzeiger, Saetze von Polya, Anwendung auf die Graphentheorie und isomere Molekuele. | |||||
401-3202-09L | Representation Theory of Finite Groups, and in Particular Symmetric Groups | W | 4 KP | 2V | A. Buryak | |
Kurzbeschreibung | The first part of the course will be devoted to the general theory of linear representations of finite groups. In the second part we will discuss in details the representation theory of the symmetric groups and some of its applications. | |||||
Lernziel | ||||||
Literatur | J.-P. Serre. Linear Representations of Finite Groups. G. D. James. The Representation Theory of the Symmetric Groups. D. M. Goldschmidt. Groups Characters, Symmetric Functions, and the Hecke Algebra. | |||||
Voraussetzungen / Besonderes | It will be assumed that the listeners know the material from a basic linear algebra course and also basic facts about groups and rings. | |||||
401-4149-65L | Reading Course: Geometric Invariant Theory | W | 2 KP | 4A | J. Fresán, P. S. Jossen | |
Kurzbeschreibung | Geometric Invariant Theory (GIT) is concerned with the problem of defining quotients of algebraic varieties by group actions, a crucial step in the construction of moduli spaces. Although some of the ideas go back to Hilbert, it was developed in its present form by Mumford in the 60s. | |||||
Lernziel | The goal of this reading course is to give an introduction to GIT, with emphasis on examples rather than the most general statements. After a couple of introductory sessions, participants will contribute with talks. | |||||
Inhalt | We will cover topics as: -existence of affine and projective quotients -the Hilbert-Mumford criterion -construction of the moduli space of elliptic curves -toric varieties as GIT quotients -semistable vector bundles on curves | |||||
Literatur | D. Mumford and K. Suominen. "Introduction to the theory of moduli". Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer-School in Math.), pp. 171-222. Wolters-Noordhoff, Groningen, 1972. J. Le Potier. Lectures on vector bundles. Cambridge Studies in Advanced Mathematics, 54. Cambridge University Press, Cambridge, 1997. | |||||
Voraussetzungen / Besonderes | Basic knowledge of algebraic geometry will be assumed. | |||||
Auswahl: Geometrie | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3523-65L | Equidecomposability of Polytopes | W | 4 KP | 2V | L. Parapatits | |
Kurzbeschreibung | A polygon in the plane can be decomposed into finitely many (convex) pieces and reassembled to form another polygon if and only if they have the same area. Hilbert's third problem asks if the analogous is also true for two polyhedra in space. Whether or not it is possible to define volume without the use of approximation arguments depends on the answer to this question. | |||||
Lernziel | The course will cover classical results on equidecomposabilty including the Dehn-Sydler theorem, i.e. the solution to Hilbert's third problem. We will then describe the connection between equidecomposability and valuation theory. Finally, we will discuss some recent classification results of valuations that are invariant under certain groups of motions. | |||||
Voraussetzungen / Besonderes | Office hours: Thursday 11:00 - 12:00 | |||||
401-4573-65L | Surfaces and 3-Manifolds | W | 4 KP | 2V | A. Sisto | |
Kurzbeschreibung | This course is an introduction and invitation to the theory of manifolds of dimension 2 and 3, with focus on the connections between the two dimensions. | |||||
Lernziel | The goal is to give an overview of hyperbolic surfaces, Mapping Class Groups, construction of 3-manifolds, and the geometrisation theorem. The starting point will be the statement of the geometrisation theorem in dimension 2 and the goal the statement of the geometrisation theorem in dimension 3. The choice of topics to discuss, especially in the second part of the course, can vary depending on the interests of the audience. | |||||
Voraussetzungen / Besonderes | The prerequisite is essentially just knowing the definition of manifold. It could help but it's not strictly necessary to know basic covering theory and Riemannian geometry. The exam will consist in presenting a result from the course whose proof has been skipped during the course. | |||||
401-3057-00L | Endliche Geometrien II Findet dieses Semester nicht statt. | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Endliche Geometrien I, II: Endliche Geometrien verbinden Aspekte der Geometrie mit solchen der diskreten Mathematik und der Algebra endlicher Körper. Inbesondere werden Modelle der Inzidenzaxiome konstruiert und Schliessungssätze der Geometrie untersucht. Anwendungen liegen im Bereich der Statistik, der Theorie der Blockpläne und der Konstruktion orthogonaler lateinischer Quadrate. | |||||
Lernziel | Endliche Geometrien I, II: Die Studierenden sind in der Lage, Modelle endlicher Geometrien zu konstruieren und zu analysieren. Sie kennen die Schliessungssätze der Inzidenzgeometrie und können mit Hilfe der Theorie statistische Tests entwerfen sowie orthogonale lateinische Quadrate konstruieren. Sie sind vertraut mit Elementen der Theorie der Blockpläne. | |||||
Inhalt | Endliche Geometrien I, II: Endliche Körper, Polynomringe, endliche affine Ebenen, Axiome der Inzidenzgeometrie, Eulersches Offiziersproblem, statistische Versuchsplanung, orthogonale lateinische Quadrate, Transformationen endlicher Ebenen, Schliessungsfiguren von Desargues und Pappus-Pascal, Hierarchie der Schliessungsfiguren, endliche Koordinatenebenen, Schiefkörper, endliche projektive Ebenen, Dualitätsprinzip, endliche Möbiusebenen, selbstkorrigierende Codes, Blockpläne | |||||
Literatur | - Max Jeger, Endliche Geometrien, ETH Skript 1988 - Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983 - Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press - Dembowski: Finite Geometries. |
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