Paul Biran: Katalogdaten im Frühjahrssemester 2012 |
Name | Herr Prof. Dr. Paul Biran |
Lehrgebiet | Mathematik |
Adresse | Professur für Mathematik ETH Zürich, HG G 63.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telefon | +41 44 632 64 50 |
paul.biran@math.ethz.ch | |
URL | http://www.math.ethz.ch/~biranp |
Departement | Mathematik |
Beziehung | Ordentlicher Professor |
Nummer | Titel | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|
401-3002-12L | Algebraic Topology II | 8 KP | 4G | P. Biran | |
Kurzbeschreibung | This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology such as: products, duality, cohomology operations, characteristic classes, spectral sequences etc. | ||||
Lernziel | |||||
Literatur | 1) A. Hatcher, "Algebraic topology", Cambridge University Press, Cambridge, 2002. Book can be downloaded for free at: http://www.math.cornell.edu/~hatcher/AT/ATpage.html See also: http://www.math.cornell.edu/~hatcher/#anchor1772800 2) E. Spanier, "Algebraic topology", Springer-Verlag 3) G. Bredon, "Topology and geometry", Graduate Texts in Mathematics, 139. Springer-Verlag, 1997. 4) R. Bott & L. Tu, "Differential forms in algebraic topology", Graduate Texts in Mathematics, 82. Springer-Verlag, 1982. 5) J. Milnor & J. Stasheff, "Characteristic classes", Annals of Mathematics Studies, No. 76. Princeton University Press, 1974. | ||||
Voraussetzungen / Besonderes | General topology, linear algebra. Basic knowledge of singular homolgoy and cohomology of topological spaces (e.g. as taught in "Algebraic topology I"). Some knowledge of differential geometry and differential topology is useful but not absolutely necessary. | ||||
401-5580-00L | Symplectic Geometry Seminar ![]() | 0 KP | 2K | D. A. Salamon, P. Biran, A. Cannas da Silva | |
Kurzbeschreibung | Forschungskolloquium | ||||
Lernziel | |||||
406-2303-AAL | Complex Analysis ![]() Die Lerneinheit kann nur von MSc Studierenden mit Zulassungsauflagen belegt werden. | 6 KP | 13R | P. Biran | |
Kurzbeschreibung | Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem. | ||||
Lernziel | |||||
Literatur | L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co. B. Palka: "An introduction to complex function theory." Undergraduate Texts in Mathematics. Springer-Verlag, 1991. R.Remmert: Theory of Complex Functions.. Springer Verlag E.Hille: Analytic Function Theory. AMS Chelsea Publication |