Suchergebnis: Katalogdaten im Herbstsemester 2018
Hochenergie-Physik MSc (Joint Master mit EP Paris)  | ||||||
 Physikalische und mathematische Wahlfächer | ||||||
| Wahlfächer in Mathematik | ||||||
| Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|---|
| 401-3531-00L | Differential Geometry I Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. | W | 10 KP | 4V + 1U | W. Merry | |
| Kurzbeschreibung | This will be an introductory course in differential geometry. Topics covered include: - Smooth manifolds, submanifolds, vector fields, - Lie groups, homogeneous spaces, - Vector bundles, tensor fields, differential forms, - Integration on manifolds and the de Rham theorem, - Principal bundles. | |||||
| Lernziel | ||||||
| Skript | I will produce full lecture notes, available on my website at www.merry.io/differential-geometry | |||||
| Literatur | There are many excellent textbooks on differential geometry. A friendly and readable book that covers everything in Differential Geometry I is: John M. Lee "Introduction to Smooth Manifolds" 2nd ed. (2012) Springer-Verlag. A more advanced (and far less friendly) series of books that covers everything in both Differential Geometry I and II is: S. Kobayashi, K. Nomizu "Foundations of Differential Geometry" Volumes I and II (1963, 1969) Wiley. | |||||
| 401-3461-00L | Functional Analysis I Höchstens eines der drei Bachelor-Kernfächer 401-3461-00L Funktionalanalysis I / Functional Analysis I 401-3531-00L Differentialgeometrie I / Differential Geometry I 401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory ist im Master-Studiengang Mathematik anrechenbar. | W | 10 KP | 4V + 1U | M. Einsiedler | |
| Kurzbeschreibung | Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications. | |||||
| Lernziel | Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps. | |||||
| Literatur | We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. | |||||
| Voraussetzungen / Besonderes | Solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces). | |||||
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