Suchergebnis: Katalogdaten im Herbstsemester 2017

Mathematik Bachelor Information
Kernfächer
Kernfächer aus Bereichen der reinen Mathematik
NummerTitelTypECTSUmfangDozierende
401-3531-00LDifferential Geometry I Information
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.
W10 KP4V + 1UD. A. Salamon
KurzbeschreibungSubmanifolds of R^n, tangent bundle,
embeddings and immersions, vector fields, Lie bracket, Frobenius' Theorem.
Geodesics, exponential map, completeness, Hopf-Rinow.
Levi-Civita connection, parallel transport,
motions without twisting, sliding, and wobbling.
Isometries, Riemann curvature, Theorema Egregium.
Cartan-Ambrose-Hicks, symmetric spaces, constant curvature,
Hadamard's theorem.
LernzielIntroduction to Differential Geometry.
Submanifolds of Euclidean space, tangent bundle,
embeddings and immersions, vector fields and flows,
Lie bracket, foliations, the Theorem of Frobenius.
Geodesics, exponential map, injectivity radius, completeness
Hopf-Rinow Theorem, existence of minimal geodesics.
Levi-Civita connection, parallel transport, Frame bundle,
motions without twisting, sliding, and wobbling.
Isometries, the Riemann curvature tensor, Theorema Egregium.
Cartan-Ambrose-Hicks, symmetric spaces, constant curvature,
nonpositive sectional curvature, Hadamard's theorem.
LiteraturJoel Robbin and Dietmar Salamon "Introduction to Differential Geometry",
Link
401-3461-00LFunctional Analysis I Information
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.
W10 KP4V + 1UA. Carlotto
KurzbeschreibungBaire 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.
LernzielAcquire 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.
SkriptLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteraturA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

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 / BesonderesSolid 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).
401-3001-61LAlgebraic Topology I Information W8 KP4GW. Merry
KurzbeschreibungThis is an introductory course in algebraic topology. Topics covered include: the fundamental group, covering spaces, singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. Along the way we will introduce the basics of homological algebra and category theory.
Lernziel
SkriptI will produce full lecture notes, available on my website at

Link
Literatur"Algebraic Topology" (CUP, 2002) by Hatcher is excellent and covers all the material from both Algebraic Topology I and Algebraic Topology II. You can also download it (legally!) for free from Hatcher's webpage:

Link

Another classic book is Spanier's "Algebraic Topology" (Springer, 1963). This book is very dense and somewhat old-fashioned, but again covers everything you could possibly want to know on the subject.
Voraussetzungen / BesonderesYou should know the basics of point-set topology (topological spaces, and what it means for a topological space to be compact or connected, etc).

Some (very elementary) group theory and algebra will also be needed.
401-3132-00LCommutative Algebra Information W10 KP4V + 1UP. D. Nelson
KurzbeschreibungThis course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.
LernzielWe shall cover approximately the material from
--- most of the textbook by Atiyah-MacDonald, or
--- the first half of the textbook by Bosch.
Topics include:
* Basics about rings, ideals and modules
* Localization
* Primary decomposition
* Integral dependence and valuations
* Noetherian rings
* Completions
* Basic dimension theory
LiteraturPrimary Reference:
1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)
Secondary Reference:
2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
Tertiary References:
3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)
Voraussetzungen / BesonderesPrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).
401-3581-67LSymplectic GeometryW8 KP4V + 1UA. Cannas da Silva
KurzbeschreibungThis course is an introduction to symplectic geometry -- the geometry of manifolds equipped with a closed non-degenerate 2-form.
We will discuss symplectic manifolds and transformations, the relation of symplectic to other geometries and some of the interplay with dynamics, eventually in the presence of symmetry groups.
Guided homework assignments will complement the exposition.
LernzielIntroduction to symplectic geometry
» Kernfächer aus Bereichen der reinen Mathematik (Mathematik Master)
  •  Seite  1  von  1