# Search result: Catalogue data in Autumn Semester 2016

Mathematics Master | ||||||

Core Courses For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Core Courses: Pure Mathematics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|---|

401-3225-00L | Introduction to Lie Groups | W | 8 credits | 4G | P. D. Nelson | |

Abstract | 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. | |||||

Objective | 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. | |||||

Literature | 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) | |||||

Prerequisites / Notice | 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: http://www.math.ethz.ch/education/bachelor/lectures/hs2014/math/introlg |

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