Search result: Catalogue data in Autumn Semester 2017

Mathematics Master Information
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
NumberTitleTypeECTSHoursLecturers
401-3225-00LIntroduction to Lie GroupsW8 credits4GA. Iozzi
AbstractTopological 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.
ObjectiveThe 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.
LiteratureA. 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 / NoticeTopology 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
401-3001-61LAlgebraic Topology I Information W8 credits4GW. Merry
AbstractThis 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.
Objective
Lecture notesI will produce full lecture notes, available on my website at

Link
Literature"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.
Prerequisites / NoticeYou 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.
401-4147-67LAlgebraic Geometry IIW10 credits4V + 1UR. Pink
AbstractQuasicoherent sheaves, cohomology, Serre duality, Riemann-Roch theorem, algebraic curves, moduli schemes
Objective
LiteraturePrimary reference:
* Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer.
* Ulrich Görtz and Torsten Wedhorn: Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.

Secondary reference:
* Qing Liu: Algebraic Geometry and Arithmetic Curves, Oxford Science Publications.
* Siegfried Bosch: Algebraic Geometry and Commutative Algebra (Springer 2013).

Other good textbooks and online texts are:
* David Eisenbud, Joe Harris: The Geometry of Schemes, Graduate Texts in Mathematics, Springer.
* Ravi Vakil, Foundations of Algebraic Geometry, Link
* Jean Gallier and Stephen S. Shatz, Algebraic Geometry Link

"Classical" Algebraic Geometry over an algebraically closed field:
* Joe Harris, Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.
* J.S. Milne, Algebraic Geometry, Link

Further readings:
* Günter Harder: Algebraic Geometry 1 & 2
* I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
* Alexandre Grothendieck et al.: Elements de Geometrie Algebrique EGA
* Saunders MacLane: Categories for the Working Mathematician, Springer-Verlag.
Prerequisites / NoticeAlgebraic Geometry I Spring 2017
401-3132-00LCommutative Algebra Information W10 credits4V + 1UP. D. Nelson
AbstractThis course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry.
ObjectiveWe 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
LiteraturePrimary 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)
Prerequisites / NoticePrerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory).
401-3581-67LSymplectic GeometryW8 credits4V + 1UA. Cannas da Silva
AbstractThis 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.
ObjectiveIntroduction to symplectic geometry
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