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This entry is from Winter semester 2019/20 and might be obsolete. No current equivalent could be found.

Applied Algebraic Geometry (Small Specialization Module)
(dt. Algorithmische und Angewandte Algebraische Geometrie (Kleines Vertiefungsmodul))

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS) or lecture (2 SWS), seminar (2 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises or presentation with written assignment.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Volkmar Welker

Contents

Algorithmic methods of algebraic geometry are presented (e.g. Gröbner bases). In addition to theoretical principles and algorithms, exemplary applications can also be explained (e.g. in optimization, statistics, algorithmic complexity, etc.).


Qualification Goals

Students

  • understand und use algorithmic methods in the theory of commutative rings,
  • can use algorithmic methods to analyze and solve problems in applied mathematics,
  • can formulate problems of applied mathematics as problems of polynomial systems of equations (resp. in terms of affine or projective varieties).

They deepen

  • the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof methods),
  • in the problem sets, their oral communication skills through discussion and free speech in front of an audience.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Algebra.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • LAaG Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.


Recommended Reading

  • W.W. Adams, P. Loustaunau, An introduction to Gröbner bases, AMS, 1994.
  • G. Blekherman, P.A. Parillo, R. Thomas, Semidefinite optimization and convex algebraic geometry, SIAM, 2013.
  • M. Drton, B. Sturmfels, S. Sullivant, Lectures on algebraic statistics, Birkhäuser, 2010.
  • J.M. Landsberg, Tensors and applications, AMS, 2012.



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2019/20. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.