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This entry is from Winter semester 2018/19 and might be obsolete. No current equivalent could be found.
Applied Algebraic Geometry
(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): Written or oral examination Examination type: Successful completion of at least 50 percent of the points from the weekly exercises or presentation with written assignment. |
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
Translation is missing. Here is the German original:
Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Aufbaumodul Algebra vermittelt werden.
Applicability
Module imported from M.Sc. Mathematics.
It can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- M.Sc. Computer Science
- M.Sc. Mathematics
When studying M.Sc. Computer Science, this module can be attended in the study area Minor subject Mathematics.
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 2018/19. 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:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24 (no corresponding element)
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.