Applied Algebraic Geometry (Small Specialization Module)
(dt. Algorithmische und Angewandte Algebraische Geometrie (Kleines Vertiefungsmodul))
|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (3 SWS), recitation class (1 SWS) oder lecture (2 SWS), seminar (2 SWS), |
180 hours (60 h attendance, 120 h private study)
Course requirement: 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
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
|Person in charge of the module's outline||Prof. Dr. Volkmar Welker|
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.).
- 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).
- 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.
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.
- 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.
This page describes a module according to the latest valid module guide in Sommersemester 2021. 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:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
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.