Algebraic Equations and Varieties
(dt. Algebraische Gleichungen und Varietäten)
|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
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, |
Regelmäßig im Wechsel mit anderen advanced moduleen in Algebra und Geometrie
|Person in charge of the module's outline||Prof. Dr. Thomas Bauer, Prof. Dr. István Heckenberger|
Galois theory: algebraic field extensions, constructions with ruler and compass, normal and separable field extensions, cyclotomic polynomials, finite fields, solvable groups, symmetric polynomials, fundamental theorem of Galois theory, solvability of algebraic equations
Algebraic varieties: Affine varieties and Hilbert Nullstellensatz, Morphisms of Affine Varieties, Rational Functions and maps, Smooth Points, Tangent Spaces and Dimensions
The students shall
- learn the essential features of Galois theory and its applications and appreciate its historical significance,
- learn about the applicability of algebraic methods for the description of geometric objects (algebraic varieties),
- Understand the translation process between geometry and algebra and be able to apply it to posed problems,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, either Elementary Algebraic Geometry or Algebra.
- G. Fischer, R. Sacher: Einführung in die Algebra. Teubner.
- K. Hulek: Elementare Algebraische Geometrie. Vieweg.
This page describes a module according to the latest valid module guide in Wintersemester 2022/23. 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
- WiSe 2022/23
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.