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German original

Elementary Algebraic Geometry
(dt. Elementare Algebraische Geometrie)

Level, degree of commitment in original study programme Intermediate module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Mathematics.
Original study programme B.Sc. Mathematik / Mathematik Wahlpflichtmodule
Duration,
frequency		 One semester,
Regelmäßig im Wechsel mit den anderen intermediate moduleen
Person in charge of the module's outline Prof. Dr. Thomas Bauer

Contents

Geometry in affine, euclidean and projective spaces; comparison of the underlying transformations and invariants, as well as the respective ways of working.

Geometry of plane algebraic curves: curves and their equations, Bézout's theorem, singularities, linear systems.


Qualification Goals

The students shall

  • get to know different ways of working with geometry,
  • learn about the interaction of geometric and algebraic-analytical methods,
  • 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.

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.


Recommended Reading

  • Coxeter: Introduction to Geometry, John Wiley & Sons
  • Fischer, G.: Ebene algebraische Kurven, Vieweg
  • Koecher, Krieg: Ebene Geometrie, Springer
  • Agricola, Friedrich: Elementargeometrie, Vieweg



Please note:

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:

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.