RISC RISC Research Institute for Symbolic Computation  


Kommutative Algebra und Algebraische Geometrie
(Commutative Algebra and Algebraic Geometry)
(326.0KA lecture, 326.0UK exercises)
Sommersemester 2018
Prof. Dr. Franz Winkler

 

 

Time / Place: Tue14:30 -- 16:00  (VL) HS 12
16:15 -- 17:00  (UE) / HS 12
Fri 10:15 -- 11:45   (VL) / HS 14
 
first lecture:TueMarch 6

Classical algebraic geometry is the theory of algebraic curves, surfaces, and varieties in higher dimensions. Nowadays, such algebraic varieties are of high importance in computer aided geometric design, computer vision, cryptography, and other areas.

The algebraic theory which allows us to compute with such varieties is called commutative algebra. It is concerned with polynomial equations, polynomial ideals, and polynomial and rational mappings.

Participants in the course are expected to be acquainted with basics in (computer) algebra. Much of the material for this course will be taken from the book

      J.R. Sendra, F. Winkler, S. Perez-Diaz,
Rational Algebraic Curves - A Computer Algebra Approach,
Springer-Verlag Berlin Heidelberg, 2008 (ISBN 978-3-540-73724-7)

Skriptum:    00-Title.pdf
01-Introduction.pdf
02-elimination.pdf
03-algset.pdf
04-corr.pdf
05-proj.pdf
06-func.pdf
07-local.pdf
08-para.pdf
09-puiseux.pdf
10-dimension.pdf

Exercises:

The exercise part consists of homework exercises and a project.

                    exercises-01.pdf
exercises-02.pdf
exercises-03.pdf
exercises-04.pdf
exercises-05.pdf
exercises-06.pdf
exercises-07.pdf
exercises-08.pdf
Project:project.pdf

Webpage: www.risc.jku.at/education/courses/ss2018/caag/

syllabus.pdf