**Commutative Algebra and Algebraic Geometry**

**(326.0KA lecture, 326.0UK exercises)**

**winter semester 2020/21**

**Prof. Dr. Franz Winkler**

**DI. Dr. Sebastian Falkensteiner**

Time / Place: | Thu 08:30 -- 10:00 (VL) | / | HS 14 | |

Tue 12:00 -- 13:30 (UE) | / | T406/1 | ||

First lecture: | October 8 | |||

First exercise: | October 13 | |||

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) |

Lecture Notes: |
00-Title.pdf |

01-Introduction.pdf |

**Exercises:**

The exercise part consists of homework exercises and a project.

Exercises-01.pdf | |

Project: | Projects.pdf |

syllabus.pdf |