Credits: 5

Schedule: 09.09.2019 - 16.10.2019

Contact information for the course (applies in this implementation): Office hours are on Mondays from 12:00-13:00. The instructor can be reached over email at

Teaching Period (valid 01.08.2018-31.07.2020): 

Not lectured (2018-2019)

I Autumn (2019-2020)

Lectured every other year

Learning Outcomes (valid 01.08.2018-31.07.2020): 

You will learn the definitions of an affine variety and an ideal together with examples, basic properties and the correspondence between ideals and varieties. You will familiarize yourself with the method of Groebner basis which allows to study ideals computationally. You will learn how to eliminate variables from systems of polynomial equations. You will discover how the theory about affine varieties and ideals is applied to robotics.

Content (valid 01.08.2018-31.07.2020): 

The aim of this course is to give an introduction to computational algebraic geometry. We will cover chapters 1-4 and 6 from “Ideals, Varieties and Algorithms” by Cox, Little and O’Shea.

Assessment Methods and Criteria (valid 01.08.2018-31.07.2020): 

Teaching methods: lectures and homework exercises.

Assessment methods: active participation, homework exercises and a final exam.

Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation): 

There will be weekly homework assignments (40% of the grade) and a final exam at the end of the course (50% of the grade). 10% of the grade is given for active participation in lectures and exercises. Grades for the four best homework assignments out of five will be taken into account. Homework assignments contain exercises to be solved by hand or by a computer algebra software. Introduction to a computer algebra software Macaulay2 will be given in the first exercise session.

Workload (valid 01.08.2018-31.07.2020): 

Contact hours 36h (no compulsory attendance), self-study ca 100h.

Study Material (valid 01.08.2018-31.07.2020): 

Cox, Little, O’Shea “Ideals, Varieties and Algorithms”

Course Homepage (valid 01.08.2018-31.07.2020):

Prerequisites (valid 01.08.2018-31.07.2020): 

MS-C134X (or a similar course in linear algebra). The course MS-C1081 may also be useful.

Grading Scale (valid 01.08.2018-31.07.2020): 



Registration and further information