Course Syllabus for

Algebraic Geometry and Solving Systems of Polynomial Equations
Algebraisk geometri och lösning av system av polynomekvationer

FMA150F, 7.5 credits

Valid from: Spring 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-08-24

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching languages: English, Swedish


The aim of the course is to prepare postgraduate students for research using Gröbner bases for solving and interpreting systems of polynomial equations in several variables mainly within algebraic geometry.


Knowledge and Understanding

For a passing grade the doctoral student must be able to explain the concept of a Gröbner basis and describe why they are useful for solving systems of polynomial equations.

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Affine varieties and ideals in the ring of polynomials. Gröbner bases. Elimination theory. Algebraic-Geometric Correspondences. Polynomial and Rational Functions on a Variety.

Course Literature

The books are available as e-books via the Mathematics library.

Instruction Details

Types of instruction: Lectures, exercises, project. If the number of participants is small, the course is given as a reading course.

Examination Details

Examination formats: Written exam, oral exam, written assignments. Take-home exam.
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FMAN10 Algebraic structures.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

Complete view