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# Details for Course FMA150F Algebraic Geometry and Solving Systems of Polynomial Equations

General
• FMA150F
• Temporary
Course Name
• Algebraic Geometry and Solving Systems of Polynomial Equations
Course Extent
• 7.5
Type of Instruction
• Third-cycle course
• 7151 (Centre of Mathematical Sciences / Mathematics)
•  -08-24
• Professor Thomas Johansson

## Current Established Course Syllabus

General
Aim
• 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.
Contents
• Affine varieties and ideals in the ring of polynomials.
Gröbner bases.
Elimination theory.
Algebraic-Geometric Correspondences.
Polynomial and Rational Functions on a Variety.
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
• be able to reproduce key results and give rigorous and detailed proofs of them,

be able to compare key results,

be able to apply the basic techniques, results and concepts of the course to concrete examples and exercises,

be able to combine concepts from the course with other important topics in algebra.

be able to use different methods for solving and for interpreting systems of polynomial equations.
Judgement and Approach
• For a passing grade the doctoral student must
Types of Instruction
• Lectures
• Exercises
• Project
• If the number of participants is small, the course is given as a reading course.
Examination Formats
• Written exam
• Oral exam
• Written assignments
• Take-home exam.
• Failed, pass
Assumed Prior Knowledge
• FMAN10 Algebraic structures.
Selection Criteria
Literature
• Cox, D. & Little, J.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 2016. ISBN 9783319374277.
Cox, D. & Little, J.: Using Algebraic Geometry. Springer Science & Business Media, 2005. ISBN 9780387207339.
• The books are available as e-books via the Mathematics library.
Further Information
Course code
• FMA150F
•  -08-24
• Professor Thomas Johansson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2018 2018‑05‑28 15:37:21 2018‑05‑29 07:29:39 2018‑08‑24

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

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