LEARNING OUTCOMES
At the end of this course, the student can
- describe the theory of solving systems of polynomial equations
- solve systems of polynomial equations symbolically and numerically
- solve problems in various applications that reduce to solving a system of polynomial equations
Credits: 5
Schedule: 22.04.2024 - 03.06.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Kaie Kubjas
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
You will learn the definitions of an affine variety and an ideal together with examples, basic properties and the correspondence between ideals on the algebra side and affine varieties on the geometry side. 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, and how this is applied to solving systems of polynomial equations and describing images of polynomial maps. You will see an application of the theory.
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: lectures and exercises.
Assessment methods: see syllabus for each edition.
Workload
valid for whole curriculum period:
Contact hours 36h (no compulsory attendance), self-study ca 100h.
DETAILS
Study Material
valid for whole curriculum period:
"Ideals, Varieties and Algorithms" by Cox, Little and O Shea
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language : English
Teaching Period : 2022-2023 No teaching
2023-2024 Spring IIIEnrollment :
sisu.aalto.fi