Syllabus

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: 19.04.2022 - 27.05.2022

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

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 No teaching
  2023-2024 Spring III

  Enrollment :

  sisu.aalto.fi

Description