# MATA241 Analytic Geometry - for Subject Teachers (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

Analytic plane geometry: Conic sections and their different representations, theory of affine geometry. GebGebra as a tool for teaching.

## Learning outcomes

After completing the course the student knows

• how to determine a conic section using the focus and directrix, and their connection to algebraic equations.
• the most essential results about conic sections and their proofs
• a conic section from a second order algebraic equation of two variables
• how to parametrise conic sections and obtain the equations of the tangents using the parametrisation
• basic properties of isometries
• basic properties of affine mas and fundamental theorems in affine geometry
• how to apply affine maps to prove geometric results
• basic properties of the GeoGebra-program and how to make simple geometric demonstrations
• how to apply the GeoGebra-program in identifying geometric properties and how to formulate mathematical statements from them

## Description of prerequisites

Lineaarinen algebra ja geometria 1. Euklidinen tasogeometria ja Lineaarinen algebra ja geometria 2 suositeltavia mutta eivät välttämättömiä.

## Literature

• Brannan D. A., Esplen M. F. , Gray J. J., Geometry, Cambridge University Press, 1999, ISBN:9780511807503

## Completion methods

### Method 1

Evaluation criteria:
Grading is based on points from exam, weekly exercises and a mandatory practical work.
Select all marked parts

### Method 2

Evaluation criteria:
Grading is based on points from the final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Grading is based on points from exam, weekly exercises and a mandatory practical work.
Language:
Finnish
Study methods:

Lectures 28 h, 7 exercises.

Study materials:

Literature:
• Brannan D. A., Esplen M. F. , Gray J. J., Geometry, Cambridge University Press, 1999, ISBN:9780511807503

x

Type:
Exam