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

**Study level:**

Intermediate studies

**Grading scale:**

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.

## Study materials

Kurssilla jaettava luentomoniste.

## 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

**Grading scale:**

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:**

Kurssilla jaettava luentomoniste.

**Literature:**

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

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

Gradin is based on final exam.

**Language:**

English, Finnish

**Study materials:**

Kurssillla jaettava luentomoniste.

**Literature:**

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