# MATA230 Geometry (5 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, 2023-2024

## Description

Hilbert's axioms and neutral geometry, Euclidean plane geometry, hyperbolic geometry, Poincaré model for hyperbolic geometry

## Learning outcomes

After the course student

• knows the basic structure of axiomatic systems and the concept of independence for axioms
• understands the role of models for axiomatic systems
• can prove basic results in neutral geometry
• is aware of the common ground and the differences of Euclidean and hyperbolic geometries
• can use models to illustrate hyperbolic geometry

## Description of prerequisites

Euklidinen tasogeometria on suositeltava, mutta ei välttämätön esitieto.

## Study materials

Luentomoniste (Kurittu, Hokkanen, Kahanpää: Geometria)

## Literature

• Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
• Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464

## Completion methods

### Method 1

Evaluation criteria:
Homeworks and Course exam.
Select all marked parts

### Method 2

Evaluation criteria:
Final Exam
Select all marked parts
Parts of the completion methods
x

### Teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Homeworks and Course exam.
Language:
Finnish
Study methods:

28h lectures, 7 exercise sessions

Study materials:

Lecture notes (in Finnish): Kurittu, Hokkanen, Kahanpää: Geometria

Literature:
• Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
• Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464

x

### Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Final Exam
Language:
English, Finnish
Study methods:

Final Exam

Study materials:

Luentomoniste (Kurittu, Hokkanen, Kahanpää: Geometria)

Literature:
• Hartshorne, R., Geometry : Euclid and beyond, Springer cop. 2000.; ISBN: 0-387-98650-2
• Greenberg, M.J., Euclidean and non-Euclidean geometries : development and history, W.H. Freeman cop. 1993. 3rd ed; ISBN: 0716724464