MATA241 Analytic Geometry - for Subject Teachers (4 cr)

Open the course unit brochure on Sisu
Study level:
Intermediate studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

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

Additional information

Planned to be lectured in fall 2024 and 2026

Description of prerequisites

Linear algebra and geometry 1.

Euclidean plane geometry and Linear algebra and geometry 2 are recommended, but not mandatory.

Study materials

Lecture notes (in Finnish)

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 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
Language:
Finnish

Teaching

x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
Finnish

Teaching