Affine and Projective Geometry

6 ECTS credits
150 h study time

Offer 1 with catalog number 1000508BNR for all students in the 1st semester at a (B) Bachelor - advanced level.

Semester

1st semester

Enrollment based on exam contract

Impossible

Grading method

Grading (scale from 0 to 20)

Can retake in second session

Yes

Enrollment Requirements

Students who want to enroll for this course, must have passed for "Linear Algebra: Systems, Matrices and Images" and "Introduction to Group Theory".

Taught in

Dutch

Faculty

Faculty of Sciences and Bioengineering Sciences

Department

Mathematics

Educational team

Philippe Cara (course titular)

Activities and contact hours

26 contact hours Lecture
13 contact hours Seminar, Exercises or Practicals

Course Content

Introduction to affine and projective geometry, based on finite dimensional vector spaces and automorphisms. We shall also pay attention to axiomatic theories and show their connection with the classical theory.

Chapter 0: Group actions, orbits and orbit-stabilizer theorem

Chapter 1: Affine Geometry

(Affine spaces - Affinities and collineations - Affine theorems of Thales,
Pappus and Desargues - Synthetic affine planes)

Chapter 2: Projective Geometry

(Introduction - Projective spaces - Projectivities and collineations -
- Projective theorems of Pappus and Desargues - Duality - Relationship
between affine and projective spaces - Cross-ratio - Conics and theorem
of Pascal - Synthetic projective planes)

Course material

Digital course material (Required) : Affiene en Projectieve Meetkunde, R.KIEBOOM en P.CARA

Additional info

Course notes are available in Dutch.

Complementary study material:
- M.K. Bennett, Affine and Projective Geometry, John Wiley 1995
- M. Berger, Geometry I, Springer 1994.
- A. Beutelspacher and U. Rosenbaum, Projective geometry: from foundations
to applications, Cambridge Univ.Press 1998
- L.M. Blumenthal, A modern view of geometry, W.H. Freeman & Co. 1961
- R. Casse, Projective geometry: an introduction, Oxford University Press, 2006
- L. Kadison and M.T. Kromann, Projective geometry and modern algebra,
Birkhäuser 1996
- W. Klingenberg, Lineare Algebra und Geometrie, Springer 1990 (2nd Edition)
- P. Samuel, Projective geometry, Springer 1988.

Learning Outcomes

General competencies

Knowledge and construction of affine and projective spaces over a vector space (the so-called analytic approach), of their individual advantages and drawbacks, and of the relations between these geometries.
Comparison with the synthetic (axiomatic) approach.
Understand and prove the crucial role of the classical theorems of Pappus and Desargues.

Grading

The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

Other exam with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

Oral examination of the theory (for 50% of the marks).
Written examination of the exercises (for 50% of the marks).

Allowed unsatisfactory mark

The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context