Objectives and competences
Students get familiar with axiomatic approach to Euclidean geometry and the basic concepts of afffine and projective geometry.
Content (Syllabus outline)
Hilbert's axiomatic system for absolute geometry: incidence axioms, ordering axioms, congruence axioms and continuity axioms. Parallel postulate and its equivalents. The arithmetic model of Euclidean plane.
Affine spaces, affine transformations, axiomatic definition of affine geometry.
Axioms of projective geometry, Desargues' theorem. Harmonic elements. Homogeneous and non-homogeneous coordinate systems in the projective plane. Projective transformations.
Learning and teaching methods
Written exam – practical part
Written exam – theoretical part
Intended learning outcomes - knowledge and understanding
Knowledge and Understanding:
On completion of this course the student will be able to
• understand the Hilbert axiomatic system for Euclidean geometry.
• explain and use basic theorems from Euclidean geometry.
• recognize the basic concepts of affine and projective geometry
• distinguish between different non-Euclidean geometries.
Intended learning outcomes - transferable/key skills and other attributes
Transferable/Key Skills and other attributes:
• The obtained knowledge contributes to better understanding of other subjects in fields of geometry and topology.
Readings
M. Hvidsten, Geometry with Geometry Explorer, McGraw-Hill, NY 2005
M. Mitrović, Projektivna geometrija, DMFA-založništvo, Ljubljana 2009
H. S. M. Coxeter, Projective Geometry, Springer 2003
C.-A. Faure, A. Frölicher, Modern Projective Geometry, Kluwer 2000
D. Pagon, Osnove evklidske geometrije, DZS, Ljubljana 1995
M. Berger, Geometry I, Springer-Verlag Berlin Heidelberg, 1987
Prerequisits
There are none.
Additional information on implementation and assessment Type (examination, oral, coursework, project):
Written exam – practical part 50 %
Oral exam – theoretical part 50 %
Written exam – practical part can be replaced by two partial tests (mid-term testing).
Passing grade of the written test is required for taking the oral exam.
