Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMG0010	Projectiv Geometry	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Hungarian	5	2+1+0	speciality	optional	
Mathematics-Computer Science - in Hungarian	5	2+1+0	speciality	optional	

Teaching Staff in Charge	Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro	
Aims	This course  is an introduction in the syntetic and differential projective geometry. The course covers the following chapters: anarmonic rate,  projections, affinities,   the principle of duality,  homogeneous coordinates, analitycal representation of  projective transformations, projective groups,  geomtry attached to a group. 
	
Content	I. Sintetic study 
   1. Anarmonic rate
   2. Projections
   3. Affinities
   4. Similarity
   5. The principle of duality. 

II. Analytical study
  1. Homogeneous coordinates
  2. Analytical representation of  projective transformations
  3. Quadratic forms
  4. Projective groups
  5. Geometry attached to a group. 
	
Bibliography	1. VASIU A. -VASIU ANGELA, Geometrie proiectiva si structuri algebrice, 1998  
2. HYGHENS D.-PIPER F., Projective planes, Springer Verlag, New-York, Heidelberg, Berlin, 1973  
3. ANDRICA, D.-VARGA, CS.- VACARETU, D., Teme de geometrie, Ed. Promedia-Plus, Cluj-Napoca, 1997  
4. MIHAILEANU N. N., Elemente de geometrie proiectiva, Ed. Tehnica, Bucuresti, 1966  
5. COXETER, H.S.M., A geometriak alapjai, Muszaki Konyvkiado, Budapest, 1973.
6. KEREKJARTO, BELA, Les Fondements de la Geometrie, Akademia Kiado, 1966.

	
Assessment	30% from the final mark is the activity during one semester
70% from the final mark is the mark from a written test.