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

Code	Subject	
MMG1013	Classical Theorems in Elemetary Geometry	

Section	Sem.	Hours: C+S+L	Category	Type	
Didactic Mathematics - in Hungarian	1	2+1+0	speciality	compulsory	
Didactic Mathematics - in Hungarian	3	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro	
Aims	1. Acquiring of some notions and results of Geometry, which are useful for understanding some modern directions in Mathematics.
2. Forming the ability to apply the new theoretical knowledge in approaching and studying some research problmes with multiple applications.
3. Realization of some connections with other mathematical disciplines.	
Content	Curs 1. Elements of vector calculus in plane and space.
Seminar. Problems with collinearity. 

Curs 2. Dot product. Lagrange Theorem.
Seminar. Distance Problems solved by dot product.

Curs 3.Cross Product. Triple Scalar Product.
Seminar.Problems with areas and volumes.

Curs 4. Group of isometries.
Seminar.Problems using symmetries and translations.

Curs 5. Non-Isometric Transformations: Homotheties.
Seminar. Problems using the homotheties.

Curs 6. Non-Isometric Transformations: Inversions.
Seminar. Problems using the inversions.

Curs 7. Real Product of two complex numbers.
Seminar. Applications.

Curs 8. Complex Product of two complex numbers.
Seminar. Partial written exam. 

Curs 9. n-th roots of a complex number.
Seminar. Solving Area problems using the complex product.

Curs 10. Classical Geometric Theorems proved by complex numbers.
Seminar. Advantages and disadvantage in using Complex Numbers in the Geometry of Plane.

Curs 11. Coordinate systems in the study of euclidean geometry of plane.
Seminar. Plane Curves given by different equations.

Curs 12. Algebraic Curves in Euclidean Plane.
Seminar. Examples: Algebraic Curves of second order. 

Curs 13. Affine invariants. Affine classification.
Seminar. Algorithm of classification.

Curs 14. Metric properties of second order algebraic curves.
Seminar. Problems involving geometrical properties of conics.
	
Bibliography	1.Andreescu,T., Andrica,T.,Complex Numbers from A to&#8230;Z,Birkhauser,2006.
2.Andrica,D.,s.a., Teme si probleme alese de geometrie,Editura Plus,Bucuresti,2002.
3.Andrica,D.,s.a., Matematica de baza,Editura Studium,Editia a 4-a,Cluj-Napoca,2004.
4.Berger,M., Geometrie,CEDUC NathanParis,1977-1978.
5.Coxeter,H.S.M.,Greitzer,S.L., Geometry Revisited,Random House,New York,1967.
6.Mihalescu,C., Geometria elementelor remarcabile,Societatea de Stiinte Matematice din Romania,2007.
7.Branzei,D., Notes on Geometry,Paralela 45,Pitesti,1999.
8.Engel,A.,Problem-Solving Strategies,Springer Verlag,1998.
9.Fenn,R.,Geometry,Springer Verlag,2001.
10.Hahn,L.,Complex Numbers & Geometry,The Mathematical Association of America,1994.
	
Assessment	1. Activity at courses 15%
2. Activity at seminars 25 %
3. Presentation of an essay 30%
4. Oral exam  30%