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

Code	Subject	
MMG1012	Topics in Geometry III (for teachers education)	

Section	Semester	Hours: C+S+L	Category	Type	
Didactic Mathematics	4	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Prof. ANDRICA Dorin, Ph.D., dandrica@math.ubbcluj.ro
Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro	
Aims	1. The study of some important notions and results in Geometry which are useful in understandinf od some modern directions in Mathematics.
2. The applications of the theoretical results to some research problems in a modern setting.
3. The connexions to other fields in Mathematics.	
Content	Course 1.Vectors in plane and space.
Seminar.Some problems about colinearity solved by using vectors.

Course 2.The inner product and Lagrange@s theorem.
Seminar.Some metric problems solved by using vectors.

Course 3.The cross product and other vector products.
Seminar.Problems involving areas and volumes.

Course 4.The group of isometries.
Seminar.Problems involving symmetry and translation.

Course 5.Non-isometric transformations: homotethy.
Seminar.Problems solved by homotethy.

Course 6.Non-isometric transformations: inversion.
Seminar.Problems solved by inversion.

Course 7.The real product of two complex numbers.
Seminar.Applications in solving some metric problems.

Course 8.The complex product of two complex numbers.
Seminar.Working paper.

Course 9.The n-th roots of unity.
Seminar.Applications of the complex product to some problems involving areas.

Course 10.Some classical theorems proved by using complex numbers.
Seminar.How useful are complex combers in solving  problems in plane geometry.

Course 11.The coordinates method in the study of the Euclidean Geometry.
Seminar.Plane curves described by various equations.

Course 12.Algebraic curves in the Euclidean plane.
Seminar.The main plane algebraic curves of degree 2.

Course 13.Affine invariants.Centers.Affine classification.
Seminar.The canonical form of conics.

Course 14.Metric properties of algebraic curves of degree 2.
Seminar.Problems about geometric 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.
	
Assessment	The final evaluation is given as follows:
-	the working paper during the semester 20%
-	the evaluation of the reports during the semester 10%
-	the final examination 70%