Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Algebră şi Geometrie (în limba engleză)
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MG264	Critical Points and Applications	

Semester	Hours: C+S+L	Category	Status	
1	2+1+1		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
PINTEA Cornel	Ph.D.	Assoc.Prof.	Geometry	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The course is studing on the one hand the local behaviour of a real differentiable function around a non-degenerate critical point and the Morse Theory as an immediate application, and on the other hand is studing the critical set of mappings with values in manifolds of dimension greater than one.	

IV. Course contents
I. ELEMENTS OF CRITICAL POINT THEORY
   1.1 Generalties on Critical Point Theory;
   1.2 The first Deformation Lemma;
   1.3 The second deformation Lemma;
II. MORSE THEORY AND APPLICATIONS
   2.1 Morse Lemma;
   2.2 Passing a critical level;
   2.3 Morse Inequalities;
III CRITICAL POINTS OF MAPPINGS BETWEEN MANIFOLDS
   3.1 Functions with finitely many critical points
   3.2 Functions with infinitely many critical points.	

V. Bibliography
1. BURGHELEA, D., HANGAN, TH. MOSCOVICI, H., VERONA, A., Introducere in topologia diferentiala, Ed. Stiintifica, Bucuresti, 1973.
2. MILNOR, J., Morse Theory, Annals of Math. Studies, Princeton Univ. Press, 1963.
3. PALAIS, R.S., TERNG, C-L., Critical Point Theory and Submanifold Geometry, Lectures Notes in Mathematics, Springer-Verlag.
4. PINTEA, C., Continuous Mappings with an Infinite Number of Topologically Critical Points, Annales Polonici Mathematici, LXVII.1, 1997.
5. PINTEA, C., Geometrie. Geometrie Diferentiala, Geometrie Riemannian. Grupuri si Algebre Lie, Presa Universitara Clujeana, 2006.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Exam+Quiz+Reports.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Assoc.Prof. PINTEA Cornel, Ph.D.