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

Code	Subject	
MMC1013	Topics in Numerical and Statistical Calculus (for teachers education)	

Section	Sem.	Hours: C+S+L	Category	Type	
Didactic Mathematics	2	2+1+1	speciality	compulsory	

Teaching Staff in Charge	Prof. AGRATINI Octavian, Ph.D., agratini@math.ubbcluj.ro	
Aims	1. The course provides the graduate students with selected topics of numerical and statistical calculus training the audience to be drawn into a didactic activity.
2. The lectures achieve a well balanced approach between theoretical developments, examples and exercises, numerical experiments and historical mathematical notes.
3. The seminars offer students a proven pedagogical programme for teachers education.	
Content	1. Quadratic and cubic spline. Properties. B-spline. Spline interpolation. Optimal approximation of linear functionals. Convergence properties. 
2. Orthogonal polynomials. Bernoulli and Euler polynomials.  Binomial type polinomials. Properties.
3. Approximation of functions by using linear positive operators. On the rate of convergence. Operators generated by probabilistic methods.Discrete type operators. 
4. Recurrence equations. The calculus of finite differences. Generating functions. 
5. Shannon entropy. Fisher information. Properties.
6. Classification of states. Poisson processes. Birth and death processes and their applications in insurances. Service systems: a mathematical model of queuring systems.	
Bibliography	1. Aigner, M., Discrete Mathematics, American Mathematical Society,2007.
2. Agratini, O., Blaga, P., Coman, Gh., Lectures on Wavelets, Numerical Methods and Statistics, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.
3. Agratini, O., Chiorean, I., Coman, Gh., Trîmbiţaş, R., Analiză Numerică şi Teoria Aproximării, Vol. III, Presa Universitară Clujeană, Cluj-Napoca, 2002.
4. Blaga, P., Lupaş, Al., Mureşan, A.S., Matematici financiare şi actuariale, Editura Constant, Sibiu, 2001.
5. Harshbarger, R.J., Reynolds, J.J., Calculus with Applications, D.C. Jeath and Company, Lexington, Massachusettes, 1990.
6. Micula, Gh., Funcţii spline şi aplicaţii, Editura Tehnică, Bucureşti, 1978.
7. Stancu, D.D., Coman, Gh., Agratini, O.,Trîmbiţaş, R., Analiză Numerică şi Teoria Aproximării, Vol. I, Presa Universitară Clujeană, Cluj-Napoca, 2001.
8. Trîmbiţaş, R., Analiză numerică. O introducere bazată pe Matlab,Presa Universitară Clujeană, Cluj-Napoca, 2005.    	
Assessment	The final grade is composed as follows:
 - the mark obtained at a Control Paper (weight 1/4),
 - the mark obtained at written exam (weight 3/4).