Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare si simulare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMC1008	Efficient Numerical Models in Computational Sciences	

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

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
CHIOREAN Ioana Rodica	Ph.D.	Assoc.Prof.	Numerical and Statistical Calculus	*	*	*	

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

III. Course objectives
The purpose of this course is to accustom the students to numerical methods for solving problems arising in Biology, Genetics, Mathematical Finance, etc. A study of efficiency of the presented methods, by comparing serial and parallel algorithms, will be made.

IV. Course contents
In Biology and Genetics:

-sequences comparison
-the fitting or not fitting of some subsequences in long genetic sequences
-the insertion of some subsequences in given sequences etc.

In Mathematical Finance:

-numerical methods to discretize differential equations 
-the Black-Scholes method
-serial and parallel algorithms for solving exactly and approximate the Black-Scholes equation
-comparison among the presented algorithms, etc.

V. Bibliography
1.	Chiorean, I., Catinas, T., Coman, Gh., An Advanced Course on Numerical Analysis (2007)- sub tipar
2.	Chiorean,I., Remarks on some recurrence relations in life annuities, Studia Univ.Babes-Bolyai, Mathematica, vol.LI, nr,2, 2006, pp.39-43
3.	Chiorean, I., A cyclic odd-even reduction technique applied to a parallel evaluation of an explicit scheme in Mathematical finance, Studia Univ.Babes-Bolyai, Mathematica, vol.LI, nr.4, 2006, pp.65-69 
4.	Chiorean, I., Parallel Prefix Computation in Biological Sequences Comparison using Linear Recurrence Relations, Proceedings of  the Mediteranean Conference on Medical and Biological Engineering, MEDICON 2004, Ischia (Italia), 31 iul-5 aug, 2004
5.	Chiorean, I., Remarks on some Parallel Algorithms for Prefix Computation, International Journal of Pure and Applied Mathematics, vol.18, no.3, 2005, pp.363-369.
6.	Chiorean, I., On some Numerical Methods for Solving the Black-Scholes Formula, 
Creative mathematics journal, vol.13, 2004, Pub.by Dep.of Math.and Comp.Science, North Univ.Baia-Mare, pp.31-36 (conf.ICAM4, Suior, Baia-Mare)
7.	Chiorean, I., On the Complexity of some Parallel Algorithms for Biological  Sequences Comparison, Proc.of MEDINF 2003 Int.Conference, Craiova, 2003, pp.117-118
8.	Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994
9.	Berger, B., Introduction to Computational Molecular Biology, MIT comp Biology Ed., 1998

VI. Thematic of didactic activities per weeks
1.a. Introduction in Parallel calculus (lecture)

-Chiorean,I., Calcul paralel, Ed.Microinformatica, 1994, pp.9-20

   b. Pipeline execution for a vector array (seminar)

2.a. Connecting networks (lecture)

-Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994, pp. 32-42

   b. The Star-formula of Laplace equation on a lattice network. (seminar)

3.a. Double reccursive technique (lecture)

-Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994, pp.43-45
-Chiorean, I., Parallel Prefix Computation in Biological Sequences Comparison using Linear Recurrence Relations, Proceedings of  the Mediteranean Conference on Medical and Biological Engineering, MEDICON 2004, Ischia (Italia), 31 iul-5 aug, 2004

   b. The double reccursive technique applied to the reccurence relations (seminar)
4.a. Cyclic odd-even reduction technique (lecture)

- Chiorean,I., Remarks on some recurrence relations in life annuities, Studia Univ.Babes-Bolyai, Mathematica, vol.LI, nr,2, 2006, pp.39-43
- Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994, 46-49

   b. The cyclic odd-even reduction technique applied to the solving a system of linear equations with a tridiagonal matrix ( seminar)

5.a. Slicing and crinkling techniques. Parallel Data Transforms (lecture)

- Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994, pp.50-58

   b. Obtaining the vector mapping (seminar)

6.a. Parallel algorithms (lecture)

- Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994, 59-69

   b. Parallel matrix multiplication (seminar)

7.a. Algorithms for biological sequences comparison (lecture)

-Berger, B., Introduction to Computational Molecular Biology, MIT comp Biology Ed., 1998

   b. The alignment matrix(seminar –paper)

8.a. Parallel algorithms for sequences comparison (lecture)

-Chiorean, I., Parallel Prefix Computation in Biological Sequences Comparison using Linear Recurrence Relations, Proceedings of  the Mediteranean Conference on Medical and Biological Engineering, MEDICON 2004, Ischia (Italia), 31 iul-5 aug, 2004
-Chiorean, I., Remarks on some Parallel Algorithms for Prefix Computation, International Journal of Pure and Applied Mathematics, vol.18, no.3, 2005, pp.363-369.

   b. Parallel algorithms for the alignment matrix (seminar-paper)

9.a. Basic Option theory (lecture)

-Etheridge, A., A Course in Financial Calculus, University Oxford

    b. The study of European and American Option (seminar –paper)

10.a. The model of an option : the Black-Scholes equation (lecture)

-Chiorean, I., On some Numerical Methods for Solving the Black-Scholes Formula, Creative mathematics journal, vol.13, 2004, Pub.by Dep.of Math.and Comp.Science, North Univ.Baia-Mare, pp.31-36 (conf.ICAM4, Suior, Baia-Mare)
     b. The Black-Scholes equation for an European and for an American option (seminar- paper)

11.a. Explicit numerical methods for solving the Black-scholes equation (lecture)

-Chiorean, I., On some Numerical Methods for Solving the Black-Scholes Formula, Creative mathematics journal, vol.13, 2004, Pub.by Dep.of Math.and Comp.Science, North Univ.Baia-Mare, pp.31-36 (conf.ICAM4, Suior, Baia-Mare)

     b Implicit numerical methods for solving the Black-scholes equation (seminar –paper)

12.a. Parallel algorithms for the presented explicite methods (lecture)

	- Chiorean, I., A cyclic odd-even reduction technique applied to a parallel evaluation of an explicit scheme in Mathematical finance, Studia Univ.Babes-Bolyai, Mathematica, vol.LI, nr.4, 2006, pp.65-69 

     b. Parallel algorithms for the presented implicit methods (seminar –paper)

13.a. Factorization techniques (lecture)

-Chiorean, I., Catinas, T., Coman, Gh., An Advanced Course on Numerical Analysis (2007)- sub tipar
	-Modi, J.J., Parallel Algorithms and Matrix Computation, Clarendon Press, 1988

     b.Apllying this techniques to solve the Black-Scholes equation . (seminar+ computer)

14.a. Parallel iterative methods (lecture)
	
-Chiorean, I., Catinas, T., Coman, Gh., An Advanced Course on Numerical Analysis (2007)- sub tipar
-Coman, Gh., Analiza Numerica, Ed.Libris, 1994

     b. Solving the Black-Scholes discretized equation by means of parallel iterative methods (seminar- + computer)

	

	

VII. Didactic methods used
Lectures, proof, individual work, conversation.

VIII. Assessment
Every student will get the final mark composed by a mark for a paper (50%) and a mark for a parallel program (50%).

IX. Additional references
1.	Etheridge, A., A Course in Financial Calculus, University Oxford
2.	Modi, J.J., Parallel Algorithms and Matrix Computation, Clarendon Press, 1988
3.	Coman, Gh., Analiza numerica, Ed.Libris, 1994

	Dean,						Cheaf of the Chair,
            Prof.Leon Tambulea, PhD			Prof.Petru Blaga, PhD						

	Date,							Course responsible,
The 15-th of Sept. 2008			Assoc.Prof. CHIOREAN Ioana, PhD