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

SYLLABUS

I. General data
Code	Subject	
MC270	Efficient Numeric Methods in Computational Science	

Semester	Hours: C+S+L	Category	Status	
2	2+2+0		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 aquainted the students with 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
1. The DNA molecules, which are the most important carrier of genetic material, are sequences defined on an alphabet composed by the letters A,G,C and T which represent the four nucleotides that enter in their composition. So, the study of biological sequences consists in the study of sequences in general, informatics in particular.
Under this circumstances, we take into account:
-sequences comparison
-the fitting or not fitting of some subsequences in long genetical sequences
-the insertion of some subsequences in given sequences etc.

 The methods involved: dinamic programming, prefix computation, etc.
Due to the fact that the biological sequences are very long, the problem of reducing the execution time is very important. In order to solve this, some parallel algorithms are presented.

2. Many problems in Finance are mathematicaly modeled by means of differential equations. For instance, the problem of determining the value of an option is modeled by means of the Black-Scholes equation. The study of some numerical methods in this domain implies:

-numerical methods for discretizing differential equations 
-the Black-Scholes method
-serial and parallel algorithms for solving exactly and approximatly the Black-Scholes equation
-compariosn among the presented algorithms etc.	

V. Bibliography
1.	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
2.	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.
3.	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)
4.	Chiorean, I., On the Complexity of some Parallel Algorithms for Biological  sequences Comparison, Proc.of MEDINF 2003 Int.Conference, Craiova, 2003, pp.117-118
5.	Chiorean, I., Calcul paralel, Ed.Microinformatica, 1994
6.	Berger, B., Introduction to Computational Molecular Biology, MIT comp Biology Ed., 1998
7.	Etheridge, A., A Course in Financial Calculus, University Oxford

	

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,	
Prof.dr.Leon Tambulea						Chair head,
								Prof.dr.Petre Blaga

	Date,							Course responsible,
15-th.Sept.2009				Assoc.Prof. CHIOREAN Ioana Rodica, PhD