Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MML0002	Algebra	

Semester	Hours: C+S+L	Category	Status	
1	2+2+0	fundamental	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
CRIVEI Septimiu	Ph.D.	Assoc.Prof.	Algebra, Analysis and Geometry	*			

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

III. Course objectives
The aim of the course is to introduce the basic notions of linear algebra as well as some of its applications to computer science.	

IV. Course contents
1. Preliminary notions. Functions. Equivalence relations and partitions. Groups. Rings and fields. Substructures. Homomorphisms.
2. Vector spaces.  Definition of a vector space, examples. Subspaces. Linear maps. Linear dependence and independence. The exchange theorem (Steinitz). Bases.  Dimension and related formulas. 
3. Matrices and linear systems of equations. Elementary operations. Matrices and determinants. Rank and inverse of a matrix. Matrix of a linear map. Change of basis. Systems of linear equations, solving methods. Eigenvectors and eigenvalues. Bilinear and quadratic forms. Reduction of quadratic forms to the canonical form.
4. Introduction to coding theory. Linear codes. Examples. Generator matrix and parity-check matrix. Decoding linear codes.	

V. Bibliography
1. N. Both, S. Crivei, Culegere de probleme de algebra, Lito UBB Cluj-Napoca, 1996. 
2. R. Covaci, Algebra si programare liniara, Lito UBB, Cluj-Napoca, 1986.
3. S. Crivei, Basic abstract algebra, Casa Cartii de Stiinta, Cluj-Napoca, 2002, 2003.
4. C. Gherghe, D. Popescu, Criptografie. Coduri. Algoritmi, Editura Univ. Bucuresti, 2005. 
5. C. Udriste si colectiv, Algebra, geometrie si ecuatii diferentiale, Editura Didactica si Pedagogica, Bucuresti, 1982.	

VI. Thematic of didactic activities per weeks
Week 1: Functions. Equivalence relations and partitions. [3, Ch. 1]
Week 2: Binary operations. Groups, subgroups, group homomorphisms. [3, Ch. 2] 
Week 3: Rings and fields, subrings and subfields, ring homomorphisms. [3, Ch. 2]
Week 4: Vector spaces, examples. Subspaces. Linear maps. [3, Ch. 3]
Week 5: Linear dependence and independence. Bases, dimension. Steinitz theorem. [3, Ch. 3]
Week 6: Bases and coordinates. Dimension related formulas. [3, Ch. 3] 
Week 7: Elementary operations. Matrices and determinants. [3, Ch. 4]
Week 8: Rank and inverse of a matrix. Matrix of a list of vectors. [3, Ch. 4]
Week 9: Matrix of a linear map. Change of basis. [3, Ch. 4]
Week 10: Systems of linear equations, solving methods. [3, Ch. 4]
Week 11: Eigenvectors and eigenvalues. [3, Ch. 4]
Week 12: Bilinear and quadratic forms. Reduction of quadratic forms to the canonical form. [5, Ch. 2]
Week 13: Linear codes, examples. Generator matrix and parity-check matrix. [4, Ch. 14]
Week 14: Decoding linear codes. [4, Ch. 14]	

VII. Didactic methods used
Exposition, didactic proof, algorithmization, problematization, exercise. 	

VIII. Assessment
Written test and written final exam. The test (optional), of 1 hour, consists of problems on the first 2 chapters. The final exam is of 1.5 hours for the students for which the test is considered, respectively 2.5 hours for the others. The final grade is computed as follows: G=1+T+E, where G= the final grade, T= either the grade from the test or the grade from the exam for the subjects corresponding to the topic of the test (max. 4), E= the grade from the exam (max. 5).	

IX. Additional references
1. Both, N., Algebra, Lito UBB, Cluj-Napoca, 1996.
2. Calugareanu, G., Lectii de algebra liniara, Lito UBB, Cluj-Napoca, 1995.
4. Gilbert, J., Gilbert, L., Elements of modern algebra, PWS-Kent, Boston, 1992.
5. Gilbert W.J., Nicholson, W.K., Modern algebra with applications, John Wiley, 2004.
6. Lidl, R., Pilz, G., Applied abstract algebra, Springer-Verlag, 1998.
7. Purdea, I., Pelea, C., Probleme de algebra, Editura EFES, Cluj-Napoca, 2005.
8. Purdea, I., Pop, I., Algebra, Editura GIL, Zalau, 2003.	

	Dean,							Chair head,
Prof. TAMBULEA Leon, Ph.D.   Assoc. Prof. BREAZ Simion, Ph.D.

	Date,						Course responsible,
   23.11.2009			   Assoc. Prof. CRIVEI Septimiu, Ph.D.