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+P	Category	Status	
1	2+2+0+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, Mathematical Analysis and Geometry	*			

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

III. Course objectives
We will present basic notions and results concerning algebraic structures. These will be applied to construct (algorithmic) solutions to some concrete problems.	

IV. Course contents
1. Groups: basic notions and results. Generated subgroup, cyclic groups. Connections between subgroups which are induced by homomorphisms.
2. Rings and (skew) fields: basic notions and results. Examples. Subrings and subfields. Prime fields.
3. Linear Algebra: Linear spaces; Subspaces; Linear applications; Examples: Linear maps; Linear (in)dependent systems; Bases; Dimension and formulas; Exchange Theorem and applications. Algorithmic methods.
4. Matrices and linear equations. Matrices and determinants; The rank of a matrix; Linear equations systems; Algorithmic methods.
5. Codes: The general problem; Linear codes; Decoding.    

V. Bibliography
1. G.PIC, I. PURDEA: Tratat de algebra moderna, vol.1, Editura Academiei, 1977. 
2. I. PURDEA, Tratat de algebra moderna, vol.2, Editura Academiei, 1982. 
3. I. PURDEA, I. POP, Algebra, Editura GIL, Zalau, 2003.
4. G. CALUGAREANU, Lectii de algebra liniara, Litografiat Univ. Babes-Bolyai, 1995. 
5. I.D. ION, N. RADU, Algebra (ed.3-a), Editura Didactica si Pedagogica, 1981. 
6. N. BOURBAKI, Algebre, chap.1 -3, Editura Hermann, 1970.
7. G. CALUGAREANU, P. HAMBURG: Exercises in basic ring theory, Kluwer Academic Publishers, Dordrecht, Boston 1998.
8. S. CRIVEI:  Basic Abstract Algebra, Casa Cartii de Stiinta, Cluj-Napoca 2002.
9. M. BALINT, G. CZEDLI, A. SZENDREI: Absztrakt algebrai feladatok, Tankonyvkiado, Budapest1988.
10. A. MARCUS : Algebra [http://math.ubbcluj.ro/~marcus]
11. J. SZENDREI:  Algebra es szamelmelet, Tankonyvkiado, Budapest1974.
12. G. SCHEJA, U. STORCH: Lehrbuch der Algebra 1,2, B.G. Teubner, Stuttgart  1994
13. M. ARTIN:   Algebra, Birkhauser, Basel  1998.

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
A written final exam (grade E) and a test at the seminar (grade T). The exam subjects have theoretical questions
from all the studied topics, and one problem, among the problems
studied at the course and last 5 seminars. The test subject have
practical questions (exercices and problems) from topics studied
in first 9 weeks. The final grade is the weighted mean of the
three grades mentioned above, conditioned by all the grades being
at least 5 from 10. Otherwise, the exam will not be passed.
The final grade = 75%E + 25%T

IX. Additional references

	Dean,							Chair head,

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