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

Code	Subject	
MML0002	Algebra	

Section	Semester	Hours: C+S+L	Category	Type	
Computer Science	1	3+2+0	fundamental	compulsory	
Information engineering	1	3+2+0		compulsory	

Teaching Staff in Charge	Assoc.Prof. BREAZ Simion Sorin, Ph.D., bodo@math.ubbcluj.ro
Assoc.Prof. CRIVEI Septimiu, Ph.D., crivei@math.ubbcluj.ro
Assoc.Prof. SZANTO Csaba Lehel, Ph.D., szanto@math.ubbcluj.ro	
Aims	We will present basic notions and results concerning algebraic structures. These will be applied to construct (algorithmic) solutions to some concrete problems. 	
Content	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.    
	
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.
	
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