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

Code	Subject	
MML0009	Supplement of Algebra	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Romanian	6	2+1+0	speciality	optional	
Mathematics-Computer Science - in Romanian	6	2+1+0	speciality	optional	
Applied Mathematics	6	2+1+0	speciality	optional	

Teaching Staff in Charge	Assoc.Prof. COVACI Rodica, Ph.D., rcovaci@math.ubbcluj.ro	
Aims	Completion of the knowledge in number theory, group theory and combinatorics studied in the courses of algebra of previous semesters.	
Content	1. Induction. Combinatorics: deduction and induction, mathematical induction (different forms) and Peano's axiomatic study of the set of natural numbers, some applications of the induction; arrangements, permutations and combinations - their general form and applications (number of terms in the canonical form of a polynomial, product of binomials, power of a sum).
2. Arithmetic of numbers and polynomials (comparative study): the division algorithm with remainder - proof for integers and for polynomials.
3. Algebraic structures: an elementary construction of rings and fields, the structure of some finite groups, some applications of finite groups (the symmetry group of a figure, the action of a group on a set, the Polya-Burnside counting method).
4. Algebraic equations: the fundamental theorem of Algebra, complex numbers expressible by radicals, formulae for solving the algebraic equations of second, third and fourth degree.	
Bibliography	1. Becheanu, M. si colectiv, Algebra, Editura ALL, Bucuresti, 1998.
2. Breaz, S.; Covaci, R., Elemente de logica, teoria multimilor si aritmetica, Editura Fundatiei pentru Studii Europene, Cluj-Napoca, 2006.
3. Ion, I.D.; Nita, C., Nastasescu, C., Complemente de algebra, Editura Stiintifica si Enciclopedica, Bucuresti, 1984.
4. Nastasescu, C.; Nita, C., Teoria calitativa a ecuatiilor algebrice, Editura Tehnica, Bucuresti, 1979.
5. Popescu, D.; Vraciu, C., Elemente de teoria grupurilor finite, Editura Stiintifica si Enciclopedica, Bucuresti, 1986.
6. Purdea, I.; Pelea, C., Probleme de algebra, Editura EIKON, Cluj-Napoca, 2008.	
Assessment	Test paper(25%) + Oral exam(75%).