MML0009 | Supplement of Algebra |
Teaching Staff in Charge |
Assoc.Prof. COVACI Rodica, Ph.D., rcovacimath.ubbcluj.ro |
Aims |
Completion of the knowledge in set theory, combinatorics, arithmetic of numbers and polynomials, group theory and algebraic equations theory 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. |
References |
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%) + Exam(75%). |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |