Supplement of algebra 
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Teaching Staff in Charge 

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 PolyaBurnside 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 pentru perfectionarea profesorilor, Ed. Didactica si Pedagogica, Bucuresti, 1983.
2. Ion, I.D.; Nastasescu, C.; Nita, C., Complemente de algebra, Ed. Stiintifica si Enciclopedica, Bucuresti, 1984. 3. Kurosh A., Higher Algebra, Mir Publishers, Moscow, 1975. 4. Nastasescu, C.; Nita, C., Teoria calitativa a ecuatiilor algebrice, Editura Tehnica, Bucuresti, 1979. 5. Vraciu C., Vraciu M., Elemente de aritmetica, Editura ALL, Bucuresti, 1998. 
Assessment 
Exam. 