"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Supplement of algebra |
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| Teaching Staff in Charge |
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| Aims |
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Completion of the knowledge in number theory, group theory and combinatorics studied in the courses of algebra of previous semesters. |
| Content |
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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 |
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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 |
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Exam. |