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

SUBJECT

Code
Subject
MML1006 Topics in Algebra I (for teachers education)
Section
Semester
Hours: C+S+L
Category
Type
Didactic Mathematics
1
2+1+0
speciality
compulsory
Teaching Staff in Charge
Assoc.Prof. PELEA Cosmin Razvan, Ph.D.,  cpeleamath.ubbcluj.ro
Aims
To deepen and complete the knowledge on combinatorics. To present some combinatorics results related to set theory, polynomials, number theory and group theory. To introduce some basics of graph theory. To remember some properties of permutation groups, to complete and to apply them in some colouring problems.
Content
1. Sets, relations, functions.
2. Arrangements, permutations and combinations.
3. The Newton@s binomial formula and the multinomial formula.
4. The principle of inclusion and exclusion.
5. The numbers of Stirling, Bell, Fibonacci and Catalan.
6. Partitions (of a positive integer).
7. Graphs. Counting trees.
8. Permutation groups. Burnside@s theorem.
9. Colouring problems. The Polya-de Bruijn enumeration method.
10. Inversion formulas. The group of arithmetic functions. The Mobius function.
References
1. Berge, C., Graphes et hypergraphes, Dunod, Paris, 1970.
2. Berge, C., Teoria grafurilor si aplicatiile ei, Editura Tehnica, 1969.
3. Breaz, S.; Covaci, R., Elemente de logica, teoria multimilor si aritmetica, Editura Fundatiei pentru Studii Europene, Cluj-Napoca, 2006.
4. Covaci, R., Algebra si programare liniara, Litografia Universitatii Babes-Bolyai, Cluj-Napoca, 1986.
5. Ion, D. I.; Nita, C.; Nastasescu, C., Complemente de algebra, Editura Stiintifica si Enciclopedica, Bucuresti, 1984.
6. Nastasescu, C.; Nita, C.; Brandiburu, M.; Joita, D., Exercitii si probleme de algebra, Editura Didactica si Pedagogica, Bucuresti, 1981.
7. Popescu, D.; Oboroceanu, G., Exercitii si probleme de algebra, combinatorica si teoria numerelor, Editura Didactica si Pedagogica, Bucuresti, 1979.
8. Purdea, I.; Pelea, C., Probleme de algebra, Editura Fundatiei pentru Studii Europene, Cluj-Napoca, 2005.
9. Tomescu, I., Introducere in combinatorica, Editura Tehnica, Bucuresti, 1972. (Editia engleza: Introduction to combinatorics, Collet’s Publishers Ltd., London and Wellingborough, 1975).
10. Tomescu, I., Probleme de combinatorica si teoria grafurilor, Editura Didactica si Pedagogica, Bucuresti, 1981. (Editia engleza: Problems in combinatorics and graph theory, John Wiley, New York, 1985).
Assessment
Written exam (grade E). Each student makes a presentation containing solved problems and applications on a topic from the above list (grade R). The final grade N is obtained as follows: N = (E + R) / 2.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject