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

Code	Subject	
MME1012	Number Theory and Combinatorics	

Section	Semester	Hours: C+S+L	Category	Type	
Computational Mathematics - in Hungarian	2	2+2+0	speciality	compulsory	
Didactic Mathematics - in Hungarian	2	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Lect. ANDRAS Szilard Karoly, andrasz@math.ubbcluj.ro	
Aims	Introduction to number theory and combinatorics
Applications in the process of teaching undergraduate mathematics

	
Content	1. Basic notions: divisors, primes, lcm, gcd, integer parts, motion of a billiard ball
2. Linear Diophantine equations 
3. Systems of congruencies, the Chinese remainder theorem
4. Applications and simulations
5. Pythagorean numbers and applications
6. The Pell equation
7. Contest problems
8. The Euler-Fermat, Wilson theorem, combinatorial aspects
9. Arithmetical functions, the Mobius function, the inversion formula
10. Counting of periodical points and orbits
11. Euler&#8217;s totient function, the number and the sum of divisors, Dirichlet convolutions and applications

Bibliography	1. AIGNER, M.-ZIEGLER, G. M.:  Proofs from the BOOK,  Springer Verlag, 1998.
2. AIGNER, M.-ZIEGLER, G. M.:   Bizonyitasok a KONYVBOL, Budapest: Typotex, 2004.
3. ORE OYSTEIN: Invitation to number theory, Random House, 1967
4. BEGE, ANTAL: Beveztes a szamelmeletbe, Cluj Napoca: Scientia Kiado,  2002.
5. BEGE, ANTAL-DEMETER, ALBERT-LUKACS ANDOR: Szamelmeleti feladatgyujtemeny, Cluj Napoca: Scientia Kiado,  2002.
6. A.Y. KINCHIN: Three pearls of number theory, Dover publications, 1952
7. ERDOS, P.-GRAHAM, R. L.: Old and new problems and results in combinatorial number theory, L. Enseigment Math., 1980.
8. GRAHAM, R. L.-KNUTH D, E-PATASHNIK, O.: Konkret matematika, Budapest: Muszaki Konyvkiado, 1998.
9. TITU ANDREESCU, DORIN ANDRICA, ZUMING FHENG: 104 number theoretic problems, Birkhauser, 2007
10. ANDRÁS SZILÁRD: Dinamikus rendszerek, Editura didactica si pedagogica, 2008

Assessment	Activity (courses and seminars): 30%
Project: 30%
Final exam 40%

If a student&#8217;s absentees is greater than 40% from the number of all activities, the student has to prepare a special presentation (paper) in a subject specified by the professor.