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

Code	Subject	
MO265	Algorithmic Combinatorics	

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

Teaching Staff in Charge	Lect. ANDRAS Szilard Karoly, andrasz@math.ubbcluj.ro	
Aims	We present some problems and recent results concerning arithmetical functions, prime numbers pseudo prime numbers and about special combinatorial problems.	
Content	 Basic notions: divisors, primes, lcm, gcd, integer parts, motion of a billiard ball
Asymptotic formulas and complexity 
The Bertrand postulate and combinatorial algorithms for finding primes
Arithmetical functions, the Mobius function, the inversion formula, Euler&#8217;s totient function, the number and the sum of divisors, Dirichlet convolutions and applications
Arithmetical functions and algorithms
Primes and pseudoprimes, Carmichael numbers
Complexity of algorithms, the Euclidian algorithm

	
Bibliography	1. AIGNER, M.-ZIEGLER, G. M.:  Proofs from the BOOK,  Springer Verlag, 1998.
2. BACH E.- SHALLIT, J.: Algorithmic number theory,  Cambridge: MIT Press,  1996.
3. BRESSOUD, D.-WAGON, S.: A course in computational number theory, Springer Verlag, 2000.
4. ERDOS, P.-GRAHAM, R. L.: Old and new problems and results in combinatorial number theory, L. Enseigment Math., 1980.
5. GRAHAM, R. L.-KNUTH D, E-PATASHNIK, O.: Konkret matematika, Budapest: Műszaki Konyvkiado, 1998.
6. VAN LINT, J. H.-WILSON, R. M.: A course in combinatorics, Cambridge: Cambridge University Press,  2001.
7. ANDRÁS SZILÁRD: Dinamikus rendszerek, Editura didactica si pedagogica, 2008
8. J.G. MICHAELS, J.L. GROSS, J.W. GROSSMAN, D.R. SHIER: Handbook of discrete and combinatorial mathematics, CRC Press, 1999
9. H.S.WILF: Algorithms and complexity, www.math.upenn.edu/~wilf/AlgoComp.pdf 1994

	
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.