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,  andraszmath.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’s totient function, the number and the sum of divisors, Dirichlet convolutions and applications

References
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’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.

Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject