MME1012 | Number Theory and Combinatorics |
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 |