Discrete Mathematics

• Uvod u propozicionalni račun, formula, interpretacija (istinosna vrijednost formule)
• Predikatni račun, modeli, glavni test – provjera je li formula ispunjiva, oboriva… 1. kolokvij
• Kongruencije
• Euklidov algoritam, linearna
• Diofantova jednadžba
• Moebiusova i
• Eulerova funkcija
• Polugrupa, grupa, prsten, polje 2. kolokvij
• Rekurzivne relacije
• Fibonaccijevi brojevi, linearne rekurzije s konstantnim koeficijentima 3. kolokvij nema nastave nema nastave nema nastave nema nastave nema nastave nema nastave nema nastave

1. ability to establish the algebra of statements truth value of predefined variable values
2. ability to find if a given formula of the algebra of statements is a tautology
3. ability to find if a given formula of a predicate calculus is a valid one
4. Boole´s algebra
5. ability to find if a structure is a semi-group, a group, a ring or a field
6. divisibility, using the remainder theorem
7. ability to find the final value of Euclid's algorithm for a given data input
8. ability to find the values of both Möbius and Euler functions for given arguments
9. ability to find solutions to linear Diofant equations
10. ability to understand the implementation of variations, permutations and combinations in combinatorics; to to understand the implementation of the inclusion/exclusion formula
11. ability to establish the generating functions and Dirchlet principle
12. ability to understand recursive relations, Fibonacci sequence, linear and inhomogenous recursive relations
13. relations

Required reading

• D. Žubrinić, Diskretna matematika, Element, Zagreb, 1997.
  D. Veljan, Kombinatorika i diskretna matematika, Algoritam, Zagreb, 2001.
  E. A. Bender, S. G. Williamson, A short sourse in discrete mathematics, Dover Publications, 2004.
  S. S. Epp, Discrete mathematics with mpplications, Brooks Cole, 2004.
  D. Veljan, Kombinatorika s teorijom grafova, Školska knjiga, Zagreb, 1989.
  R. Johnsonbaugh, Discrete mathematics, Prentice Hall, 2000.