Splošno
Diskretne strukture VSŠ 63705
Diskretne strukture VSŠ 63705
Predavanja: Matematična indukcija. Izjave, izjavni vezniki.
Lectures: Mathematical induction (pages 5-7); Introduction into propositional logic: atoms, logical connectives, logical formulas, truth tables, equivalence of formulas (pages 95-99).
Predavanja: Izjavni izrazi, resničnostna tabela, enakovredni izjavni izrazi. Zakoni izjavnega računa. DNO in KNO.
Lectures: Laws of propositional logic (pages 11-15); Disjunctive and conjuctive normal form (pages 4-6);
Predavanja: Polni nabori izjavnih veznikov. Sklepanje v izjavnem računu. Formalizacija sklepov, definicija pravilnega sklepa, pravila sklepanja, dokaz pravilnosti sklepa.
Lectures: Functionally complete sets of logical operators (pdf; the proof of Theorem 2.7 is not required). Logical inference - formalization, rules of inferece, derivation of rules (pages 100-104).
Predavanja: Pomožni sklepi - sklep s protislovjem, pogojni sklep in sklep z analizo primerov.
Predikatni račun - jezik predikatnega računa, izjavne formule. Doseg kvantifikatorjev, proste in vezane spremenljivke.
Lectures: Proof by contradiction (section 8 - on this link you can freely download the book), proof by conditional derivation (section 6.2), proof by cases (explained at the bottom of section 3.2).
Predicate logic: predicates; universe of discourse, universal and existential quantifier. (link) Scope of quantifiers. Free and bound variables.
No lectures this week.
Predavanja: Interpretacija izjavne formule, enakovrednost izjavnih formul, preimenovanje spremenljivk, zakoni predikatnega računa, preneksna normalna oblika.
Lectures: Order of quantifiers, well-formed formula. Interpretation of the formula, equivalence of formulas, renaming of variables, laws of predicate logic, prenex normal form (link, link to the notes for the last three topics).
Predavanja: Množice, osnovne operacije z množicami ($\cap, \cup, +, \setminus, ^c$), lastnosti komplementiranja, osnovne enakosti množic.
Lectures: Sets, basic operations with sets ($\cap, \cup, +, \setminus, ^c$), laws for operations with sets. (notes, on this link there are some proofs of laws of set theory).
Predavanja: Preslikave, njihove lastnosti, kompozitum preslikav, inverzna preslikava. Lastnosti kompozituma preslikav. Definicija relacije, grafična predstavitev relacij, lastnosti relacij, operacije z relacijami, potence relacij.
Lectures: Mappings (link), properties (link), inverse mapping (link), composition of functions (link). Properties of a composition of functions (link). Relations: definition and examples, graphical representation (link to last two topics), properties of relations (link), operations with relations (link).
Predavanja: Teorija grafov - lema o rokovanju, grafična zaporedja, družine grafov (polni in prazni grafi, polni dvodelni grafi, cikli, poti), podgrafi, izomorfizem grafov.
Lectures: Graph theory - definition of a graph (link), degree of a vertex, handshaking lemma (Theorem 5.1.1), graphical sequences (link), isomorphism of graphs (link), families of graphs (complete and empty graphs, complete bipartite graphs, cycles, paths) (link) , subgraphs. (link)
Predavanja: Sprehod, pot, obhod, cikel. Povezanost in komponente za povezanost. Razdalja v grafu. Karakterizacija dvodelnih grafov. Eulerjev problem. Drevesa in gozdovi. Hamiltonovi grafi.
Lectures: Walk, path , closed walk, cycle. (link) Connected graphs and components. Distance in graphs. (link) Characterization of bipartite graphs. (link) Euler's problem (link). Trees, forests (link). Hamiltonian graphs (link).
Predavanja: Permutacije, igra 15. Potenčne enačbe.