General
Diskretne strukture VSŠ 63705
Weekly outline
3. oktober - 9. oktober
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).
- Izročki predavanj, indukcija in izjavni račun File Modified 4/10/22, 23:18
10. oktober - 16. oktober
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);
- Naloge za vaje, 2. teden File Uploaded 7/10/22, 06:57
17. oktober - 23. oktober
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).
- Naloge za vaje, 3. teden File Uploaded 14/10/22, 12:49
24. oktober - 30. oktober
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.
- Predikatni račun - izročki predavanj File Uploaded 24/10/22, 20:09
- Zakoni predikatnega računa File Uploaded 7/12/22, 16:14
31. oktober - 6. november
No lectures this week.
- Naloge za vaje, 5. teden File Uploaded 28/10/22, 08:11
7. november - 13. november
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).
- Teorija množic - izročki predavanj File Uploaded 6/11/22, 23:55
- Naloge za vaje, 6. teden File Uploaded 4/11/22, 10:20
14. november - 20. november
- Moč množic, preslikave, izročki predavanj (osveženo) File Modified 24/11/22, 16:18
21. november - 27. november
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).
- Relacije, izročki predavanj File Modified 24/11/22, 16:12
- Naloge za vaje, 8. teden File Uploaded 18/11/22, 08:47
28. november - 4. december
Predavanja: Potence relacij, tranzitivna in tranzitivno-refleksivna ovojnica relacije, ekvivalenčna relacija, ekvivalenčni razredi, faktorska množica.
Lectures: Transitive closure and reflexive-transitive closure (pages 28-30), equivalence relation (link), equivalence classes, factor set. (link)5. december - 11. december
- Teorija števil, izročki predavanj File Modified 29/12/22, 10:50
- Naloge za vaje, 10. teden File Uploaded 2/12/22, 20:46
12. december - 18. december
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)
- Teorija grafov, izročki File Uploaded 9/12/22, 15:48
- Teorija grafov, drevesa in gozdovi, izročki File Uploaded 16/01/23, 23:05
19. december - 25. december
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).- Naloge za vaje, 12. teden File Uploaded 14/12/22, 07:38
26. december - 1. januar
- Naloge za vaje, 13. teden File Uploaded 23/12/22, 09:39
- Zapiski z vaj File Uploaded 27/12/22, 12:27
- predavanja, 27. december 2022, pre File Uploaded 27/12/22, 11:47
- predavanja, 27. december 2022, post File Uploaded 27/12/22, 13:47
2. januar - 9. januar
Predavanja: Permutacije.
Lectures: Permutations (link).
- Izročki, permutacije File Modified 3/01/23, 16:08
- Naloge za vaje, 14. teden File Uploaded 31/12/22, 06:41
9. januar - 15. januar
Predavanja: Permutacije, igra 15. Potenčne enačbe.
- Naloge za vaje, 15. teden File Uploaded 9/01/23, 07:29