Discrete Structures

Weekly outline

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  General

  Diskretne strukture VSŠ 63705

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  • Obveznosti študenta Page
  • Gradiva Page
  • References in English Page
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  • Preverjanja znanja Page
  • Forum novic
  • Forum vprašanj in odgovorov
  • Prvi poskusni kolokvij File Uploaded 29/11/21, 09:06
  • Rešitve s točkovnikom - prvi poskusni kolokvij File Uploaded 5/12/21, 15:06
  • Drugi poskusni kolokvij File Uploaded 10/01/22, 18:21
  • Rešitve s točkovnikom - drugi poskusni kolokvij File Uploaded 15/01/22, 20:19
  • Izpit, 19.01.2022, računski del, pola A File Uploaded 21/01/22, 19:10
  • Izpit, 19.01.2022, računski del, pola A, rešitve File Uploaded 21/01/22, 19:12
  • Izpit, 19.01.2022, računski del, pola B File Uploaded 21/01/22, 19:11
  • Izpit, 19.01.2022, računski del, pola B, rešitve File Uploaded 21/01/22, 19:14
  • Izpit, 19.01.2022, teoretični del File Uploaded 21/01/22, 19:06
  • Izpit, 19.01.2022, teoretični del, rešitve File Uploaded 21/01/22, 19:07
  • Izpit, 07.02.2022, računski del File Uploaded 8/02/22, 22:53
  • Izpit, 07.02.2022, računski del, rešitve File Uploaded 8/02/22, 22:54
  • Izpit, 07.02.2022, teoretični del, poli AB File Uploaded 8/02/22, 22:55
  • Izpit, 07.02.2022, teoretični del, poli CD File Uploaded 8/02/22, 22:56
  • Izpit, 07.02.2022, teoretični del, rešitve File Uploaded 8/02/22, 22:58
  • Izpit, 24.03.2022, računski del File Uploaded 28/03/22, 08:50
  • Izpit, 24.03.2022, računski del, rešitve File Uploaded 28/03/22, 08:51
  • Izpit 24.03.2022, teoretični del File Uploaded 28/03/22, 08:52
  • Izpit 24.03.2022, teoretični del, rešitve File Uploaded 28/03/22, 08:52
  • Izpit 19.08.2022, računski del File Uploaded 22/08/22, 13:32
  • Izpit 19.08.2022, računski del, rešitve File Uploaded 22/08/22, 13:32
  • Izpit 19.08.2022, teoretični del File Uploaded 22/08/22, 13:30
  • Izpit 19.08.2022, teoretični del, rešitve File Uploaded 22/08/22, 13:30
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  4. oktober - 10. 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 - 8. oktober File Uploaded 8/10/21, 16:57
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  11. oktober - 17. 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);

  • Izročki predavanj - 15. oktober File Uploaded 14/10/21, 11:32
  • Naloge za vaje, 2. teden File Uploaded 9/10/21, 10:08
  • Zakoni izjavnega računa File
  • Domača naloga, 2. teden Quiz
  • Testna naloga Quiz
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  18. oktober - 24. 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).

  • Izročki predavanj - 22. oktober File Modified 22/10/21, 16:52
  • Naloge za vaje, 3. teden File Uploaded 16/10/21, 20:58
  • Domača naloga, 3. teden Quiz
  • Neobvezen kviz: Izjavni račun Quiz
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  25. oktober - 31. oktober

  Predavanja: Pomožni sklepi - sklep s protislovjem, pogojni sklep in sklep z analizo primerov. Predikatni račun - jezik predikatnega računa, izjavne formule.
  

  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)

  • Izročki predavanj - 29. oktober File Modified 29/10/21, 16:49
  • Naloge za vaje, 4. teden File Uploaded 25/10/21, 10:02
  • Pravila sklepanja File
  • Pravilni in nepravilni sklep File
  • Domača naloga, 4. teden Quiz
  • Neobvezen kviz: izjavni in predikatni račun Quiz
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  1. november - 7. november

  Predavanja: Doseg kvantifikatorjev, vezane in proste spremenljivke. Interpretacija izjavne formule, enakovrednost izjavnih formul, preimenovanje spremenljivk, zakoni predikatnega računa, preneksna normalna oblika.
  

  Lectures: Free and bound variables, scope of quantifier, 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).

  • Izročki predavanj - 5. november File Modified 5/11/21, 17:14
  • Naloge za vaje, 5. teden File Uploaded 1/11/21, 07:24
  • Pomožni sklepi File
  • Interpretacija in formalizacija File
  • Domača naloga, 5. teden Quiz
  • Neobvezen kviz: predikatni račun Quiz
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  8. November - 14. november

  Predavanja: Množice, osnovne operacije z množicami ($\cap, \cup, +, \setminus, ^c$), lastnosti komplementiranja, osnovne enakosti množic, potenčna množica, kartezični produkt.
  

  Lectures: Sets, basic operations with sets ($\cap, \cup, +, \setminus, ^c$), laws for operations with sets, power set, cartesian product and properties. (notes, on this link there are some proofs of laws of set theory).

  • Izročki predavanj - 12. november File Modified 12/11/21, 16:53
  • Naloge za vaje, 6. teden File Uploaded 7/11/21, 10:28
  • Zakoni predikatnega računa. File
  • Domača naloga, 6. teden Quiz
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  15. november - 21. november

  Predavanja: Moč končnih množic. Načelo vključitev in izključitev. Preslikave, njihove lastnosti, kompozitum preslikav, inverzna preslikava.
  
  Lectures: Cardinality of finite sets. (link) Principle of inclusion and exclusion. (link) Mappings (link), properties (link), inverse mapping (link), composition of functions (link).
  

  • Izročki predavanj - 19. november File Modified 19/11/21, 16:55
  • Naloge za vaje, 7. teden File
  • Enakosti z množicami File
  • Domača naloga, 7. teden Quiz
  • Naloge za vajo Quiz
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  22. november - 28. november

  Predavanja: Lastnosti kompozituma preslikav. Definicija relacije, grafična predstavitev relacij, lastnosti relacij, operacije z relacijami, potence relacij.
  

  Lectures: 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).

  • Izročki predavanj - 26. november File Modified 26/11/21, 17:13
  • Naloge za vaje, 8. teden File Uploaded 21/11/21, 19:46
  • Lastnosti kartezičnega produkta File
  • Domača naloga, 8. teden Quiz
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  29. november - 5. december

  Predavanja: 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)

  • Izročki predavanj - 3. december File Uploaded 2/12/21, 13:41
  • Naloge za vaje, 9. teden File Uploaded 29/11/21, 08:55
  • Operacije z relacijami File
  • Lastnosti relacij File
  • Domača naloga, 9. teden Quiz
  • Domača naloga, 9. teden (kopiraj) Quiz

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  6. december - 12. december

  Predavanja: Teorija števil - deljivost, razširjeni Evklidov algoritem, linearne diofantske enačbe.

  Lectures: Number theory - divisibility, extended Euclidean algorithm (link), linear diophantine equations (link).

  • Izročki predavanj - 10. december (dopolnjeni 12. decembra) File Modified 12/12/21, 19:46
  • Naloge za vaje, 10. teden File Uploaded 5/12/21, 21:29
  • Kompozitum preslikav File
  • Inverzna preslikava File
  • Domača naloga, 10. teden Quiz
  • Domača naloga, 10. teden (kopiraj) Quiz

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• 

  13. december - 19. 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) 

  • Izročki predavanj - 17. december File Modified 17/12/21, 16:48
  • Naloge za vaje, 11. teden File
  • Rešitve - vaje 11. teden File
  • Domača naloga, 11. teden Quiz
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  20. december - 26. december

  Predavanja: Sprehod, pot, obhod, cikel. Povezanost in komponente za povezanost. Razdalja v grafu. Karakterizacija dvodelnih grafov. Eulerjev problem. 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). Hamiltonian graphs (link).

  • Izročki predavanj - 21. december File Modified 21/12/21, 20:06
  • Zapiski predavanj, 21.12.2021 File Uploaded 23/12/21, 23:04
  • Naloge za vajo Quiz
  • Naloge za vaje, 12. teden File Uploaded 20/12/21, 08:46
  • Rešitve - vaje 12. teden File
  • Domača naloga, 12. teden Quiz
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  27. december - 2. januar

  
  

  • Bonus domača naloga, 13. teden Quiz
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  3. januar - 9. januar

  Predavanja: Barvanja garfov, drevesa, gozdovi.

  Lectures: Graph coloring (link), trees, forests (link).

  • Izročki predavanj - 7. januar File Uploaded 6/01/22, 13:24
  • Naloge za vaje, 14. teden File Uploaded 3/01/22, 07:30
  • Domača naloga, 14. teden Quiz
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  10. januar - 16. januar

  Predavanja: Permutacije.

  Lectures: Permutations (link).

  • Izročki predavanj - 11. januar File Modified 12/01/22, 09:03
  • Naloge za vaje, 15. teden File Uploaded 10/01/22, 08:48
  • Posnetek vaj, 12.1.2022 URL
  • Zapiski z vaj, 12.1.2022 File Uploaded 12/01/22, 17:58
  • Bonus domača naloga, 15. teden Quiz