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Matematica discreta Indice Descrizione | Applicazioni | Bibliografia | Voci correlate | Altri progetti | Collegamenti esterni | Menu di navigazioneWikimedia CommonsWikimedia Commonsmatematica discretaMatematica discretaM4129143-8

Matematica discreta


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Matematica discreta




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La matematica discreta, alle volte chiamata matematica finita (che è propriamente solo una sua parte), è lo studio di strutture matematiche che sono fondamentalmente discrete, nel senso che non supportano o richiedono il concetto di continuità. La maggior parte degli oggetti studiati nella matematica discreta (se non tutti) sono insiemi numerabili come gli interi.




Indice





  • 1 Descrizione


  • 2 Applicazioni


  • 3 Bibliografia


  • 4 Voci correlate


  • 5 Altri progetti


  • 6 Collegamenti esterni




Descrizione |


La matematica discreta è diventata famosa per le sue applicazioni in informatica.
I concetti e le notazioni della matematica discreta sono utili per lo studio o la modellazione di oggetti o problemi negli algoritmi informatici e nei linguaggi di programmazione.


Per i concetti opposti, vedere continuo, topologia, e analisi matematica.


La matematica discreta include normalmente:



  • logica - lo studio della ragione;


  • teoria degli insiemi - uno studio delle collezioni di elementi;


  • teoria dei numeri;


  • combinatoria - lo studio del contare;


  • teoria dei grafi;


  • teoria degli algoritmi - lo studio dei metodi di calcolo;


  • teoria dell'informazione;

  • la teoria della computabilità e complessità - uno studio dei limiti teorici degli algoritmi;

  • la teoria della probabilità e le catene di Markov;


  • algebra lineare - uno studio delle equazioni lineari.


Applicazioni |


La matematica discreta trova applicazione nei seguenti ambiti:



  • teoria dei giochi;


  • teoria delle code;


  • geometria discreta;


  • topologia discreta;


  • programmazione lineare;


  • crittologia (che include crittografia e crittoanalisi);


  • analisi musicale della musica atonale.


Bibliografia |


  • (EN) Donald E. Knuth, The Art of Computer Programming

  • (EN) Kenneth H. Rosen, Handbook of Discrete and Combinatorial Mathematics CRC Press. ISBN 0-8493-0149-1.

  • (EN) Kenneth H. Rosen, Discrete Mathematics and Its Applications 5th ed. McGraw Hill. ISBN 0-07-293033-0. Companion Web site: http://www.mhhe.com/math/advmath/rosen/

  • (EN) Richard Johnsonbaugh, Discrete Mathematics 6th ed. Macmillan. ISBN 0-13-045803-1. Companion Web site: http://wps.prenhall.com/esm_johnsonbau_discrtmath_6/

  • (EN) Norman L. Biggs, Discrete Mathematics 2nd ed. Oxford University Press. ISBN 0-19-850717-8. Companion Web site: https://web.archive.org/web/20060525015110/http://www.oup.co.uk/isbn/0-19-850717-8 include quesiti e soluzioni

  • (EN) Neville Dean, Essence of Discrete Mathematics Prentice Hall. ISBN 0-13-345943-8. Non in profondità come i testi precedenti, ma una buona introduzione.

  • (EN) Archivi Matematici, Matematica Discreta: collegamenti a syllabi, tutorial, programmi, ecc. http://archives.math.utk.edu/topics/discreteMath.html

  • (EN) Ronald Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics


Voci correlate |


  • Progetto:Matematica/Elenco di voci di base per la matematica discreta


Altri progetti |



Altri progetti


  • Wikimedia Commons


  • Collabora a Wikimedia CommonsWikimedia Commons contiene immagini o altri file su matematica discreta


Collegamenti esterni |





  • Matematica discreta, su thes.bncf.firenze.sbn.it, Biblioteca Nazionale Centrale di Firenze. Modifica su Wikidata


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