Foundations of Logic and Mathematics: Applications to Computer Science and CryptographySpringer Science & Business Media, 2002 - Broj stranica: 415 This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: • Why is the truth table for the logical implication so unintuitive? • Why are there no recipes to design proofs? • Where do these numerous mathematical rules come from? • What are the applications of formal logic and abstract mathematics? • What issues in logic, mathematics, and computer science still remain unresolved? Answers to such questions must necessarily present both theory and significant applica tions, which explains the length of the book. The text first shows how real life provides some guidance for the selection of axioms for the basis of a logical system, for instance, Boolean, classical, intuitionistic, or minimalistic logic. From such axioms, the text then derives de tailed explanations of the elements of modem logic and mathematics: set theory, arithmetic, number theory, combinatorics, probability, and graph theory, with applications to computer science. The motivation for such detail, and for the organization of the material, lies in a continuous thread from logic and mathematics to their uses in everyday life. |
Ostala izdanja - Prikaži sve
Foundations of Logic and Mathematics: Applications to Computer Science and ... Yves Nievergelt Ograničeni pregled - 2012 |
Foundations of Logic and Mathematics: Applications to Computer Science and ... Yves Nievergelt Pregled nije dostupan - 2012 |
Uobičajeni izrazi i fraze
algorithm alphabet arithmetic atoms axiom of extensionality axiom P1 bijection Cartesian product circuit classical implicational calculus commutativity Consequently consists contraposition converse law Deduction Theorem defined definition denoted directed graph disjoint divisor double negation edge element empty set ENIGMA ENIGMA machine F F F F T F False finite following theorem shows full propositional calculus function F graph G Hence induction hypothesis informal proof injective instance integer intersection intuitionistic logic inverse Karnaugh table law of contraposition law of double LCCC letters logical connective logical formula logical implication logically equivalent mathematics modulo Modus Ponens multiplication natural numbers non-empty notation ordinal path-connected Peirce's law permutation positive integer proceeds by induction propositional calculus propositional form Prove or disprove rational numbers rotor set theory subset surjective tautology theorem 175 theorem holds transitive transposition True Truth tables Truth values variables verify vertex vertices VX(P VX(Q well-formed sets well-ordered whence
Reference za ovu knjigu
Logic Functions and Equations: Binary Models for Computer Science Christian Posthoff,Bernd Steinbach Ograničeni pregled - 2005 |