Foundations of Logic and Mathematics: Applications to Computer Science and CryptographyThis 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. |
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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
addition algorithm allows alphabet Apply arithmetic associativity assume atoms axiom bijection called circuit classical common commutativity complete composition concept connective Consequently Consider consists contains contraposition converse corresponds defined definition denoted Determine digit directed disjoint divides double negation edge element empty equals equivalent exactly Example Exercise exists False finite following theorem function gives graph Hence holds hypothesis induction injective instance integer intersection intuitionistic logic inverse letters logical formula mathematics method minimal Modus Ponens Moreover multiplication natural numbers notation pairs path permutation prime probability proceeds proof propositional calculus Prove Provide reasoning relation remain repetition rules selection sequence specified step subset substitution tautology theorem shows transitive True Truth tables Truth values union universally variables verify vertex vertices walk well-formed whence X E A yields
Reference za ovu knjigu
Logic Functions and Equations: Binary Models for Computer Science Christian Posthoff,Bernd Steinbach Ograničeni pregled - 2005 |