Foundations of Logic and Mathematics: Applications to Computer Science and CryptographySpringer Science & Business Media, 6. pro 2012. - 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. |
Sadržaj
3 | |
7 | 41 |
8 | 52 |
Logic and Deductive Reasoning 555555 | 54 |
Set Theory | 97 |
3 | 110 |
Induction Recursion Arithmetic Cardinality | 159 |
0 | 223 |
8 | 299 |
5 | 328 |
PROBABILITY | 339 |
Graph Theory | 361 |
Exercises | 379 |
Bibliography | 398 |
405 | |
8 | 260 |
Ostala izdanja - Prikaži sve
Foundations of Logic and Mathematics: Applications to Computer Science and ... Yves Nievergelt Ograničeni pregled - 2002 |
Foundations of Logic and Mathematics: Applications to Computer Science and ... Yves Nievergelt Pregled nije dostupan - 2012 |
Uobičajeni izrazi i fraze
algorithm alphabet Apply theorem atoms axiom of extensionality axiom of pairing axiom P1 bijection common commutativity consists contains contraposition converse law Deduction Theorem defined definition denoted Derived rule Determine disjoint disjunction divisor double negation edge element empty set exactly Example exists F F F F T F False finite following exercises following theorem shows formal proof function F Hence implicational calculus informal proof injective instance intersection intuitionistic logic inverse Karnaugh table law of contraposition law of double logical connective logical formula logical implication logically equivalent mathematical Modus Ponens natural numbers non-empty notation pairs path-connected Peirce's law permutation positive integer prime propositional calculus propositional form Prove or disprove rotor set F set theory subset substitution surjective tautology theorem 175 theorem 202 transitivity Truth table Truth values union universally valid value True variables verify vertex vertices VX(P VX(Q well-formed sets well-ordered whence