Nievergelt Foundations of Logic and Mathematics
Erscheinungsjahr 2012
ISBN: 978-1-4612-0125-0
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
Applications to Computer Science and Cryptography
E-Book, Englisch, 415 Seiten, Web PDF
ISBN: 978-1-4612-0125-0
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
A Theory.- 0 Boolean Algebraic Logic.- 1 Logic and Deductive Reasoning.- 2 Set Theory.- 3 Induction, Recursion, Arithmetic, Cardinality.- 4 Decidability and Completeness.- B Applications.- 5 Number Theory and Codes.- 6 Ciphers, Combinatorics, and Probabilities.- 7 Graph Theory.
