Bøger af Yves Nievergelt

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.

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory.

Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets.