Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy co

We are living in a world where complexity of systems created and studied by people grows beyond all imaginable limits. Computers, their software and their networks are among the most complicated systems of our time. Science is the only efficient tool for dealing with this overwhelming complexity. One of the methodologies developed in science is the axiomatic approach. It proved to be very powerful in mathematics. In this book, the authors developed further an axiomatic approach in computer science initiated by Floyd, Manna, Blum and other researchers. In the traditional constructive setting,...

Set theory has become one of the most respected fields in mathematics due to the situation in which sets are used to build all mathematical structures, pervading the whole of modern mathematics, and objects, while set theory guarantees soundness of this approach. The language of set theory, in its relative simplicity, is sufficiently powerful to formalise virtually all mathematical concepts popular in the mathematical community. As a result, the majority of mathematicians assume that a set is the most fundamental object for the whole mathematics and consequently, set theory along with logical...

Mark Burgin examines the deep mysteries of structures, exploring different faces of reality, explicating the structure of the world's existence and explicating fundamental issues of symbols, signs and concepts. This book is aimed at a wide audience of readers who want to better understand the world in which they live.