Uncertaintybased Information Elements of Generalized Information Theory

This book is an introduction to finite model theory which stresses the computer science origins of the area. In addition to presenting the main techniques for analyzing logics over finite models, the book deals extensively with applications in databases, complexity theory, and formal languages, as well as other branches of computer science. It covers Ehrenfeucht-Fraïssé games, locality-based techniques, complexity analysis of logics, including the basics of descriptive complexity, second-order logic and its fragments, connections with finite automata, fixed point logics, finite variable logics, zero-one laws, and embedded finite models, and gives a brief tour of recently discovered applications of finite model theory.

During the last few years several good textbooks on nonlinear dynamics have ap­ peared for graduate students in applied mathematics. It seems, however, that the majority of such books are still too theoretically oriented and leave many practi­ cal issues unclear for people intending to apply the theory to particular research problems. This book is designed for advanced undergraduate or graduate students in mathematics who will participate in applied research.

This new edition book is all that you will ever need for learning piano chords, scales, arpeggios, how to read music, and basic music theory!

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients.