The debate over Intelligent Design seemingly represents an extension of the fundamental conflict between creationists and evolutionists. ID proponents, drawing on texts such as Darwin's Black Box and Of Pandas and People, urge schools to "teach the controversy" in biology class alongside evolution. The scientific mainstream has reacted with fury, branding Intelligent Design as pseudoscience and its advocates as religious fanatics.But stridency misses the point, ar...

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

This unique book provides a new and well-motivated introduction to calculus and analysis, historically significant fundamental areas of mathematics that are widely used in many disciplines. It begins with familiar elementary high school geometry and algebra, and develops important concepts such as tangents and derivatives without using any advanced tools based on limits and infinite processes that dominate the traditional introductions to the subject. This simple algebraic method is a mode...

The book has an active table of contents for readers to access each chapter of the following titles: 1) THE METHOD OF FLUXIONS AND INFINITE SERIES 2) LIFE OF SIR ISAAC NEWTON One of the key contribution by Newton to mathematical field is the book THE METHOD OF FLUXIONS AND INFINITE SERIES. In this book, Newton made contributions to all branches of mathematics then studied and his solutions to the contemporary problems in analytical geometry of drawing tangents to cu...

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner.To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axio...

One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite vo...

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable sour...

The book deals with the development of continual models of turbulent natural media. Such models serve as a ground for the statement and numerical evaluation of the key problems of the structure and evolution of the numerous astrophysical and geophysical objects. The processes of ordering (self-organization) in an originally chaotic turbulent medium are addressed and treated in detail with the use of irreversible thermodynamics and stochastic dynamics approaches which underlie the respectiv...

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological ap...

As Albert Einstein lay on his death bed he asked for his glasses, his writing implements and his latest equations. He knew he was dying, yet he continued to work. In those final hours of his life, while fading in and out of consciousness, he was working on what he hoped would be the greatest work of all. It was a project of monumental complexity. It was a project that he hoped would unlock the mind of God.

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, n...

These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering.The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference E...