Provability, Computability and Reflection.
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Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques con…
Everyone has stared at the crumpled page of a math assignment and wondered, where on Earth will I ever use this? It turns out, Earth is precisely the place. As teen math prodigy Agnijo Banerjee and his teacher David Darling reveal, complex math surrounds us. If we think long eno…
Dan Velleman's lively text prepares students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. This new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Desig…
Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover re…
Drawing on the science and mathematics of infinity, H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics, he explores key questions…
A combinatorial method is developed in this book to explore the mysteries of chaos, which has became a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviors of dynamical systems is classifi…
This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up the developments of the 19…
Why should mathematical logic be grounded on the basis of some formal requirements in the way that it has been developed since its classical emergence as a hybrid field of mathematics and logic in the 19th century or earlier? Contrary to conventional wi.
Although there are some books dealing with algebraic theory ofautomata, their contents consist mainly of Krohn-Rhodes theory andrelated topics. The topics in the present book are ratherdifferent. For example, automorphism groups of automata and thepartially ordered sets of autom…
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with proofs that rely on (and interplay with) other areas of mathematics. It concludes …
The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of s…
The book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stoc…
The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given …
This book introduces the reader to the general theory of partially ordered sets, i.e., posets. The text is presented in a rather informal manner, with interesting examples and computations, which rely on the Hasse diagram to build graphical intuition for the structure of finite …
"Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the bo…