Logic Computation And Rigorous Methods
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Logic, Computation and Rigorous Methods
This Festschrift was published in honor of Egon Börger on the occasion of his 75th birthday. It acknowledges Prof. Börger's inspiration as a scientist, author, mentor, and community organizer. Dedicated to a pioneer in the fields of logic and computer science, Egon Börger's research interests are unusual in scope, from programming languages to hardware architectures, software architectures, control systems, workflow and interaction patterns, business processes, web applications, and concurrent systems. The 18 invited contributions in this volume are by leading researchers in the areas of software engineering, programming languages, business information systems, and computer science logic.
Structures of Computing
Structures of Computing explains the behavioral meaning of fundamental concepts of computing from a practical viewpoint and in generic terms, unrestricted by specific computing devices or programming languages. To compute is understood as processing structures by a set of cooperating agents each of which executes an algorithm assigned to it and interacts with the other agents. Part I of the book defines the conceptual constituents of interactive processes: (i) data, i.e. structured objects with associated properties, relations and functions the algorithmic processes operate upon, (ii) basic operations that affect the data in single execution steps, and (iii) control mechanisms that determine the combination of single steps in multi-agent computations where the interaction happens via communication or other forms of data sharing. Part II analyses these constituents concerning (i) methods to achieve process correctness (inspection, experimental validation, reasoning), (ii) principal computational paradigms (architectures, programming styles, communication structures, control patterns from sequential and reflective to concurrent, mixed synchronous/asynchronous and data flow control), and (iii) complexity (power and limits of computing structures). The book is mainly addressed to students and professionals who want to understand the conceptual foundation of computing. It does not assume any specific programming experience but only a basic understanding of what are mechanically executable processes and their descriptions. Any unnecessary formalism is thus avoided, and definitions are formulated as much as possible in natural language, using common mathematical notation only where needed to prevent ambiguities. Numerous examples and exercises serve as comprehension checkpoints.
Core Concepts in Real Analysis
"Core Concepts in Real Analysis" is a comprehensive book that delves into the fundamental concepts and applications of real analysis, a cornerstone of modern mathematics. Written with clarity and depth, this book serves as an essential resource for students, educators, and researchers seeking a rigorous understanding of real numbers, functions, limits, continuity, differentiation, integration, sequences, and series. The book begins by laying a solid foundation with an exploration of real numbers and their properties, including the concept of infinity and the completeness of the real number line. It then progresses to the study of functions, emphasizing the importance of continuity and differentiability in analyzing mathematical functions. One of the book's key strengths lies in its treatment of limits and convergence, providing clear explanations and intuitive examples to help readers grasp these foundational concepts. It covers topics such as sequences and series, including convergence tests and the convergence of power series. The approach to differentiation and integration is both rigorous and accessible, offering insights into the calculus of real-valued functions and its applications in various fields. It explores techniques for finding derivatives and integrals, as well as the relationship between differentiation and integration through the Fundamental Theorem of Calculus. Throughout the book, readers will encounter real-world applications of real analysis, from physics and engineering to economics and computer science. Practical examples and exercises reinforce learning and encourage critical thinking. "Core Concepts in Real Analysis" fosters a deeper appreciation for the elegance and precision of real analysis while equipping readers with the analytical tools needed to tackle complex mathematical problems. Whether used as a textbook or a reference guide, this book offers a comprehensive journey into the heart of real analysis, making it indispensable for anyone interested in mastering this foundational branch of mathematics.