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Author: Jan von Plato
Publisher: Princeton University Press
ISBN: 1400885035
Category : Science
Languages : en
Pages : 400
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Book Description
The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.
Author: Jan von Plato
Publisher: Princeton University Press
ISBN: 1400885035
Category : Science
Languages : en
Pages : 400
Get Book Here
Book Description
The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.
Author: Song Y Yan
Publisher: World Scientific
ISBN: 9814500836
Category : Mathematics
Languages : en
Pages : 419
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Book Description
This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.
Author: Song Y. Yan
Publisher: World Scientific
ISBN: 9789810234225
Category : Computers
Languages : en
Pages : 424
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Book Description
This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field.
Author: Sébastien Combéfis
Publisher: Presses universitaires de Louvain
ISBN: 2875582526
Category : Science
Languages : en
Pages : 302
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Book Description
There are more and more automated systems with which people are led to interact everyday. Their complexity increases, and badly designed systems may result in automation surprises. The contribution of this thesis is a formal analysis framework to assess whether a system is prone to potential automation surprises in an interaction.
Author: Stefania Centrone
Publisher: Springer
ISBN: 9402411321
Category : Philosophy
Languages : en
Pages : 541
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Book Description
Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.
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Category : Music
Languages : en
Pages : 242
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Book Description
Author: Isaak Iosifovich Revzin
Publisher:
ISBN:
Category : Machine translating
Languages : en
Pages : 158
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Book Description
Author: John Stillwell
Publisher: Princeton University Press
ISBN: 0691234361
Category : Mathematics
Languages : en
Pages : 456
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Book Description
How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.
Author: Eduardo Noble
Publisher: Springer Nature
ISBN: 3030938204
Category : Mathematics
Languages : en
Pages : 424
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Book Description
This text presents the ideas of a particular group of mathematicians of the late 18th century known as “the German combinatorial school” and its influence. The book tackles several questions concerning the emergence and historical development of the German combinatorial analysis, which was the unfinished scientific research project of that group of mathematicians. The historical survey covers the three main episodes in the evolution of that research project: its theoretical antecedents (which go back to the innovative ideas on mathematical analysis of the late 17th century) and first formulation, its consolidation as a foundationalist project of mathematical analysis, and its dissolution at the beginning of the 19th century. In addition, the book analyzes the influence of the ideas of the combinatorial school on German mathematics throughout the 19th century.
Author: Bertrand Meyer
Publisher: Springer Nature
ISBN: 3031345185
Category : Computer programming
Languages : en
Pages : 451
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Book Description
Zusammenfassung: The French School of Programming is a collection of insightful discussions of programming and software engineering topics, by some of the most prestigious names of French computer science. The authors include several of the originators of such widely acclaimed inventions as abstract interpretation, the Caml, OCaml and Eiffel programming languages, the Coq proof assistant, agents and modern testing techniques. The book is divided into four parts: Software Engineering (A), Programming Language Mechanisms and Type Systems (B), Theory (C), and Language Design and Programming Methodology (D). They are preceded by a Foreword by Bertrand Meyer, the editor of the volume, a Preface by Jim Woodcock providing an outsider's appraisal of the French school's contribution, and an overview chapter by Gérard Berry, recalling his own intellectual journey. Chapter 2, by Marie-Claude Gaudel, presents a 30-year perspective on the evolution of testing starting with her own seminal work. In chapter 3, Michel Raynal covers distributed computing with an emphasis on simplicity. Chapter 4, by Jean-Marc Jézéquel, former director of IRISA, presents the evolution of modeling, from CASE tools to SLE and Machine Learning. Chapter 5, by Joëlle Coutaz, is a comprehensive review of the evolution of Human-Computer Interaction. In part B, chapter 6, by Jean-Pierre Briot, describes the sequence of abstractions that led to the concept of agent. Chapter 7, by Pierre-Louis Curien, is a personal account of a journey through fundamental concepts of semantics, syntax and types. In chapter 8, Thierry Coquand presents "some remarks on dependent type theory". Part C begins with Patrick Cousot's personal historical perspective on his well-known creation, abstract interpretation, in chapter 9. Chapter 10, by Jean-Jacques Lévy, is devoted to tracking redexes in the Lambda Calculus. The final chapter of that part, chapter 11 by Jean-Pierre Jouannaud, presents advances in rewriting systems, specifically the confluence of terminating rewriting computations. Part D contains two longer contributions. Chapter 12 is a review by Giuseppe Castagna of a broad range of programming topics relying on union, intersection and negation types. In the final chapter, Bertrand Meyer covers "ten choices in language design" for object-oriented programming, distinguishing between "right" and "wrong" resolutions of these issues and explaining the rationale behind Eiffel's decisions. This book will be of special interest to anyone with an interest in modern views of programming -- on such topics as programming language design, the relationship between programming and type theory, object-oriented principles, distributed systems, testing techniques, rewriting systems, human-computer interaction, software verification... -- and in the insights of a brilliant group of innovators in the field
