Computation, Proof, Machine: Mathematics Enters a New Age

Computation is revolutionizing our world, even the inner world of the "pure" mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation. Along the way it invites us to reconsider the dialog between mathematics and the natural sciences, as well as the relationship between mathematics and computer science. It also sheds new light on philosophical concepts, such as the notions of analytic and synthetic judgment. Finally, it brings us to the brink of the new age, in which machine intelligence offers new ways of solving mathematical problems previously inaccessible. This book is the 2007 Winner of the Grand Prix de Philosophie de l'Académie Française.

Computers & Technology

Dowek, Gilles

Computer Science

Cambridge University Press

This book sets unites the various formalisms that define a programming language: ‘small steps’ operational semantics, ‘big steps’ operational semantics, and denotational semantics. It illustrates them with typical features of programming languages.

Introduction to the Theory of Programming Languages (Undergraduate Topics in Computer Science)

Lévy, Jean-Jacques

Springer

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)

The Age of Algorithms

Algorithms are probably the most sophisticated tools that people have had at their disposal since the beginnings of human history. They have transformed science, industry, society. They upset the concepts of work, property, government, private life, even humanity. Going easily from one extreme to the other, we rejoice that they make life easier for us, but fear that they will enslave us. To get beyond this vision of good vs evil, this book takes a new look at our time, the age of algorithms. Creations of the human spirit, algorithms are what we made them. And they will be what we want them to be: it's up to us to choose the world we want to live in.

Abiteboul, Serge

Programming

The development of programming languages has radically modified our relation to language, complexity and machines. This book is an introduction to the principles around which these languages are organised - imperative constructions, functional constructions, reference, dynamic data types, objects and more. Using Java as a main language, but systematically comparing it to other languages it enables the reader to understand the unifying concepts that lie beneath each particular language and provides the tools that allow the students to adapt to new programming languages.

Principles of Programming Languages (Undergraduate Topics in Computer Science)

Les démonstrations et les algorithmes: Introduction à la logique et à la calculabilité

ECOLE POLYTECH

Plusieurs avancées mathématiques importantes remettent en cause, depuis la fin du XXième siècle, la longue prééminence du raisonnement sur le calcul. Cette véritable révolution nous amène à repenser le dialogue des mathématiques avec les sciences de la nature. Elle éclaire d'une lumière nouvelle des concepts philosophiques, comme ceux de jugement analytique et synthétique. Et elle nous laisse entrevoir de nouvelles manières de résoudre des problèmes mathématiques, qui s'affranchissent de certaines limites arbitraires que la technologie du passé a imposé à la taille des démonstrations : les mathématiques sont peut-être en train de partir à la conquête d'espaces jusqu'alors inaccessibles..

metamorphoses du calcul (les)

POMMIER

See the best price to sell, buy, or rent books by Dowek, Gilles. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Dowek, Gilles

See the best price to sell, buy, or rent books by Dowek, Gilles. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Computation, Proof, Machine: Mathematics Enters a New Age

Computation, Proof, Machine: Mathematics Enters a New Age

Introduction to the Theory of Programming Languages (Undergraduate Topics in Computer Science)

Proofs and Algorithms: An Introduction to Logic and Computability (Undergraduate Topics in Computer Science)

The Age of Algorithms

The Age of Algorithms

Principles of Programming Languages (Undergraduate Topics in Computer Science)

Les démonstrations et les algorithmes: Introduction à la logique et à la calculabilité

metamorphoses du calcul (les)