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Théorie des ensembles Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Le Livre de Théorie des ensembles qui vient en tête du traité présente les fondements axiomatiques de la théorie des ensembles. Il comprend les chapitres : Description de la mathématique formelle ; Théorie des ensembles ; Ensembles ordonnés. Cardinaux. Nombres entiers ; Structures. Il contient également un fascicule de résultats et une note historique. Ce volume est une réimpression de l'édition de 1970.

Mathematical logic --- wiskunde --- logica

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Mathematical logic --- wiskunde --- logica

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Advance praise for 18 Unconventional Essays on the Nature of Mathematics: "I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician." - Sir Michael Atiyah, University of Edinburgh "A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated." - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University This startling new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths. The following essays are included: * Alfred Renyi: Socratic Dialogue * Carlo Cellucci: Filosofia e Matematica, introduction * William Thurston: On Proof and Progress in Mathematics * Andrew Aberdein: The Informal Logic of Mathematical Proof * Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology * Brian Rotman: Towards a Semiotics of Mathematics * Donald Mackenzie: Computers and the Sociology of Mathematical Proof * Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management * Rafael Nunez: Do Numbers Really Move? * Timothy Gowers: Does Mathematics Need a Philosophy? * Jody Azzouni: How and Why Mathematics is a Social Practice * Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy * Jack Schwartz: The Pernicious Influence of Mathematics on Science * Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For? * Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions * Eduard Glas: Mathematics as Objective Knowledge and as Human Practice * Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote * Reuben Hersh: Inner Vision, Outer Truth

Mathematical logic --- Mathematics --- wiskunde --- logica

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Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

Mathematical logic --- Algebra --- Mathematics --- algebra --- wiskunde --- logica

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Philosophy --- Mathematical logic --- Logic --- filosofie --- wiskunde --- logica