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Studies In Logic And The Foundations Of Mathematics The Axiomatic Method With Special Reference To Geometry And Physics
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Book Synopsis Studies in Logic and the Foundations of Mathematics - The Axiomatic Method with Special Reference to Geometry and Physics by : L. Brouwer
Download or read book Studies in Logic and the Foundations of Mathematics - The Axiomatic Method with Special Reference to Geometry and Physics written by L. Brouwer and published by Brouwer Press. This book was released on 2008-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
Book Synopsis Non-Euclidean Geometries by : András Prékopa
Download or read book Non-Euclidean Geometries written by András Prékopa and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: "From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
Book Synopsis Provability, Computability and Reflection by : Lev D. Beklemishev
Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2009-06-15 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Book Synopsis Causality, Meaningful Complexity and Embodied Cognition by : A. Carsetti
Download or read book Causality, Meaningful Complexity and Embodied Cognition written by A. Carsetti and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and “anchorage” realised on semantic grounds. It is the work of “invention” and g- eration (in invariance), linked with the “rooting” of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of “possibles”, offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the “ le” in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity,whichalsotakes place through the “narration” of the effected construction.
Book Synopsis Towards the Future of Fuzzy Logic by : Rudolf Seising
Download or read book Towards the Future of Fuzzy Logic written by Rudolf Seising and published by Springer. This book was released on 2015-05-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a snapshot of the state-of-the art in fuzzy logic. Throughout the chapters, key theories developed in the last fifty years as well as important applications to practical problems are presented and discussed from different perspectives, as the authors hail from different disciplines and therefore use fuzzy logic for different purposes. The book aims at showing how fuzzy logic has evolved since the first theory formulation by Lotfi A. Zadeh in his seminal paper on Fuzzy Sets in 1965. Fuzzy theories and implementation grew at an impressive speed and achieved significant results, especially on the applicative side. The study of fuzzy logic and its practice spread all over the world, from Europe to Asia, America and Oceania. The editors believe that, thanks to the drive of young researchers, fuzzy logic will be able to face the challenging goals posed by computing with words. New frontiers of knowledge are waiting to be explored. In order to motivate young people to engage in the future development of fuzzy logic, fuzzy methodologies, fuzzy applications, etc., the editors invited a team of internationally respected experts to write the present collection of papers, which shows the present and future potentials of fuzzy logic from different disciplinary perspectives and personal standpoints.
Author :Charles Coulston Gillispie Publisher :Springer Science & Business Media ISBN 13 :9401780110 Total Pages :490 pages Book Rating :4.4/5 (17 download)
Book Synopsis Lazare and Sadi Carnot by : Charles Coulston Gillispie
Download or read book Lazare and Sadi Carnot written by Charles Coulston Gillispie and published by Springer Science & Business Media. This book was released on 2014-02-03 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lazare Carnot was the unique example in the history of science of someone who inadvertently owed the scientific recognition he eventually achieved to earlier political prominence. He and his son Sadi produced work that derived from their training as engineering and went largely unnoticed by physicists for a generation or more, even though their respective work introduced concepts that proved fundamental when taken up later by other hands. There was, moreover, a filial as well as substantive relation between the work of father and son. Sadi applied to the functioning of heat engines the analysis that his father had developed in his study of the operation of ordinary machines. Specifically, Sadi's idea of a reversible process originated in the use his father made of geometric motions in the analysis of machines in general. This unique book shows how the two Carnots influenced each other in their work in the fields of mechanics and thermodynamics and how future generations of scientists have further benefited from their work.
Book Synopsis Quantifier Elimination and Cylindrical Algebraic Decomposition by : Bob F. Caviness
Download or read book Quantifier Elimination and Cylindrical Algebraic Decomposition written by Bob F. Caviness and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the-art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.
Book Synopsis Rough Set Methods and Applications by : Lech Polkowski
Download or read book Rough Set Methods and Applications written by Lech Polkowski and published by Physica. This book was released on 2012-10-07 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rough set approach to reasoning under uncertainty is based on inducing knowledge representation from data under constraints expressed by discernibility or, more generally, similarity of objects. Knowledge derived by this approach consists of reducts, decision or association rules, dependencies, templates, or classifiers. This monograph presents the state of the art of this area. The reader will find here a deep theoretical discussion of relevant notions and ideas as well as rich inventory of algorithmic and heuristic tools for knowledge discovery by rough set methods. An extensive bibliography will help the reader to get an acquaintance with this rapidly growing area of research.
Download or read book Calculus written by Karl Menger and published by Courier Corporation. This book was released on 2014-08-11 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool. The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a "mini-calculus" which brings out the fundamental results without recourse to the notions of limit and continuity. The standard subject matter is then presented as a pure and unambiguous calculus of functions. The issues surrounding the applications of pure calculus to problems in the sciences are faced in a forthright manner by carefully analyzing the meaning of "variable quantity" and clarified by resuscitating Newton's concept of fluents. The accompanying exercises are original, insightful and an integral part of the text. This Dover edition features a new Preface and Guide to Further Reading by Bert Schweizer and Abe Sklar.
Book Synopsis Computing in Euclidean Geometry by : Ding-Zhu Du
Download or read book Computing in Euclidean Geometry written by Ding-Zhu Du and published by World Scientific. This book was released on 1992-09-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going. Contents:Mesh Generation and Optimal Triangulation (M Bern & D Eppstein)Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)Randomized Geometric Algorithms (K L Clarkson)Voronoi Diagrams and Delauney Triangulations (S Fortune)The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)On the Development of Quantitative Geometry from Pythagoras to Grassmann (W-Y Hsiang)Computational Geometry and Topological Network Design (J M Smith & P Winter)Polar Forms and Triangular B-Spline Surfaces (H-P Seidel) Readership: Computer scientists and mathematicians. keywords:Computational Geometry;Triangulation;Machine Proof;Randomized Geometric Algorithm;Voronoi Diagram;Delaunay Triangulation;B-Spline;Polar Form;Steiner Tree;Analytic Geometry “D-Z Du and F Hwang have put to rest an optimization problem known as the Steiner ratio conjecture. Their solution closes the book on a problem that had frustrated a generation of geometers, but it also writes the first chapter of a new volume. The key to Du and Hwang's successful attack on the conjecture is a new method that has potential for solving a raft of other optimization problems.” SIAM News, USA “… the eight surveys are well organized. Each survey is preceded by a good introductory section with a rich bibliography. Both beginners and experts will benefit from this book.” Mathematical Reviews “The papers are not just summaries; the authors present new material or fresh points of view … I recommend the book to anyone who works in one of the areas surveyed or who is interested in the interaction of Euclidean geometry and computers.” IEEE Parallel & Distributed Technology
Book Synopsis Computing in Euclidean Geometry by : Ding-Zhu Du
Download or read book Computing in Euclidean Geometry written by Ding-Zhu Du and published by World Scientific. This book was released on 1995-01-25 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm. Contents:On the Development of Quantitative Geometry from Phythagoras to Grassmann (W-Y Hsiang)Computational Geometry: A Retrospective (B Chazelle)Mesh Generation and Optimal Triangulation (M Bern & D Eppstein)Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)Randomized Geometric Algorithms (K L Clarkson)The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)Voronoi Diagrams and Delaunay Triangulations (S Fortune)Geometric Constraint Solving in R2 and R3 (C M Hoffmann & P J Vermeer)Polar Forms and Triangular B-Spline Surfaces (H-P Seidel)Computational Geometry and Topological Network Design (J M Smith & P Winter)The Exact Computation Paradigm (C Yap & T Dubé) Readership: Computer scientists and mathematicians. keywords:Computational Geometry;Triangulation;Machine Proof;Randomized Geometric Algorithm;Voronoi Diagram;Delaunay Triangulation;B-Spline;Polar Form;Steiner Tree;Analytic Geometry;Exact Computation Review on First Edition: “The papers are not just summaries; the authors present new material or fresh points of view … I recommend the book to anyone who works in one of the areas surveyed or who is interested in the interaction of Euclidean geometry and computers.” IEEE Parallel & Distributed Technology
Download or read book Proceedings written by Leon Henkin and published by American Mathematical Soc.. This book was released on 1974 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Lattice Theory by : G. Grätzer
Download or read book General Lattice Theory written by G. Grätzer and published by Birkhäuser. This book was released on 2012-12-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce the lattice concept. Independently, Richard Dedekind's research on ideals of algebraic numbers led to the same discov ery. In fact, Dedekind also introduced modularity, a weakened form of distri butivity. Although some of the early results of these mathematicians and of Edward V. Huntington are very elegant and far from trivial, they did not attract the attention of the mathematical community. It was Garrett Birkhoff's work in the mid-thirties that started the general develop ment of lattice theory. In a brilliant series of papers he demonstrated the importance of lattice theory and showed that it provides a unifying framework for hitherto unrelated developments in many mathematical disciplines. Birkhoff himself, Valere Glivenko, Karl Menger, John von Neumann, Oystein Ore, and others had developed enough of this new field for Birkhoff to attempt to "seIl" it to the general mathematical community, which he did with astonishing success in the first edition of his Lattice Theory. The further development of the subject matter can best be followed by com paring the first, second, and third editions of his book (G. Birkhoff [1940], [1948], and [1967]).
Book Synopsis Approximate Reasoning by Parts by : Lech Polkowski
Download or read book Approximate Reasoning by Parts written by Lech Polkowski and published by Springer Science & Business Media. This book was released on 2011-08-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set Theory ideas of the containment to a degree. The result is a theory based on the notion of a part to a degree. One can invoke here a formula Rough: Rough Mereology : Mereology = Fuzzy Set Theory : Set Theory. As with Mereology, Rough Mereology finds important applications in problems of Spatial Reasoning, illustrated in this monograph with examples from Behavioral Robotics. Due to its involvement with concepts, Rough Mereology offers new approaches to Granular Computing, Classifier and Decision Synthesis, Logics for Information Systems, and are--formulation of well--known ideas of Neural Networks and Many Agent Systems. All these approaches are discussed in this monograph. To make the exposition self--contained, underlying notions of Set Theory, Topology, and Deductive and Reductive Reasoning with emphasis on Rough and Fuzzy Set Theories along with a thorough exposition of Mereology both in Lesniewski and Whitehead--Leonard--Goodman--Clarke versions are discussed at length. It is hoped that the monograph offers researchers in various areas of Artificial Intelligence a new tool to deal with analysis of relations among concepts.
Book Synopsis Essay on Machines in General (1786) by : Raffaele Pisano
Download or read book Essay on Machines in General (1786) written by Raffaele Pisano and published by Springer Nature. This book was released on 2021-02-01 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot – l'organisateur de la victoire – in Essai sur le machine en général (1786) assumed that the generalization of machines was a necessity for society and its economic development. Subsequently, his new coming science applied to machines attracted considerable interest for technician, as well, already in the 1780’s. With no lack in rigour, Carnot used geometric and trigonometric rather than algebraic arguments, and usually went on to explain in words what the formulae contained. His main physical– mathematical concepts were the Geometric motion and Moment of activity–concept of Work . In particular, he found the invariants of the transmission of motion (by stating the principle of the moment of the quantity of motion) and theorized the condition of the maximum efficiency of mechanical machines (i.e., principle of continuity in the transmission of power). While the core theme remains the theories and historical studies of the text, the book contains an extensive Introduction and an accurate critical English Translation – including the parallel text edition and substantive critical/explicative notes – of Essai sur les machines en général (1786). The authors offer much-needed insight into the relation between mechanics, mathematics and engineering from a conceptual, empirical and methodological, and universalis point of view. As a cutting–edge writing by leading authorities on the history of physics and mathematics, and epistemological aspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology).
Book Synopsis The Philosopher's Handbook by : Stanley Rosen
Download or read book The Philosopher's Handbook written by Stanley Rosen and published by Random House Reference. This book was released on 2009-02-19 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ideal introduction for the casual reader and a beneficial reference for the student, The Philosopher's Handbook features the writings of some of the world's most influential philosophers. Based on the premise that all human beings are curious about their existence, Rosen's collection brings together primary excerpts from the works of prominent thinkers such as Plato, Nietzsche, Descartes, Machiavelli, and Kant. Experts in each field have carefully selected the sources and provided brief introductions to help readers gain insight into the readings. Newly revised in order to emphasize its broad appeal, The Philosopher's Handbook is a solid introduction to Western philosophy for all inquiring minds.
Book Synopsis The Logic of Number by : Neil Tennant
Download or read book The Logic of Number written by Neil Tennant and published by Oxford University Press. This book was released on 2022-02-25 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic.
