• Science & Mathematics
      December 2018

      Philosophy of Mathematics

      by Thomas Bedürftig, Roman Murawski

      This work is an introduction to the philosophical problems and underpinnings of mathematical thinking, teaching, and learning. It includes thematic and philosophical problems and questions, a historical summary that covers contemporary currents, and chapters on set theory, logic, axiomatics, fundamental results, and unsolved and insoluble problems.

    • Science & Mathematics
      October 1979

      Mengenlehre

      by Dieter Klaua

    • Science & Mathematics
      February 2018

      Fundamentals of Functions and Measure Theory

      by Valeriy K. Zakharov, Timofey V. Rodionov, Alexander V. Mikhalev

      This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

    • Science & Mathematics
      February 2018

      Fundamentals of Set and Number Theory

      by Valeriy K. Zakharov, Timofey V. Rodionov

      This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

    • Technology, Engineering & Agriculture
      July 1996

      Fuzzy Control

      Optimale Nachbildung und Entwurf optimaler Entscheidungen

      by Koch

    • Science & Mathematics
      August 2018

      [Set Fundamentals of Set and Number Theory, Vol 1+2]

      by Valeriy K. Zakharov, Timofey V. Rodionov

      This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

    • Science & Mathematics
      November 1971

      Mengenlehre

      by E. Kamke

    • Philosophy of mathematics
      January 2012

      From Foundations to Philosophy of Mathematics

      An Historical Account of their Development in the XX Century and Beyond

      by Author(s): Joan Roselló

      From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Gödel.Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell’s type theory, Zermelo’s set theory and Gödel’s incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.

    • Philosophy of science
      July 2014

      From a Heuristic Point of View

      Essays in Honour of Carlo Cellucci

      by Editor(s): Emiliano Ippoliti, Cesare Cozzo

      How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception.This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge.This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.

    • Buddhist life & practice
      March 2009

      The Future of Post-Human Geometry

      A Preface to a New Theory of Infinity, Symmetry, and Dimensionality

      by Author(s): Peter Baofu

      Why should some essential properties of geometry (i.e., infinity, symmetry, and dimensionality) be both necessary and desirable in the way that they have been constructed—albeit with different modifications over time—since time immemorial?Contrary to the conventional wisdom in all history hitherto existing, the essential properties of geometry do not have to be both necessary and desirable. This is not to suggest, of course, that one has nothing to learn from geometry. On the contrary, geometry has contributed to the advancement of knowledge in many ways since its inception as a field of knowledge some millennia ago.The point in this book, however, is to show an alternative (better) way to understand the nature of geometry, which goes beyond human conception, intuition, and imagination, together with worldly experience of course, as its foundation, while learning from them all—with theoretical implications for time travel, hyperspace, and other important issues.If true, this seminal view will fundamentally change the way that the nature of abstraction in the thinking process is to be understood, with its enormous implications for the future advancement of knowledge, in a small sense, and what I originally called its “post-human” fate, in a large one.

    • Psycholinguistics
      September 2014

      Constraints and Language

      by Editor(s): Philippe Blache, Henning Christiansen, Verónica Dahl, Denys Duchier, Jørgen Villadsen

      The concept of “constraint” is widely used in linguistics, computer science, and psychology. However, its implementation varies widely depending on the research domain: namely, language description, knowledge representation, cognitive modelling, and problem solving. These various uses of constraints offer complementary views on intelligent mechanisms. For example, in-depth descriptions implementing constraints are used in linguistics to filter out syntactic or discursive structures by means of dedicated description languages and constraint ranking. In computer science, the constraint programming paradigm views constraints as a whole, which can be used, for example, to build specific structures. Finally, in psycholinguistics, experiments are carried out to investigate the role of constraints within cognitive processes (both in comprehension and production), with various applications such as dialog modelling for people with disabilities. In this context, Constraints and Language builds an extended overview of the use of constraints to model and process language. This book will be useful for researchers willing to get a grip on the various uses of constraints in natural language processing, and also as a class book for academic staff who want to set up advanced courses around the concept of constraint-based natural language processing.

    • Philosophy of mathematics
      January 2012

      From Foundations to Philosophy of Mathematics

      An Historical Account of their Development in the XX Century and Beyond

      by Author(s): Joan Roselló

      From Foundations to Philosophy of Mathematics provides an historical introduction to the most exciting period in the foundations of mathematics, starting with the discovery of the paradoxes of logic and set theory at the beginning of the twentieth century and continuing with the great foundational debate that took place in the 1920s. As a result of the efforts of several mathematicians and philosophers during this period to ground mathematics and to clarify its nature from a certain philosophical standpoint, the four main schools in the philosophy of mathematics that have largely dominated the twentieth century arose, namely, logicism, intuitionism, formalism and predicativism. It was due precisely to the insufficiencies of the first three foundational programs and the objections raised against them, that interest in Platonism was renewed in the 1940s, mainly by Gödel.Not only does this book pay special attention to the foundational programs of these philosophies of mathematics, but also to some technical accomplishments that were developed in close connection with them and have largely shaped our understanding of the nature of mathematics, such as Russell’s type theory, Zermelo’s set theory and Gödel’s incompleteness theorems. Finally, it also examines some current research programs that have been pursued in the last decades and have tried, at least to some extent, to show the feasibility of the foundational programs developed in the schools mentioned above. This is the case of neologicism, constructivism, and predicativist and finitist reductionism, this last one developed closely with the research program of reverse mathematics.

    • Buddhist life & practice
      March 2009

      The Future of Post-Human Geometry

      A Preface to a New Theory of Infinity, Symmetry, and Dimensionality

      by Author(s): Peter Baofu

      Why should some essential properties of geometry (i.e., infinity, symmetry, and dimensionality) be both necessary and desirable in the way that they have been constructed—albeit with different modifications over time—since time immemorial?Contrary to the conventional wisdom in all history hitherto existing, the essential properties of geometry do not have to be both necessary and desirable. This is not to suggest, of course, that one has nothing to learn from geometry. On the contrary, geometry has contributed to the advancement of knowledge in many ways since its inception as a field of knowledge some millennia ago.The point in this book, however, is to show an alternative (better) way to understand the nature of geometry, which goes beyond human conception, intuition, and imagination, together with worldly experience of course, as its foundation, while learning from them all—with theoretical implications for time travel, hyperspace, and other important issues.If true, this seminal view will fundamentally change the way that the nature of abstraction in the thinking process is to be understood, with its enormous implications for the future advancement of knowledge, in a small sense, and what I originally called its “post-human” fate, in a large one.

    • Philosophy of science
      July 2014

      From a Heuristic Point of View

      Essays in Honour of Carlo Cellucci

      by Editor(s): Emiliano Ippoliti, Cesare Cozzo

      How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception.This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge.This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.

    • Psycholinguistics
      September 2014

      Constraints and Language

      by Editor(s): Philippe Blache, Henning Christiansen, Verónica Dahl, Denys Duchier, Jørgen Villadsen

      The concept of “constraint” is widely used in linguistics, computer science, and psychology. However, its implementation varies widely depending on the research domain: namely, language description, knowledge representation, cognitive modelling, and problem solving. These various uses of constraints offer complementary views on intelligent mechanisms. For example, in-depth descriptions implementing constraints are used in linguistics to filter out syntactic or discursive structures by means of dedicated description languages and constraint ranking. In computer science, the constraint programming paradigm views constraints as a whole, which can be used, for example, to build specific structures. Finally, in psycholinguistics, experiments are carried out to investigate the role of constraints within cognitive processes (both in comprehension and production), with various applications such as dialog modelling for people with disabilities. In this context, Constraints and Language builds an extended overview of the use of constraints to model and process language. This book will be useful for researchers willing to get a grip on the various uses of constraints in natural language processing, and also as a class book for academic staff who want to set up advanced courses around the concept of constraint-based natural language processing.

    • Mathematical foundations
      September 2013

      Mathematics Olympiod For Imo Aspirants

      Highly Recommended For Cracking Olympiads

      by Jaya Ghosh

      This book has been designed to fulfil the preparation needs of candidates who aspire to crack International Mathematics Olympiad, National Talent Search Exam, and other competitive exams. The book is strictly based on the latest curriculum from International Mathematics Olympiad. It has been prepared in accordance with the latest syllabus issued from CBSE, ICSE and other school boards across the country. The book consists of three sections namely Logical Reasoning, Mathematical Reasoning and Everyday Mathematics. The Concepts, Formulae and important Tips are given in the beginning of each chapter. Fully solved Multiple Choice Questions (MCQs) with detailed explanations enhance the problem solving skills of students. Model Papers are included in the book for thorough practice, and Previous Years’ IMO papers given in the CDs help candidates to understand the level of difficulty and grasp the structure of questions asked in the exam. Salient Features:  Concepts are introduced gradually  Simple, lucid and systematic presentation  Detailed solutions at the end of each chapter  Previous years’ Question Papers and Model Test Papers Highly Recommended The book is highly recommended for the candidates who aspire to get distinction in Mathematics and Science Olympiads at national and international level. It will prove very useful for various other competitive examinations such as:  NTSE, NSTSE, SLSTSE  SSC, DSC, B. Ed, TET, CTET etc.

    • Teaching, Language & Reference
      August 2010

      Conflict, Complexity and Mathematical Social Science

      by Gordon Burt, Manas Chatterji

      "Conflict, Complexity and Mathematical Social Science" provides a foundational mathematical approach to the modelling of social conflict. The book illustrates how theory and evidence can be mathematically deepened and how investigations grounded in social choice theory can provide the evidence needed to inform social practice. Countering criticism from constructivist viewpoints it shows how discourse is grounded in mathematical logic and mathematical structure. The modelling of social conflict is viewed as an application of mathematical social science and relevant models are drawn from each field of mathematical psychology, mathematical sociology, mathematical political science and mathematical economics. Unique in its multidisciplinary focus the book brings together powerful mathematical conceptualisations of the social world from a wide range of separate areas of inquiry, thereby providing a strong conceptual framework and an integrated account of social situations. It is a vital resource for all researchers in peace science, peace and conflict studies, politics, international relations, mathematical modelling in the social sciences and complexity theory.

    • Humanities & Social Sciences
      April 2019

      Philosophie der Mathematik

      by Thomas Bedürftig, Roman Murawski

      Dieses Werk ist eine Einführung in philosophische Probleme und Hintergründe des mathematischen Denkens, Lehrens und Lernens. Es beinhaltet mathematische und philosophische Probleme und Fragen, einen umfangreichen Abriss der Geschichte bis hin zu aktuellen Strömungen, sowie Kapitel über Mengenlehre, Logik, Axiomatik, fundamentale Ergebnisse, ungelöste und unlösbare Probleme.

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