L.E.J. Brouwer – Topologist, Intuitionist, Philosopher / Dalen, Dirk van (2013)  

Público ISBD Título : L.E.J. Brouwer – Topologist, Intuitionist, Philosopher : How Mathematics Is Rooted in Life Tipo de documento: documento electrónico Autores: Dalen, Dirk van ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XII, 875 p. 97 illus., 19 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4471-4616-2 Idioma : Inglés (eng) Palabras clave: Mathematics  History  Mathematical  logic  Topology  Popular  works  of  Sciences  Logic  and  Foundations  Science,  general Clasificación: 51 Matemáticas Resumen: Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics.   Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century Nota de contenido: Child and Student -- Mathematics and Mysticism -- The Dissertation.-Cantor-Schoenflies Topology -- The New Topology -- Making a Career -- The War Years -- Mathematics after the War -- Politics and Mathematics -- The Breakthrough -- The Fathers of Dimension -- Progress, Recognition, and Frictions -- From Berlin to Vienna -- The Three Battles -- The Thirties -- War and Occupation -- Post-War Events -- The Restless Emeritus En línea: http://dx.doi.org/10.1007/978-1-4471-4616-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32191 L.E.J. Brouwer – Topologist, Intuitionist, Philosopher : How Mathematics Is Rooted in Life [documento electrónico] / Dalen, Dirk van ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - XII, 875 p. 97 illus., 19 illus. in color : online resource. ISBN : 978-1-4471-4616-2 Idioma : Inglés (eng) Palabras clave: Mathematics  History  Mathematical  logic  Topology  Popular  works  of  Sciences  Logic  and  Foundations  Science,  general Clasificación: 51 Matemáticas Resumen: Dirk van Dalen’s biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics.   Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer’s main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name ‘intuitionism’. This made him one of the main protagonists in the ‘foundation crisis’ of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century Nota de contenido: Child and Student -- Mathematics and Mysticism -- The Dissertation.-Cantor-Schoenflies Topology -- The New Topology -- Making a Career -- The War Years -- Mathematics after the War -- Politics and Mathematics -- The Breakthrough -- The Fathers of Dimension -- Progress, Recognition, and Frictions -- From Berlin to Vienna -- The Three Battles -- The Thirties -- War and Occupation -- Post-War Events -- The Restless Emeritus En línea: http://dx.doi.org/10.1007/978-1-4471-4616-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32191

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Logic and Structure / Dalen, Dirk van (2013)  

Público ISBD Título : Logic and Structure Tipo de documento: documento electrónico Autores: Dalen, Dirk van ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 263 p. 27 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-4558-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  logic  Logic  and  Foundations Clasificación: 51 Matemáticas Resumen: Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products Nota de contenido: Introduction -- Propositional Logic -- Predicate Logic -- Completeness and Applications -- Second Order Logic -- Intuitionistic Logic -- Normalization -- Gödel's theorem En línea: http://dx.doi.org/10.1007/978-1-4471-4558-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32190 Logic and Structure [documento electrónico] / Dalen, Dirk van ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - X, 263 p. 27 illus : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4471-4558-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  logic  Logic  and  Foundations Clasificación: 51 Matemáticas Resumen: Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products Nota de contenido: Introduction -- Propositional Logic -- Predicate Logic -- Completeness and Applications -- Second Order Logic -- Intuitionistic Logic -- Normalization -- Gödel's theorem En línea: http://dx.doi.org/10.1007/978-1-4471-4558-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32190

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The Selected Correspondence of L.E.J. Brouwer / Dalen, Dirk van (2011)  

Público ISBD Título : The Selected Correspondence of L.E.J. Brouwer Tipo de documento: documento electrónico Autores: Dalen, Dirk van ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2011 Colección: Sources and Studies in the History of Mathematics and Physical Sciences, ISSN 2196-8810 Número de páginas: VIII, 532 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-537-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Philosophy  Logic  History  Mathematical  logic  Topology  of  Sciences  and  Foundations  Philosophy,  general Clasificación: 51 Matemáticas Resumen: L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science Nota de contenido: Introduction -- 1900 - 1910.- 1911 - 1920.- 1921 - 1930.- 1931 - 1940.- 1941 - 1950.- 1951 - 1965.- Appendices.-  List of Enclosures, Editorial Comments and Editorial -- Supplements.-Biographical information.- List of letters.- Abbreviations -- Organizations and journals En línea: http://dx.doi.org/10.1007/978-0-85729-537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33129 The Selected Correspondence of L.E.J. Brouwer [documento electrónico] / Dalen, Dirk van ; SpringerLink (Online service) . - London : Springer London, 2011 . - VIII, 532 p : online resource. - (Sources and Studies in the History of Mathematics and Physical Sciences, ISSN 2196-8810) . ISBN : 978-0-85729-537-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Philosophy  Logic  History  Mathematical  logic  Topology  of  Sciences  and  Foundations  Philosophy,  general Clasificación: 51 Matemáticas Resumen: L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer’s biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincaré, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science Nota de contenido: Introduction -- 1900 - 1910.- 1911 - 1920.- 1921 - 1930.- 1931 - 1940.- 1941 - 1950.- 1951 - 1965.- Appendices.-  List of Enclosures, Editorial Comments and Editorial -- Supplements.-Biographical information.- List of letters.- Abbreviations -- Organizations and journals En línea: http://dx.doi.org/10.1007/978-0-85729-537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33129

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