Constructivism In Mathematics Vol 2
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Constructivism In Mathematics Vol 2
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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Constructivism In Mathematics Vol 2 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.
Constructivism In Mathematics Vol 1
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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 1988-07-01
Constructivism In Mathematics Vol 1 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07-01 with Computers categories.
These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
Constructivism In Mathematics
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Author :
language : en
Publisher:
Release Date : 1988
Constructivism In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Constructive mathematics categories.
New Computational Paradigms
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Author : S.B. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-28
New Computational Paradigms written by S.B. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-28 with Computers categories.
This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.
Constructivism
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Author : Catherine Twomey Fosnot
language : en
Publisher: Teachers College Press
Release Date : 2013-09-18
Constructivism written by Catherine Twomey Fosnot and has been published by Teachers College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-18 with Education categories.
This enduring bestseller remains the most comprehensive examination of constructivism and its relationship to teaching and learning. Closing the gap between theory and practice, well-known scholars make constructivism accessible by showing its application in everyday classrooms. Building on the success of the first edition, the authors have completely updated this popular text and expanded its scope to include examples of constructivist teaching across all grade levels and disciplines. An ambitious revision of a now classic text, Constructivism: Theory, Perspectives, and Practice, Second Edition is an invaluable resource for practicing teachers, teacher educators, and curriculum specialists in mathematics, science, social studies, and language arts. New for the Second Edition! An updated theory section that adds further contemporary biological evidence to go beyond the theories of Piaget and Vygotsky—offering a more contemporary framework for a psychological theory of learning.New chapters reflecting the school-based reforms that have been initiated since the writing of the first edition—specifically addressing the changes in mathematics, social studies, and teacher education.A new chapter on the emerging field of disability studies—including a critique that unmasks current practices and assumptions that better serve schools rather than students and their families. Contributors: Paul Cobb • Susan Cowey • Rheta DeVries • Eleanor Duckworth • Dewey I. Dykstra, Jr. • George Forman • Catherine Twomey Fosnot • Catherine A. Franklin • June S. Gould • Maxine Greene • Candace Julyan • Randall Stewart Perry • D. Kim Reid • Deborah Schifter • Jan Weatherly Valle • Ernst von Glasersfeld • Betty Zan. Praise for the First Edition! “Provides the reader with many ways of connecting to the central ideas of constructivism . . . highly readable.” —Gifted Child Quarterly “Shows how constructivist theory can inform classroom practices, and . . . provides teachers with a deeper understanding that gives substance to the rhetoric of school reform.” —Journal of Curriculum Studies
Homotopy Type Theory Univalent Foundations Of Mathematics
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Author :
language : en
Publisher: Univalent Foundations
Release Date :
Homotopy Type Theory Univalent Foundations Of Mathematics written by and has been published by Univalent Foundations this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Proceedings Of The International Conference For The Psychology Of Mathematics Education
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Author :
language : en
Publisher:
Release Date : 1998
Proceedings Of The International Conference For The Psychology Of Mathematics Education written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Twenty Years Of Theoretical And Practical Synergies
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Author : Ludovic Levy Patey
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Twenty Years Of Theoretical And Practical Synergies written by Ludovic Levy Patey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Computers categories.
This book constitutes the refereed proceedings of the 20th Conference on Computabilitty in Europe, CiE 2024, held in Amsterdam, The Netherlands, during July 8–12, 2024 The 26 full papers and 2 short papers included in this book were carefully reviewed and selected from 43 submissions. This CIE 2024 focus on development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences.
L E J Brouwer Topologist Intuitionist Philosopher
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Author : Dirk van Dalen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-04
L E J Brouwer Topologist Intuitionist Philosopher written by Dirk van Dalen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-04 with Mathematics categories.
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.
Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum
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Author : Peter Schuster
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Reuniting The Antipodes Constructive And Nonstandard Views Of The Continuum written by Peter Schuster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory.