Mathematical Rigour And Informal Proof
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Mathematical Rigour And Informal Proof
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Author : Fenner Stanley Tanswell
language : en
Publisher: Cambridge University Press
Release Date : 2024-03-28
Mathematical Rigour And Informal Proof written by Fenner Stanley Tanswell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-28 with Philosophy categories.
This Element looks at the contemporary debate on the nature of mathematical rigour and informal proofs as found in mathematical practice. The central argument is for rigour pluralism: that multiple different models of informal proof are good at accounting for different features and functions of the concept of rigour. To illustrate this pluralism, the Element surveys some of the main options in the literature: the 'standard view' that rigour is just formal, logical rigour; the models of proofs as arguments and dialogues; the recipe model of proofs as guiding actions and activities; and the idea of mathematical rigour as an intellectual virtue. The strengths and weaknesses of each are assessed, thereby providing an accessible and empirically-informed introduction to the key issues and ideas found in the current discussion.
Rigor And Structure
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Author : John P. Burgess
language : en
Publisher: Oxford University Press, USA
Release Date : 2015
Rigor And Structure written by John P. Burgess and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
John P. Burgess presents an illuminating study of the nature of mathematical rigour and of mathematical structure, and above all of the relation between them. He considers recent developments in the field including experimental mathematics and computerised formal proofs, and surveys many historical developments in mathematics, philosophy, and logic.
Proofs And Refutations
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Author : Imre Lakatos
language : en
Publisher: Cambridge University Press
Release Date : 1976
Proofs And Refutations written by Imre Lakatos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date :
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
A Logical Introduction To Proof
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Author : Daniel W. Cunningham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-19
A Logical Introduction To Proof written by Daniel W. Cunningham 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 2012-09-19 with Mathematics categories.
The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.
Logical Reasoning With Diagrams
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Author : Gerard Allwein
language : en
Publisher: Oxford University Press
Release Date : 1996-06-13
Logical Reasoning With Diagrams written by Gerard Allwein and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-13 with Computers categories.
One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information.
Objectivity Realism And Proof
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Author : Francesca Boccuni
language : en
Publisher: Springer
Release Date : 2016-07-05
Objectivity Realism And Proof written by Francesca Boccuni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-05 with Science categories.
This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat
Mathematics Mathematics Education Searching For Common Ground
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Author : Michael N. Fried
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29
Mathematics Mathematics Education Searching For Common Ground written by Michael N. Fried 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 2013-11-29 with Education categories.
This book is the fruit of a symposium in honor of Ted Eisenberg concerning the growing divide between the mathematics community and the mathematics education community, a divide that is clearly unhealthy for both. The work confronts this disturbing gap by considering the nature of the relationship between mathematics education and mathematics, and by examining areas of commonality as well as disagreement. It seeks to provide insight into the mutual benefit both stand to gain by building bridges based on the natural bonds between them.
Understanding The Generality Of Mathematical Statements
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Author : Milena Damrau
language : en
Publisher: Springer Nature
Release Date :
Understanding The Generality Of Mathematical Statements written by Milena Damrau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Connecting Mathematics And Mathematics Education
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Author : Erich Christian Wittmann
language : en
Publisher: Springer Nature
Release Date : 2020-12-09
Connecting Mathematics And Mathematics Education written by Erich Christian Wittmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-09 with Education categories.
This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.