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Author: Fenner Stanley Tanswell
Publisher: Cambridge University Press
ISBN: 1009325132
Category : Philosophy
Languages : en
Pages : 158
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Book Description
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.
Author: Fenner Stanley Tanswell
Publisher: Cambridge University Press
ISBN: 1009325132
Category : Philosophy
Languages : en
Pages : 158
Get Book
Book Description
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.
Author: John P. Burgess
Publisher: Oxford University Press, USA
ISBN: 0198722222
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
Author: Gerard Allwein
Publisher: Oxford University Press, USA
ISBN: 0195104277
Category : Knowledge representation (Information theory).
Languages : en
Pages : 287
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Book Description
Information technology has lead to an increasing need to present information visually. This volume addresses the logical aspects of the visualization of information. Properties of diagrams, charts and maps are explored and their use in problem solving and
Author: Imre Lakatos
Publisher: Cambridge University Press
ISBN: 9780521290388
Category : Mathematics
Languages : en
Pages : 190
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Book Description
Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262542234
Category : Mathematics
Languages : en
Pages : 350
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Book Description
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author: Joel David Hamkins
Publisher: MIT Press
ISBN: 0262362562
Category : Mathematics
Languages : en
Pages : 132
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Book Description
How to write mathematical proofs, shown in fully-worked out examples. This is a companion volume Joel Hamkins's Proof and the Art of Mathematics, providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs. The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.
Author: Jody Azzouni
Publisher: Oxford University Press on Demand
ISBN: 019518713X
Category : Mathematics
Languages : en
Pages : 255
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Book Description
When ordinary people including mathematicians, take something to follow from something else, they are exposing the backbone of our ability to reason. Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians.
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 1461221307
Category : Mathematics
Languages : en
Pages : 434
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Book Description
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
Author: Bharath Sriraman
Publisher: Springer Nature
ISBN: 3031408462
Category :
Languages : en
Pages : 3221
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Book Description
Author: Erich Christian Wittmann
Publisher: Springer Nature
ISBN: 3030615707
Category : Education
Languages : en
Pages : 332
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Book Description
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.
