On The Shape Of Mathematical Arguments

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On The Shape Of Mathematical Arguments

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Author : A. J. M. Gasteren
language : en
Publisher: Springer Science & Business Media
Release Date : 1990-07-24

On The Shape Of Mathematical Arguments written by A. J. M. Gasteren 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 1990-07-24 with Computers categories.

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.

On The Shape Of Mathematical Arguments

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Author : Antonetta J.M. van Gasteren
language : en
Publisher: Springer
Release Date : 2014-03-12

On The Shape Of Mathematical Arguments written by Antonetta J.M. van Gasteren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Computers categories.

This book deals with the presentation and systematic design of mathematical proofs, including correctness proofs of algorithms. Its purpose is to show how completeness of argument, an important constraint especially for the correctness of algorithms, can be combined with brevity. The author stresses that the use of formalism is indispensible for achieving this. A second purpose of the book is to discuss matters of design. Rather than addressing psychological questions, the author deals with more technical questions like how analysis of the shape of the demonstrandum can guide the design of a proof. This technical rather than psychological view of heuristics together with the stress on exploiting formalism effectively are two key features of the book. The book consists of two independently readable parts. One part includes a number of general chapters discussing techniques for clear exposition, the use of formalism, the choice of notations, the choice of what to name and how to name it, and so on. The other part consists of a series of expositional essays, each dealing with a proof or an algorithm and illustrating the use of techniques discussed in the more general chapters.

On The Shape Of Mathematical Arguments

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Author : Antonetta J. M. Gasteren
language : en
Publisher:
Release Date : 1988

On The Shape Of Mathematical Arguments written by Antonetta J. M. Gasteren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematical analysis categories.

The Argument Of Mathematics

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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01

The Argument Of Mathematics written by Andrew Aberdein 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 2013-07-01 with Philosophy categories.

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Understanding How Undergraduate Students Formalise Their Written Argumentations In Mathematics

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Author : Garry Nathan
language : en
Publisher:
Release Date : 2014

Understanding How Undergraduate Students Formalise Their Written Argumentations In Mathematics written by Garry Nathan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Logic, Symbolic and mathematical categories.

All students who take an undergraduate university course in mathematics will confront the task of having to present a written argument to someone else. This could be one or more of their colleagues, or teaching staff who are also likely to be the markers of their course assignments, tutorials, tests and examinations. During lectures and tutorials, the lecturer and tutor may provide justifications for various aspects of mathematics presented - which might include elementary proofs, or give examples of how various theorems or known results contribute to solving a range of problems. Students will very likely be exposed to modes of argumentation that encourage certain habits of mind and speech, and at the same time, foster a disposition suited to engaging successfully with mathematics. These combine to shape the first experiences students have with argumentation in mathematics. Usually, by their second year, many students will have been introduced to formal mathematics through linear algebra, differential and integral calculus, or courses that are specifically designed to teach logic, proof and formal thinking in mathematics. Certainly, by their third year, reading and writing formal arguments of proof is an established part of the student's life-world. However, literature from mathematics education shows that proof is a difficult mathematical concept for students to master. Underlying this research, is an assertion that argumentation plays an important role in developing the thinking, reasoning and communicative skills required to produce formal mathematical arguments. One way to investigate this is to see how students adapt their written argumentations from ones that give a personal conviction to ones aimed at convincing an other. This research applied Tall's model of Three Worlds of Mathematics, Toulmin's layout of an argument, and Habermas' three dimensions of rationality to create a framework that was used to examine the argumentations of students, investigate how they formalised them, and describe some obstacles that may have prevented them from doing so. Students who were taking a first year mathematics course, and a smaller number taking a second year mathematics course participated in this research by completing tasks that were designed to promote the production of written argumentations. The argumentation of four students were tracked over three years in an attempt to capture, and explain, general changes that occurred over a longer term. These were analysed using the research framework developed in this study. The results of this study suggest that the first year mathematics students had the readiness to engage successfully with writing formal mathematical arguments. When they perceived it necessary to do so, they could select the necessary cognitive and mathematical tools that allowed them to reason algebraically and deductively. By the second year, students' mathematical reasoning were well established, and they could confidently use methods of argument and logic usually associated with proof. A significant inclusion in second year students' argumentations was the use of definitions. Over time, the students used increasingly sophisticated symbols, concepts and mathematical theory to produce more complex argumentations. Although the primary form of reasoning in formalising argumentations was deductive, other forms of reasoning that provided elaboration, understanding, and further support for personal conviction often supported it. It is anticipated that this research might provide further support to the assertion that written argumentation has an important role in learning mathematics, particularly in developing an understanding of proof.

Essays On Mathematical Reasoning

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Author : Jerzy Pogonowski
language : en
Publisher:
Release Date : 2020

Essays On Mathematical Reasoning written by Jerzy Pogonowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.

Prove It

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Author :
language : en
Publisher:
Release Date : 2012-02-21

Prove It written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-21 with categories.

Talking About Numbers

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Author : Katharina Felka
language : de
Publisher:
Release Date : 2015

Talking About Numbers written by Katharina Felka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.

Proof And Knowledge In Mathematics

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Author : Michael Detlefsen
language : en
Publisher: Routledge
Release Date : 2005-08-18

Proof And Knowledge In Mathematics written by Michael Detlefsen and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-18 with Education categories.

Distinguished contributors tackle the main problem that arizes when considering an epistemology for mathematics, the nature and sources of mathematical justification.

Mathematical Reasoning

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Author : Theodore A. Sundstrom
language : en
Publisher: Prentice Hall
Release Date : 2007

Mathematical Reasoning written by Theodore A. Sundstrom and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Logic, Symbolic and mathematical categories.

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom