Mathematical Reasoning With Diagrams

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Mathematical Reasoning with Diagrams

Mateja Jamnik
Mathematical Reasoning with Diagrams Book PDF

Author : Mateja Jamnik
Publisher : Stanford Univ Center for the Study
Page : 204 pages
File Size : 55,5 Mb
Release : 2001-01
Category : Mathematics
ISBN : 1575863235

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Mathematical Reasoning with Diagrams by Mateja Jamnik Pdf

Mathematicians at every level use diagrams to prove theorems. Mathematical Reasoning with Diagrams investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system—called Diamond—which allows users to prove arithmetical theorems using diagrams.

Visual Reasoning with Diagrams

Amirouche Moktefi,Sun-Joo Shin
Visual Reasoning with Diagrams Book PDF

Author : Amirouche Moktefi,Sun-Joo Shin
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 46,5 Mb
Release : 2013-07-08
Category : Mathematics
ISBN : 9783034806008

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Visual Reasoning with Diagrams by Amirouche Moktefi,Sun-Joo Shin Pdf

Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning.

Logical Reasoning with Diagrams

Gerard Allwein,Jon Barwise
Logical Reasoning with Diagrams Book PDF

Author : Gerard Allwein,Jon Barwise
Publisher : Oxford University Press, USA
Page : 287 pages
File Size : 44,8 Mb
Release : 1996
Category : Knowledge representation (Information theory).
ISBN : 9780195104271

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Logical Reasoning with Diagrams by Gerard Allwein,Jon Barwise Pdf

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

Mathematical Reasoning

Theodore A. Sundstrom
Mathematical Reasoning Book PDF

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 55,5 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186

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Mathematical Reasoning by Theodore A. Sundstrom Pdf

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

Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics

Vitaly Kiryushchenko
Diagrams Visual Imagination and Continuity in Peirce s Philosophy of Mathematics Book PDF

Author : Vitaly Kiryushchenko
Publisher : Springer Nature
Page : 173 pages
File Size : 42,6 Mb
Release : 2023-05-12
Category : Mathematics
ISBN : 9783031232459

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Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics by Vitaly Kiryushchenko Pdf

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.

Diagrammatic Representation and Reasoning

Michael Anderson,Bernd Meyer,Patrick Olivier
Diagrammatic Representation and Reasoning Book PDF

Author : Michael Anderson,Bernd Meyer,Patrick Olivier
Publisher : Springer Science & Business Media
Page : 575 pages
File Size : 44,9 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9781447101093

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Diagrammatic Representation and Reasoning by Michael Anderson,Bernd Meyer,Patrick Olivier Pdf

The rise in computing and multimedia technology has spawned an increasing interest in the role of diagrams and sketches, not only for the purpose of conveying information but also for creative thinking and problem-solving. This book attempts to characterise the nature of "a science of diagrams" in a wide-ranging, multidisciplinary study that contains accounts of the most recent research results in computer science and psychology. Key topics include: cognitive aspects, formal aspects, and applications. It is a well-written and indispensable survey for researchers and students in the fields of cognitive science, artificial intelligence, human-computer interaction, and graphics and visualisation.

An Introduction to Mathematical Reasoning

Peter J. Eccles
An Introduction to Mathematical Reasoning Book PDF

Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 51,6 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188

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An Introduction to Mathematical Reasoning by Peter J. Eccles Pdf

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Mathematical Reasoning for Elementary Teachers

Calvin T. Long,Duane W. DeTemple
Mathematical Reasoning for Elementary Teachers Book PDF

Author : Calvin T. Long,Duane W. DeTemple
Publisher : Addison Wesley Publishing Company
Page : 1064 pages
File Size : 40,6 Mb
Release : 2000
Category : Education
ISBN : 0321043332

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Mathematical Reasoning for Elementary Teachers by Calvin T. Long,Duane W. DeTemple Pdf

Traditional skill and drill approach with activities for each chapter opener.

Mathematical Reasoning: The History and Impact of the DReaM Group

Gregory Michaelson
Mathematical Reasoning The History and Impact of the DReaM Group Book PDF

Author : Gregory Michaelson
Publisher : Springer Nature
Page : 173 pages
File Size : 48,6 Mb
Release : 2021-11-20
Category : Computers
ISBN : 9783030778798

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Mathematical Reasoning: The History and Impact of the DReaM Group by Gregory Michaelson Pdf

This collection of essays examines the key achievements and likely developments in the area of automated reasoning. In keeping with the group ethos, Automated Reasoning is interpreted liberally, spanning underpinning theory, tools for reasoning, argumentation, explanation, computational creativity, and pedagogy. Wider applications including secure and trustworthy software, and health care and emergency management. The book starts with a technically oriented history of the Edinburgh Automated Reasoning Group, written by Alan Bundy, which is followed by chapters from leading researchers associated with the group. Mathematical Reasoning: The History and Impact of the DReaM Group will attract considerable interest from researchers and practitioners of Automated Reasoning, including postgraduates. It should also be of interest to those researching the history of AI.

Visualization, Explanation and Reasoning Styles in Mathematics

P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen
Visualization Explanation and Reasoning Styles in Mathematics Book PDF

Author : P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 54,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781402033353

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Visualization, Explanation and Reasoning Styles in Mathematics by P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen Pdf

In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.

Icons of Mathematics: An Exploration of Twenty Key Images

Claudi Alsina ,Roger B. Nelsen
Icons of Mathematics An Exploration of Twenty Key Images Book PDF

Author : Claudi Alsina ,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 327 pages
File Size : 45,6 Mb
Release : 2020-06-01
Category : Education
ISBN : 9781470456160

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Icons of Mathematics: An Exploration of Twenty Key Images by Claudi Alsina ,Roger B. Nelsen Pdf

The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.

The Computer Modelling of Mathematical Reasoning

Alan Bundy
The Computer Modelling of Mathematical Reasoning Book PDF

Author : Alan Bundy
Publisher : Unknown
Page : 344 pages
File Size : 50,5 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015006389434

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The Computer Modelling of Mathematical Reasoning by Alan Bundy Pdf

This review of the work done to date on the computer modelling of mathematical reasoning processes brings together a variety of approaches and disciplines within a coherent frame. A limited knowledge of mathematics is assumed in the introduction to the principles of mathematical logic. The plan of the book is such that students with varied backgrounds can find necessary information as quickly as possible. Exercises are included throughout the book.

Mechanizing Mathematical Reasoning

Dieter Hutter,Werner Stephan
Mechanizing Mathematical Reasoning Book PDF

Author : Dieter Hutter,Werner Stephan
Publisher : Springer
Page : 570 pages
File Size : 44,5 Mb
Release : 2011-03-29
Category : Computers
ISBN : 9783540322542

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Mechanizing Mathematical Reasoning by Dieter Hutter,Werner Stephan Pdf

By presenting state-of-the-art results in logical reasoning and formal methods in the context of artificial intelligence and AI applications, this book commemorates the 60th birthday of Jörg H. Siekmann. The 30 revised reviewed papers are written by former and current students and colleagues of Jörg Siekmann; also included is an appraisal of the scientific career of Jörg Siekmann entitled "A Portrait of a Scientist: Logics, AI, and Politics." The papers are organized in four parts on logic and deduction, applications of logic, formal methods and security, and agents and planning.

The Logical Status of Diagrams

Sun-Joo Shin
The Logical Status of Diagrams Book PDF

Author : Sun-Joo Shin
Publisher : Cambridge University Press
Page : 211 pages
File Size : 43,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780521461573

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The Logical Status of Diagrams by Sun-Joo Shin Pdf

The validity of the transformation rules ensures that the correct application of the rules will not lead to fallacies. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems.

The Tools of Mathematical Reasoning

Tamara J. Lakins
The Tools of Mathematical Reasoning Book PDF

Author : Tamara J. Lakins
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 55,7 Mb
Release : 2016-09-08
Category : General -- Instructional exposition (textbooks, tutorial papers, etc.)
ISBN : 9781470428990

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The Tools of Mathematical Reasoning by Tamara J. Lakins Pdf

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.