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Mathematical Reasoning With Diagrams
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Book Synopsis Mathematical Reasoning with Diagrams by : Mateja Jamnik
Download or read book Mathematical Reasoning with Diagrams written by Mateja Jamnik and published by Stanford Univ Center for the Study. This book was released on 2001-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Visual Reasoning with Diagrams by : Amirouche Moktefi
Download or read book Visual Reasoning with Diagrams written by Amirouche Moktefi and published by Springer Science & Business Media. This book was released on 2013-07-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logical Reasoning with Diagrams by : Gerard Allwein
Download or read book Logical Reasoning with Diagrams written by Gerard Allwein and published by Oxford University Press, USA. This book was released on 1996 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematical Reasoning by : Theodore A. Sundstrom
Download or read book Mathematical Reasoning written by Theodore A. Sundstrom and published by Prentice Hall. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematical Reasoning by : Lyn D. English
Download or read book Mathematical Reasoning written by Lyn D. English and published by Routledge. This book was released on 2013-04-03 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.
Book Synopsis An Introduction to Mathematical Reasoning by : Peter J. Eccles
Download or read book An Introduction to Mathematical Reasoning written by Peter J. Eccles and published by Cambridge University Press. This book was released on 1997-12-11 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Visualization, Explanation and Reasoning Styles in Mathematics by : P. Mancosu
Download or read book Visualization, Explanation and Reasoning Styles in Mathematics written by P. Mancosu and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Reasoning: The History and Impact of the DReaM Group by : Gregory Michaelson
Download or read book Mathematical Reasoning: The History and Impact of the DReaM Group written by Gregory Michaelson and published by Springer Nature. This book was released on 2021-11-20 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diagrammatic Representation and Reasoning by : Michael Anderson
Download or read book Diagrammatic Representation and Reasoning written by Michael Anderson and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Reasoning for Elementary Teachers by : Long DeTemple
Download or read book Mathematical Reasoning for Elementary Teachers written by Long DeTemple and published by Addison Wesley Publishing Company. This book was released on 1996 with total page 1154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm readers with all the tools that they will need to become excellent elementary or middle school teachers. Thinking Critically. Sets and Whole Numbers. Numeration and Computation. Number Theory. Integers. Fractions and Rational Numbers. Decimals and Real Numbers. Algebraic Reasoning and Representation. Statistics: The Interpretation of Data. Probability. Geometric Figures. Measurement. Transformations, Symmetries, and Tilings. Congruence, Constructions, and Similarities. For all readers interested in mathematical reasoning for elementary teachers.
Book Synopsis The Tools of Mathematical Reasoning by : Tamara J. Lakins
Download or read book The Tools of Mathematical Reasoning written by Tamara J. Lakins and published by American Mathematical Soc.. This book was released on 2016-09-08 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics by : Vitaly Kiryushchenko
Download or read book Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics written by Vitaly Kiryushchenko and published by Springer Nature. This book was released on 2023-05-12 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lapses in Mathematical Reasoning by : V. M. Bradis
Download or read book Lapses in Mathematical Reasoning written by V. M. Bradis and published by Courier Dover Publications. This book was released on 2016-10-28 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as a method for teaching correct mathematical thinking to high school students, this book contains a brilliantly constructed series of what the authors call "lapses," erroneous statements that are part of a larger mathematical argument. These lapses lead to sophism or mathematical absurdities. The ingenious idea behind this technique is to lead the student deliberately toward a clearly false conclusion. The teacher and student then go back and analyze the lapse as a way to correct the problem. The authors begin by focusing on exercises in refuting erroneous mathematical arguments and their classification. The remaining chapters discuss examples of false arguments in arithmetic, algebra, geometry, trigonometry, and approximate computations. Ideally, students will come to the correct insights and conclusions on their own; however, each argument is followed by a detailed analysis of the false reasoning. Stimulating and unique, this book is an intriguing and enjoyable way to teach students critical mathematical reasoning skills.
Book Synopsis Mathematical Reasoning Level B (B/W) by : Doug Brumbaugh
Download or read book Mathematical Reasoning Level B (B/W) written by Doug Brumbaugh and published by . This book was released on 2008-03-11 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Reasoning Through Verbal Analysis by : Warren Hill
Download or read book Mathematical Reasoning Through Verbal Analysis written by Warren Hill and published by . This book was released on 1988 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essays on Mathematical Reasoning by : Jerzy Pogonowski
Download or read book Essays on Mathematical Reasoning written by Jerzy Pogonowski and published by LIT Verlag Münster. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains four essays which may attract the attention of those readers, who are interested in mathematical cognition The main issues and questions addressed include: How do we achieve understanding of mathematical notions and ideas? What benefits can be obtained from mistakes of great mathematicians? Which mathematical objects are standard and which are pathological? Is it possible characterize the intended models of mathematical theories in a unique way?
Book Synopsis Understanding Physics Using Mathematical Reasoning by : Andrzej Sokolowski
Download or read book Understanding Physics Using Mathematical Reasoning written by Andrzej Sokolowski and published by Springer Nature. This book was released on 2021-08-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book speaks about physics discoveries that intertwine mathematical reasoning, modeling, and scientific inquiry. It offers ways of bringing together the structural domain of mathematics and the content of physics in one coherent inquiry. Teaching and learning physics is challenging because students lack the skills to merge these learning paradigms. The purpose of this book is not only to improve access to the understanding of natural phenomena but also to inspire new ways of delivering and understanding the complex concepts of physics. To sustain physics education in college classrooms, authentic training that would help develop high school students’ skills of transcending function modeling techniques to reason scientifically is needed and this book aspires to offer such training The book draws on current research in developing students’ mathematical reasoning. It identifies areas for advancements and proposes a conceptual framework that is tested in several case studies designed using that framework. Modeling Newton’s laws using limited case analysis, Modeling projectile motion using parametric equations and Enabling covariational reasoning in Einstein formula for the photoelectric effect represent some of these case studies. A wealth of conclusions that accompany these case studies, drawn from the realities of classroom teaching, is to help physics teachers and researchers adopt these ideas in practice.
