Mathematical Reasoning With Diagrams
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| Author | : Mateja Jamnik |
| Publisher | : Stanford Univ Center for the Study |
| Total Pages | : 204 |
| Release | : 2001-01 |
| Genre | : Mathematics |
| ISBN | : 9781575863245 |
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.
| Author | : Theodore A. Sundstrom |
| Publisher | : Prentice Hall |
| Total Pages | : 0 |
| Release | : 2007 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : 9780131877184 |
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
| Author | : Lyn D. English |
| Publisher | : Routledge |
| Total Pages | : 407 |
| Release | : 2013-04-03 |
| Genre | : Education |
| ISBN | : 1136491147 |
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.
| Author | : Peter J. Eccles |
| Publisher | : Cambridge University Press |
| Total Pages | : 364 |
| Release | : 2013-06-26 |
| Genre | : Mathematics |
| ISBN | : 1139632566 |
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The 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.
| Author | : Gerard Allwein |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 287 |
| Release | : 1996 |
| Genre | : Knowledge representation (Information theory). |
| ISBN | : 0195104277 |
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 | : V. M. Bradis |
| Publisher | : Courier Dover Publications |
| Total Pages | : 225 |
| Release | : 2016-10-28 |
| Genre | : Mathematics |
| ISBN | : 0486816575 |
Unique, effective system for teaching mathematical reasoning leads students toward clearly false conclusions. Students then analyze problems to correct the errors. Covers arithmetic, algebra, geometry, trigonometry, and approximate computations. 1963 edition.
| Author | : Amirouche Moktefi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 210 |
| Release | : 2013-07-08 |
| Genre | : Mathematics |
| ISBN | : 3034806000 |
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.
| Author | : Marcus Giaquinto |
| Publisher | : Oxford University Press |
| Total Pages | : 298 |
| Release | : 2007-07-05 |
| Genre | : Mathematics |
| ISBN | : 0199285942 |
Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
| Author | : Tamara J. Lakins |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 233 |
| Release | : 2016-09-08 |
| Genre | : Mathematics |
| ISBN | : 1470428997 |
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.
| Author | : Doug Brumbaugh |
| Publisher | : |
| Total Pages | : 264 |
| Release | : 2008-03-11 |
| Genre | : |
| ISBN | : 9781601441829 |
