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Author: Douglas K. Brumbaugh
Publisher:
ISBN: 9780894558863
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Author: Douglas K. Brumbaugh
Publisher:
ISBN: 9780894558863
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Author: Doug Brumbaugh
Publisher:
ISBN: 9781601441829
Category :
Languages : en
Pages : 264
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Book Description
Author: Peter J. Eccles
Publisher: Cambridge University Press
ISBN: 9780521597180
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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.
Author: Theodore A. Sundstrom
Publisher: Prentice Hall
ISBN: 9780131877184
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 0
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Book Description
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: Linda Brumbaugh
Publisher:
ISBN: 9781601441973
Category : Mathematics
Languages : en
Pages : 48
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Book Description
Author: Gregory Michaelson
Publisher: Springer Nature
ISBN: 3030778797
Category : Computers
Languages : en
Pages : 173
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Book Description
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.
Author: Lyn D. English
Publisher: Routledge
ISBN: 1136491074
Category : Education
Languages : en
Pages : 393
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Book Description
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: Tamara J. Lakins
Publisher: American Mathematical Soc.
ISBN: 1470428997
Category : General -- Instructional exposition (textbooks, tutorial papers, etc.)
Languages : en
Pages : 217
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Book Description
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: Linda Brumbaugh
Publisher:
ISBN: 9780894558825
Category : Education
Languages : en
Pages : 235
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Book Description
Author: Carlo Cellucci
Publisher: College Publications
ISBN:
Category : Mathematics
Languages : en
Pages : 252
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Book Description
This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as the subject develops? What heuristics are involved in mathematical discovery, and do such heuristics constitute a logic of mathematical discovery? What new problems have been introduced by the development of mathematics since the 1930s? Other questions are concerned with the applications of mathematics both to physics and to the new field of computer science. Then there is the new question of whether the axiomatic method is really so essential to mathematics as is often supposed, and the question, which goes back to Wittgenstein, of the sense in which mathematical proofs are compelling. Taking these questions together they give part of an emerging agenda which is likely to carry philosophy of mathematics forward into the twenty first century.
