An Introduction To Mathematical Reasoning

Author : Peter J. Eccles
Publisher : Cambridge University Press
ISBN 13 : 9780521597180
Total Pages : 366 pages
Book Rating : 4.88/5 ( download)

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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.

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
ISBN 13 : 9780131877184
Total Pages : 0 pages
Book Rating : 4.86/5 ( download)

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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

Author : Keith J. Devlin
Publisher :
ISBN 13 : 9780615653631
Total Pages : 0 pages
Book Rating : 4.34/5 ( download)

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Download or read book Introduction to Mathematical Thinking written by Keith J. Devlin and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

Author : Lyn D. English
Publisher : Routledge
ISBN 13 : 1136491074
Total Pages : 393 pages
Book Rating : 4.78/5 ( download)

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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.

Author : William J. Gilbert
Publisher : Pearson
ISBN 13 : 9780131848689
Total Pages : 0 pages
Book Rating : 4.82/5 ( download)

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Download or read book An Introduction to Mathematical Thinking written by William J. Gilbert and published by Pearson. This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.

Author : Tamara J. Lakins
Publisher : American Mathematical Soc.
ISBN 13 : 1470428997
Total Pages : 217 pages
Book Rating : 4.90/5 ( download)

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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.

Author : Larry Gerstein
Publisher : Springer Science & Business Media
ISBN 13 : 1468467085
Total Pages : 355 pages
Book Rating : 4.86/5 ( download)

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Download or read book Introduction · to Mathematical Structures and · Proofs written by Larry Gerstein and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.

Author : Camilla Gilmore
Publisher : Taylor & Francis
ISBN 13 : 1317410114
Total Pages : 265 pages
Book Rating : 4.19/5 ( download)

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Download or read book An Introduction to Mathematical Cognition written by Camilla Gilmore and published by Taylor & Francis. This book was released on 2018-06-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Author : P. Mancosu
Publisher : Springer Science & Business Media
ISBN 13 : 1402033354
Total Pages : 315 pages
Book Rating : 4.53/5 ( download)

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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.

Author : Susanna S. Epp
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.73/5 ( download)

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Download or read book Discrete Mathematics written by Susanna S. Epp and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: