Lapses In Mathematical Reasoning

Author : V. M. Bradis,L. Minkovskii,A. K. Kharcheva
Publisher : Courier Dover Publications
Page : 224 pages
File Size : 53,5 Mb
Release : 2016-10-28
Category : Mathematics
ISBN : 9780486816579

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Lapses in Mathematical Reasoning by V. M. Bradis,L. Minkovskii,A. K. Kharcheva Pdf

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.

Author : V M (Vladimir Modestovich) Bradis
Publisher : Hassell Street Press
Page : 220 pages
File Size : 55,9 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1013631420

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Lapses in Mathematical Reasoning; 5 by V M (Vladimir Modestovich) Bradis Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Sherman Stein
Publisher : Courier Dover Publications
Page : 192 pages
File Size : 55,7 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9780486814117

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Adventures in Mathematical Reasoning by Sherman Stein Pdf

Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.

Author : Raymond Nickerson
Publisher : Taylor & Francis
Page : 597 pages
File Size : 47,6 Mb
Release : 2011-02-25
Category : Psychology
ISBN : 9781136945397

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Mathematical Reasoning by Raymond Nickerson Pdf

The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.

Author : Jerzy Pogonowski
Publisher : LIT Verlag Münster
Page : 128 pages
File Size : 49,9 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783643913104

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Essays on Mathematical Reasoning by Jerzy Pogonowski Pdf

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?

Author : Sherman Stein
Publisher : Courier Dover Publications
Page : 193 pages
File Size : 48,7 Mb
Release : 2016-09-21
Category : Mathematics
ISBN : 9780486806440

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Adventures in Mathematical Reasoning by Sherman Stein Pdf

Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.

Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 364 pages
File Size : 49,6 Mb
Release : 2013-06-26
Category : Mathematics
ISBN : 9781139632560

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An Introduction to Mathematical Reasoning by Peter J. Eccles Pdf

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 : Warren Hill,Ronald R. Edwards
Publisher : Unknown
Page : 128 pages
File Size : 55,8 Mb
Release : 1988
Category : Mathematics
ISBN : OCLC:28103489

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Mathematical Reasoning Through Verbal Analysis by Warren Hill,Ronald R. Edwards Pdf

Author : Douglas E. Ensley,J. Winston Crawley
Publisher : John Wiley & Sons
Page : 704 pages
File Size : 52,8 Mb
Release : 2005-10-07
Category : Mathematics
ISBN : 9780471476023

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Discrete Mathematics by Douglas E. Ensley,J. Winston Crawley Pdf

Did you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way. Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at www.wiley.com/college/ensley. Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.

Author : Andrew Aberdein,Ian J Dove
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 50,9 Mb
Release : 2013-07-01
Category : Philosophy
ISBN : 9789400765344

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The Argument of Mathematics by Andrew Aberdein,Ian J Dove Pdf

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics. ​

Author : Warren Hill,Ronald Edwards
Publisher : Unknown
Page : 282 pages
File Size : 41,5 Mb
Release : 1988
Category : Mathematical analysis
ISBN : 089455347X

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Mathematical Reasoning Through Verbal Analysis by Warren Hill,Ronald Edwards Pdf

Author : Edward Barbeau
Publisher : MAA
Page : 188 pages
File Size : 55,6 Mb
Release : 2000-06-15
Category : Mathematics
ISBN : 0883855291

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Mathematical Fallacies, Flaws, and Flimflam by Edward Barbeau Pdf

Through hard experience mathematicians have learned to subject even the most 'evident' assertions to rigorous scrutiny, as intuition can often be misleading. This book collects and analyses a mass of such errors, drawn from the work of students, textbooks, and the media, as well as from professional mathematicians themselves.

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 45,9 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

Author : Calvin T. Long
Publisher : Unknown
Page : 448 pages
File Size : 51,9 Mb
Release : 2015
Category : Mathematics
ISBN : 1269936654

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Mathematical Reasoning for Elementary Teachers by Calvin T. Long Pdf

Author : Edward J. Rothwell,Michael J. Cloud
Publisher : CRC Press
Page : 256 pages
File Size : 47,7 Mb
Release : 2020-01-30
Category : Technology & Engineering
ISBN : 9781000033045

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Engineering Writing by Design by Edward J. Rothwell,Michael J. Cloud Pdf

Engineering Writing by Design: Creating Formal Document of Lasting Value, Second Edition shows how effective writing can be achieved by thinking like an engineer. Based on the authors’ combined experience as engineering educators, the book presents a novel approach to technical writing, positioning formal writing tasks as engineering design problems with requirements, constraints, protocols, standards, and customers (readers) to satisfy. Specially crafted for busy engineers and engineering students, this quick-reading conversational text: Describes how to apply engineering design concepts to the writing process Explains how engineers fall into thinking traps, and gives techniques for avoiding them Covers the essentials of grammar, style, and mathematical exposition Highlights topics in writing ethics, including copyright, plagiarism, data presentation, and persuasion Engineering Writing by Design: Creating Formal Documents of Lasting Value, Second Edition addresses the specific combination of thinking and writing skills needed to succeed in modern engineering. Its mantra is: to write like an engineer, you must think like an engineer. Featuring illustrative examples, chapter summaries and exercises, quick-reference tables, and recommendations for further reading, this book is packed with valuable tips and information practicing and aspiring engineers need to become effective writers.