Lapses In Mathematical Reasoning
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Lapses in Mathematical Reasoning
Author | : V. M. Bradis,L. Minkovskii,A. K. Kharcheva |
Publsiher | : Courier Dover Publications |
Total Pages | : 224 |
Release | : 2016-10-28 |
Genre | : Mathematics |
ISBN | : 9780486816579 |
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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.
Lapses in Mathematical Reasoning 5
Author | : V M (Vladimir Modestovich) Bradis |
Publsiher | : Hassell Street Press |
Total Pages | : 220 |
Release | : 2021-09-09 |
Genre | : Electronic Book |
ISBN | : 1013631420 |
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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.
Adventures in Mathematical Reasoning
Author | : Sherman Stein |
Publsiher | : Courier Dover Publications |
Total Pages | : 192 |
Release | : 2016-07-19 |
Genre | : Mathematics |
ISBN | : 9780486814117 |
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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.
Mathematical Reasoning
Author | : Raymond Nickerson |
Publsiher | : Taylor & Francis |
Total Pages | : 597 |
Release | : 2011-02-25 |
Genre | : Psychology |
ISBN | : 9781136945397 |
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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.
Essays on Mathematical Reasoning
Author | : Jerzy Pogonowski |
Publsiher | : LIT Verlag Münster |
Total Pages | : 135 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9783643913104 |
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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?
An Introduction to Mathematical Reasoning
Author | : Peter J. Eccles |
Publsiher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 1997-12-11 |
Genre | : Mathematics |
ISBN | : 9781139643368 |
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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. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. 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 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. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
Adventures in Mathematical Reasoning
Author | : Sherman Stein |
Publsiher | : Courier Dover Publications |
Total Pages | : 193 |
Release | : 2016-09-21 |
Genre | : Mathematics |
ISBN | : 9780486806440 |
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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.
Mathematical Reasoning Through Verbal Analysis
Author | : Warren Hill,Ronald R. Edwards |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : OCLC:28103489 |
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