Lapses in Mathematical Reasoning

Lapses in Mathematical Reasoning
Title Lapses in Mathematical Reasoning PDF eBook
Author V. M. Bradis
Publisher Courier Corporation
Pages 225
Release 1999-01-01
Genre Mathematics
ISBN 048640918X

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Unique method of teaching high school students mathematical reasoning skills leads students deliberately toward a false conclusion. Later, teacher and student review and and analyze the reasoning lapse to correct the problem. Covers arithmetic, algebra, geometry, trigonometry and approximate computations. 1963 edition. Includes 2 prefaces and 45 figures.

Lapses in Mathematical Reasoning

Lapses in Mathematical Reasoning
Title Lapses in Mathematical Reasoning PDF eBook
Author V. M. Bradis
Publisher Courier Dover Publications
Pages 225
Release 2016-10-28
Genre Mathematics
ISBN 0486816575

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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.

Lapses in Mathematical Reasoning; 5

Lapses in Mathematical Reasoning; 5
Title Lapses in Mathematical Reasoning; 5 PDF eBook
Author V M (Vladimir Modestovich) Bradis
Publisher Hassell Street Press
Pages 220
Release 2021-09-09
Genre
ISBN 9781013631429

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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.

Mathematical Reasoning

Mathematical Reasoning
Title Mathematical Reasoning PDF eBook
Author Raymond Nickerson
Publisher Taylor & Francis
Pages 597
Release 2011-02-25
Genre Psychology
ISBN 1136945393

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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

Essays on Mathematical Reasoning
Title Essays on Mathematical Reasoning PDF eBook
Author Jerzy Pogonowski
Publisher LIT Verlag Münster
Pages
Release
Genre
ISBN 3643913109

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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?

LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS
Title LOGIC, SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS PDF eBook
Author Brahima MBODJE, Ph.D.
Publisher Author House
Pages 358
Release 2011-06-30
Genre Mathematics
ISBN 1463429665

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As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

The Argument of Mathematics

The Argument of Mathematics
Title The Argument of Mathematics PDF eBook
Author Andrew Aberdein
Publisher Springer Science & Business Media
Pages 392
Release 2013-07-01
Genre Philosophy
ISBN 9400765347

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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. ​