Lapses In Mathematical Reasoning
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Lapses In Mathematical Reasoning
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Author : V. M. Bradis
language : en
Publisher: Courier Dover Publications
Release Date : 2016-10-28
Lapses In Mathematical Reasoning written by V. M. Bradis and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-28 with Mathematics categories.
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
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Author : V M (Vladimir Modestovich) Bradis
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-09
Lapses In Mathematical Reasoning 5 written by V M (Vladimir Modestovich) Bradis and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with categories.
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
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Author : Raymond Nickerson
language : en
Publisher: Taylor & Francis
Release Date : 2011-02-25
Mathematical Reasoning written by Raymond Nickerson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Psychology categories.
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.
Lapses In Mathematical Reasoning
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Author : V. M. Bradis
language : en
Publisher:
Release Date : 1963
Lapses In Mathematical Reasoning written by V. M. Bradis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Essays On Mathematical Reasoning
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Author : Jerzy Pogonowski
language : en
Publisher: LIT Verlag Münster
Release Date : 2021-01-27
Essays On Mathematical Reasoning written by Jerzy Pogonowski and has been published by LIT Verlag Münster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-27 with Mathematics categories.
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?
Mathematical Fallacies Flaws And Flimflam
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Author : Edward Barbeau
language : en
Publisher: MAA
Release Date : 2000-06-15
Mathematical Fallacies Flaws And Flimflam written by Edward Barbeau and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-15 with Mathematics categories.
Through hard experience, mathematicians have learned to subject even the most evident assertions to rigorous scrutiny, as intuition and facile reasoning can often lead them astray. However, the impossibility and impracticality of completely watertight arguments make it possible for errors to slip by the most watchful eye. They are often subtle and difficult of detection. When found, they can teach us a lot and can present a real challenge to straighten out. Presenting students with faulty arguments to troubleshoot can be an effective way of helping them critically understand material, and it is for this reason that I began to compile fallacies and publish them first in the Notes of the Canadian Mathematical Society and later in the College Mathematics Journal in the Fallacies, Flaws and Flimflam section. I hoped to challenge and amuse readers as well as to provide them with material suitable for teaching and student assignments. This book collects the items from the first eleven years of publishing in the CMJ. One source of such errors is the work of students. Occasionally, a text book will weigh in with a specious result or solution. Nonprofessional sources, such as newspapers, are responsible for a goodly number of mishaps, particularly in arithmetic (especially percentages) and probability; their use in classrooms may help students become critical readers and listeners of the media. Quite a few items come from professional mathematicians. The reader will find in this book some items that are not erroneous but seem to be. These need a fuller analysis to clarify the situation. All the items are presented for your entertainment and use. The mathematical topics covered include algebra, trigonometry, geometry, probability, calculus, linear algebra, and modern algebra.
Logic Sets And The Techniques Of Mathematical Proofs
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Author : Brahima Mbodje Ph. D.
language : en
Publisher: AuthorHouse
Release Date : 2011-06
Logic Sets And The Techniques Of Mathematical Proofs written by Brahima Mbodje Ph. D. and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06 with Education categories.
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
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.
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.
Mathematics In Middle And Secondary School
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Author : Alexander Karp
language : en
Publisher: IAP
Release Date : 2014-11-01
Mathematics In Middle And Secondary School written by Alexander Karp and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-01 with Education categories.
The experience and knowledge acquired in teacher education courses should build important fundamentals for the future teaching of mathematics. In particular, experience in mathematical problem solving, and in planning lessons devoted to problem solving, is an essential component of teacher preparation. This book develops a problem solving approach and is intended to be a text used in mathematics education courses (or professional development) for pre-service or in-service middle and secondary school teachers. It can be used both in graduate and undergraduate courses, in accordance with the focus of teacher preparation programs. The content of the book is suited especially for those students who are further along in their mathematics education preparation, as the text is more involved with mathematical ideas and problem solving, and discusses some of the intricate pedagogical considerations that arise in teaching. The text is written not as an introduction to mathematics education (a first course), but rather as a second, or probably, third course. The book deals both with general methodology issues in mathematics education incorporating a problem solving approach (Chapters 1-6) and with more concrete applications within the context of specific topics – algebra, geometry, and discrete mathematics (Chapters 7-13). The book provides opportunities for teachers to engage in authentic mathematical thinking. The mathematical ideas under consideration build on specific middle and secondary school content while simultaneously pushing the teacher to consider more advanced topics, as well as various connections across mathematical domains. The book strives to preserve the spirit of discussion, and at times even argument, typical of collaborative work on a lesson plan. Based on the accumulated experience of work with future and current teachers, the book assumes that students have some background in lesson planning, and extends their thinking further. Specifically, this book aims to provide a discussion of how a lesson plan is constructed, including the ways in which problems are selected or invented, rather than the compilation of prepared lesson plans. This approach reflects the authors’ view that the process of searching for an answer is often more important than the formal result.
Hexaflexagons And Other Mathematical Diversions
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Author : Martin Gardner
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-05
Hexaflexagons And Other Mathematical Diversions written by Martin Gardner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-05 with Mathematics categories.
Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.