Magnificent Mistakes In Mathematics

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Magnificent Mistakes in Mathematics

Alfred S. Posamentier,Ingmar Lehmann
Magnificent Mistakes in Mathematics Book PDF

Author : Alfred S. Posamentier,Ingmar Lehmann
Publisher : Prometheus Books
Page : 298 pages
File Size : 55,6 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781616147488

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Magnificent Mistakes in Mathematics by Alfred S. Posamentier,Ingmar Lehmann Pdf

Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

How Not to Be Wrong

Jordan Ellenberg
How Not to Be Wrong Book PDF

Author : Jordan Ellenberg
Publisher : Penguin Press
Page : 480 pages
File Size : 40,5 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781594205224

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How Not to Be Wrong by Jordan Ellenberg Pdf

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Mathematics: Its Historical Aspects, Wonders And Beyond

Arthur D Kramer,Alfred S Posamentier
Mathematics Its Historical Aspects Wonders And Beyond Book PDF

Author : Arthur D Kramer,Alfred S Posamentier
Publisher : World Scientific
Page : 403 pages
File Size : 55,6 Mb
Release : 2022-06-29
Category : Mathematics
ISBN : 9789811248597

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Mathematics: Its Historical Aspects, Wonders And Beyond by Arthur D Kramer,Alfred S Posamentier Pdf

Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency 'to teach to the test'. This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ꝏ, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.

A First Course in Mathematical Logic and Set Theory

Michael L. O'Leary
A First Course in Mathematical Logic and Set Theory Book PDF

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 49,6 Mb
Release : 2015-09-14
Category : Mathematics
ISBN : 9781118548011

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A First Course in Mathematical Logic and Set Theory by Michael L. O'Leary Pdf

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

Teaching Secondary School Mathematics: Techniques And Enrichment

Alfred S Posamentier,Beverly Smith
Teaching Secondary School Mathematics Techniques And Enrichment Book PDF

Author : Alfred S Posamentier,Beverly Smith
Publisher : World Scientific
Page : 1042 pages
File Size : 46,6 Mb
Release : 2020-09-18
Category : Mathematics
ISBN : 9789811211430

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Teaching Secondary School Mathematics: Techniques And Enrichment by Alfred S Posamentier,Beverly Smith Pdf

The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.

Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12

Alfred S Posamentier
Creative Secondary School Mathematics 125 Enrichment Units For Grades 7 To 12 Book PDF

Author : Alfred S Posamentier
Publisher : World Scientific
Page : 556 pages
File Size : 52,6 Mb
Release : 2021-06-08
Category : Mathematics
ISBN : 9789811240447

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Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12 by Alfred S Posamentier Pdf

There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units — ranging from grades 7 through 12 — that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!

Innovative Teaching: Best Practices From Business And Beyond For Mathematics Teachers

Denise H Sutton,Alfred S Posamentier
Innovative Teaching Best Practices From Business And Beyond For Mathematics Teachers Book PDF

Author : Denise H Sutton,Alfred S Posamentier
Publisher : World Scientific
Page : 222 pages
File Size : 55,6 Mb
Release : 2021-01-26
Category : Mathematics
ISBN : 9789811231681

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Innovative Teaching: Best Practices From Business And Beyond For Mathematics Teachers by Denise H Sutton,Alfred S Posamentier Pdf

Innovative Teaching: Best Practices from Business and Beyond for Mathematics Teachers provides educators with new and exciting ways to introduce material and methods to motivate and engage students by showing how some of the techniques commonly used in the business world — and beyond — are applicable to the world of education. It also offers educators practical advice with regard to the changing culture of education, keeping up with technology, navigating politics at work, interacting with colleagues, developing leadership skills, group behavior, and gender differences.Innovative Teaching demonstrates how the classroom environment is similar to the marketplace. Educators, like businesses, for example, must capture and hold the attention of their audience while competing with a constant stream of 'noise.' With the introduction of the Internet and the wide use of social media, promoters understand that they must not only engage their audience, but also incorporate audience feedback into the promotional work and product or service they offer. Innovative Teaching shows educators how to take the best practices from business — and beyond — and recombine these resources for appropriate use in the classroom.

Strategy Games to Enhance Problem-Solving Ability in Mathematics

Alfred S Posamentier,Stephen Krulik
Strategy Games to Enhance Problem Solving Ability in Mathematics Book PDF

Author : Alfred S Posamentier,Stephen Krulik
Publisher : World Scientific
Page : 136 pages
File Size : 47,8 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9789813146365

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Strategy Games to Enhance Problem-Solving Ability in Mathematics by Alfred S Posamentier,Stephen Krulik Pdf

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

Problem-Solving Strategies in Mathematics

Alfred S Posamentier,Stephen Krulik
Problem Solving Strategies in Mathematics Book PDF

Author : Alfred S Posamentier,Stephen Krulik
Publisher : World Scientific Publishing Company
Page : 188 pages
File Size : 48,9 Mb
Release : 2015-03-05
Category : Mathematics
ISBN : 9789814651653

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Problem-Solving Strategies in Mathematics by Alfred S Posamentier,Stephen Krulik Pdf

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

The Mathematics Coach Handbook

Posamentier Alfred S,Krulik Stephen
The Mathematics Coach Handbook Book PDF

Author : Posamentier Alfred S,Krulik Stephen
Publisher : World Scientific
Page : 184 pages
File Size : 55,9 Mb
Release : 2018-11-07
Category : Education
ISBN : 9789813271722

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The Mathematics Coach Handbook by Posamentier Alfred S,Krulik Stephen Pdf

Many schools throughout the United States are now employing coaches to support teachers in the teaching of mathematics. Very often, these are professionals selected from the current teaching ranks who did not receive any special training to serve as a coach. This book provides the skills, knowledge, and lessons from experience that lead such a mentor to function effectively. Aside from describing the basic duties of an effective math coach, we also provide a plethora of resources to enrich instruction, improve problem-solving direction, and provide teachers with a wide variety of techniques to enhance their teaching effectiveness.

Understanding Mathematics Through Problem Solving

Alfred S Posamentier,Peter Poole
Understanding Mathematics Through Problem Solving Book PDF

Author : Alfred S Posamentier,Peter Poole
Publisher : World Scientific
Page : 530 pages
File Size : 51,5 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9789814663694

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Understanding Mathematics Through Problem Solving by Alfred S Posamentier,Peter Poole Pdf

This book will present a collection of mathematical problems — lighthearted in nature — intended to entertain the general readership. Problems will be selected largely for the unusual and unexpected solutions to which they lend themselves. Some interesting contents included: All in all, the book is meant to entertain the general readership and to convince them about the power and beauty of mathematics.

Psychology Of Problem Solving, The: The Background To Successful Mathematics Thinking

Virgadamo Danielle Sauro,Posamentier Alfred S,Keefe-cooperman Kathleen,Kose Gary
Psychology Of Problem Solving The The Background To Successful Mathematics Thinking Book PDF

Author : Virgadamo Danielle Sauro,Posamentier Alfred S,Keefe-cooperman Kathleen,Kose Gary
Publisher : World Scientific
Page : 168 pages
File Size : 54,7 Mb
Release : 2019-08-21
Category : Mathematics
ISBN : 9789811205729

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Psychology Of Problem Solving, The: The Background To Successful Mathematics Thinking by Virgadamo Danielle Sauro,Posamentier Alfred S,Keefe-cooperman Kathleen,Kose Gary Pdf

The art or skill of problem solving in mathematics is mostly relegated to the strategies one can use to solve problems in the field. Although this book addresses that issue, it delves deeply into the psychological aspects that affect successful problem-solving. Such topics as decision-making, judgment, and reasoning as well as using memory effectively and a discussion of the thought processes that could help address certain problem-solving situations.Most books that address problem-solving and mathematics focus on the various skills. This book goes beyond that and investigates the psychological aspects to solving problems in mathematics.

Mathematics Entertainment For The Millions

Alfred S Posamentier
Mathematics Entertainment For The Millions Book PDF

Author : Alfred S Posamentier
Publisher : World Scientific
Page : 304 pages
File Size : 49,7 Mb
Release : 2020-07-21
Category : Mathematics
ISBN : 9789811219306

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Mathematics Entertainment For The Millions by Alfred S Posamentier Pdf

'The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership.Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations.The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level.Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

The Best Writing on Mathematics 2014

Mircea Pitici
The Best Writing on Mathematics 2014 Book PDF

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 360 pages
File Size : 47,8 Mb
Release : 2014-11-23
Category : Mathematics
ISBN : 9780691164175

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The Best Writing on Mathematics 2014 by Mircea Pitici Pdf

Collects essays on mathematics, from the importance of big data and the varying forms of Klein bottles to fountain design and the possible shape of the universe.

Glimpses into the World of Mathematics

Szymon Chlebowski
Glimpses into the World of Mathematics Book PDF

Author : Szymon Chlebowski
Publisher : LIT Verlag Münster
Page : 128 pages
File Size : 41,9 Mb
Release : 2024-06-11
Category : Electronic
ISBN : 9783643913654

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Glimpses into the World of Mathematics by Szymon Chlebowski Pdf

Essays collected in this volume deal with various problems from the philosophy of mathematics. What connects them are two questions: how mathematics is created and how it is acquired. In 'Three Worlds of Mathematics' we are familiarized with David Tall's ideas pertaining to the embodied, symbolic and formal worlds of mathematics. In 'Basic Ideas of Intuitionism', we focus on an epistemological approach to mathematics which is distinctive to constructive mathematics. The author focuses on the computational content of intuitionistic logic and shows how it relates to functional programming. 'The Brave Mathematical Ant' carefully selects mathematical puzzles related to teaching experiences in a way that the solution requires creativity and is not obtainable by following an algorithm. Moreover the solution gives us some new insight into the underlying idea. 'Degrees Of Accessibility Of Mathematical Objects' discusses various criteria which can be used to judge accessibility of mathematical objects. We find logical complexity, range of applications, existence of a physical model as well as aesthetic values.