Expanding Mathematical Toolbox Interweaving Topics Problems And Solutions
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Expanding Mathematical Toolbox Interweaving Topics Problems And Solutions
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Author : Boris Pritsker
language : en
Publisher: CRC Press
Release Date : 2023-02-08
Expanding Mathematical Toolbox Interweaving Topics Problems And Solutions written by Boris Pritsker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-08 with Mathematics categories.
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions offers several topics from different mathematical disciplines and shows how closely they are related. The purpose of this book is to direct the attention of readers who have an interest in and talent for mathematics to engaging and thought-provoking problems that should help them change their ways of thinking, entice further exploration and possibly lead to independent research and projects in mathematics. In spite of the many challenging problems, most solutions require no more than a basic knowledge covered in a high-school math curriculum. To shed new light on a deeper appreciation for mathematical relationships, the problems are selected to demonstrate techniques involving a variety of mathematical ideas. Included are some interesting applications of trigonometry, vector algebra and Cartesian coordinate system techniques, and geometrical constructions and inversion in solving mechanical engineering problems and in studying models explaining non-Euclidean geometries. This book is primarily directed at secondary school teachers and college professors. It will be useful in teaching mathematical reasoning because it emphasizes how to teach students to think creatively and strategically and how to make connections between math disciplines. The text also can be used as a resource for preparing for mathematics Olympiads. In addition, it is aimed at all readers who want to study mathematics, gain deeper understanding and enhance their problem-solving abilities. Readers will find fresh ideas and topics offering unexpected insights, new skills to expand their horizons and an appreciation for the beauty of mathematics.
Geometrical Kaleidoscope Second Edition
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Author : Boris Pritsker
language : en
Publisher: World Scientific
Release Date : 2024-03-14
Geometrical Kaleidoscope Second Edition written by Boris Pritsker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-14 with Mathematics categories.
The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The emphasis is on the practical applications of theory in the problem-solving process. The chapters cover a myriad of topics among which are the classic theorems and formulas such as Archimedes' Law of the Lever, the Pythagorean Theorem, Heron's formula, Brahmagupta's formula, Appollonius's Theorem, Euler's line properties, the Nine-Point Circle, Fagnano's Problem, the Steiner-Lehmus Theorem, Napoleon's Theorem, Ceva's Theorem, Menelaus's Theorem, Pompeiu's Theorem, and Morley's Miracle. The book focuses on geometric thinking — what it means, how to develop it, and how to recognize it. 'Geometrical Kaleidoscope' consists of a kaleidoscope of topics that seem to not be related at first glance. However, that perception disappears as you go from chapter to chapter and explore the multitude of surprising relationships, unexpected connections, and links. Readers solving a chain of problems will learn from them general techniques, rather than isolated instances of the application of a technique. In spite of the many problems' challenging character, their solutions require no more than a basic knowledge covered in a high school geometry curriculum. There are plenty of problems for readers to work out for themselves (solutions are provided at the end of the book).In the 2nd edition of the book there are many new ideas and additional explanations that help the reader better understand the solutions of problems and connect the chapters to one another. A new chapter 'Alternative proofs of the Pythagorean Theorem' is added. It covers seven different proofs of the famous theorem and discusses its generalizations and applications. There is also Appendix and Index added, which were missing in the first edition of the book.
The Equations World
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Author : Boris Pritsker
language : en
Publisher: Courier Dover Publications
Release Date : 2019-08-14
The Equations World written by Boris Pritsker 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 2019-08-14 with Mathematics categories.
Equations are the lifeblood of mathematics, science, and technology, and this book examines equations of all kinds. With his masterful ability to convey the excitement and elegance of mathematics, author Boris Pritsker explores equations from the simplest to the most complex—their history, their charm, and their usefulness in solving problems. The Equations World bridges the fields of algebra, geometry, number theory, and trigonometry, solving more than 280 problems by employing a wide spectrum of techniques. The author demystifies the subject with efficient hints, tricks, and methods that reveal the fun and satisfaction of problem solving. He also demonstrates how equations can serve as important tools for expressing a problem's data, showing the ways in which they assist in fitting parts together to solve the whole puzzle. In addition, brief historical tours reveal the foundations of mathematical thought by tracing the ideas and approaches developed by mathematicians over the centuries. Both recreational mathematicians and ambitious students will find this book an ample source of enlightenment and enjoyment.
Mathematical Labyrinths Pathfinding
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Author : Boris Pritsker
language : en
Publisher: World Scientific
Release Date : 2021-01-04
Mathematical Labyrinths Pathfinding written by Boris Pritsker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.
Mathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10-20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.
Mathematics Education In The Digital Age
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Author : Alison Clark-Wilson
language : en
Publisher: Routledge
Release Date : 2021-05-24
Mathematics Education In The Digital Age written by Alison Clark-Wilson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Education categories.
The wide availability of digital educational resources for mathematics teaching and learning is indisputable, with some notable genres of technologies having evolved, such as graphing calculators, dynamic graphing, dynamic geometry and data visualization tools. But what does this mean for teachers of mathematics, and how do their roles evolve within this digital landscape? This essential book offers an international perspective to help bridge theory and practice, including coverage of networking theories, curriculum design, task implementation, online resources and assessment. Mathematics Education in the Digital Age details the impacts this digital age has, and will continue to have, on the parallel aspects of learning and teaching mathematics within formal education systems and settings. Written by a group of international authors, the chapters address the following themes: Mathematics teacher education and professional development Mathematics curriculum development and task design The assessment of mathematics Theoretical perspectives and methodologies/approaches for researching mathematics education in the digital age This book highlights not only the complex nature of the field, but also the advancements in theoretical and practical knowledge that is enabling the mathematics education community to continue to learn in this increasingly digital age. It is an essential read for all mathematics teacher educators and master teachers.
Maple In Mathematics Education And Research
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Author : Jürgen Gerhard
language : en
Publisher: Springer Nature
Release Date : 2020-02-27
Maple In Mathematics Education And Research written by Jürgen Gerhard and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-27 with Computers categories.
This book constitutes the refereed proceedings of the third Maple Conference, MC 2019, held in Waterloo, Ontario, Canada, in October 2019. The 21 revised full papers and 9 short papers were carefully reviewed and selected out of 37 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.
Opening The Cage
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Author : Ole Skovsmose
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-05
Opening The Cage written by Ole Skovsmose 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 2012-09-05 with Education categories.
The picture on the front of this book is an illustration for Totakahini: The tale of the parrot, by Rabindranath Tagore, in which he satirized education as a magnificent golden cage. Opening the cage addresses mathematics education as a complex socio-political phenomenon, exploring the vast terrain that spans critique and politics. Opening the cage includes contributions from educators writing critically about mathematics education in diverse contexts. They demonstrate that mathematics education is politics, they investigate borderland positions, they address the nexus of mathematics, education, and power, and they explore educational possibilities. Mathematics education is not a free enterprise. It is carried on behind bars created by economic, political, and social demands. This cage might not be as magnificent as that in Tagore’s fable. But it is strong. Opening the cage is a critical and political challenge, and we may be surprised to see what emerges.
Cognitive Hyperconnected Digital Transformation
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Author : Ovidiu Vermesan
language : en
Publisher: CRC Press
Release Date : 2022-09-01
Cognitive Hyperconnected Digital Transformation written by Ovidiu Vermesan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.
Cognitive Hyperconnected Digital Transformation provides an overview of the current Internet of Things (IoT) landscape, ranging from research, innovation and development priorities to enabling technologies in a global context. It is intended as a standalone book in a series that covers the Internet of Things activities of the IERC-Internet of Things European Research Cluster, including both research and technological innovation, validation and deployment. The book builds on the ideas put forward by the European Research Cluster, the IoT European Platform Initiative (IoT-EPI) and the IoT European Large-Scale Pilots Programme, presenting global views and state-of-the-art results regarding the challenges facing IoT research, innovation, development and deployment in the next years. Hyperconnected environments integrating industrial/business/consumer IoT technologies and applications require new IoT open systems architectures integrated with network architecture (a knowledge-centric network for IoT), IoT system design and open, horizontal and interoperable platforms managing things that are digital, automated and connected and that function in real-time with remote access and control based on Internet-enabled tools. The IoT is bridging the physical world with the virtual world by combining augmented reality (AR), virtual reality (VR), machine learning and artificial intelligence (AI) to support the physical-digital integrations in the Internet of mobile things based on sensors/actuators, communication, analytics technologies, cyber-physical systems, software, cognitive systems and IoT platforms with multiple functionalities. These IoT systems have the potential to understand, learn, predict, adapt and operate autonomously. They can change future behaviour, while the combination of extensive parallel processing power, advanced algorithms and data sets feed the cognitive algorithms that allow the IoT systems to develop new services and propose new solutions. IoT technologies are moving into the industrial space and enhancing traditional industrial platforms with solutions that break free of device-, operating system- and protocol-dependency. Secure edge computing solutions replace local networks, web services replace software, and devices with networked programmable logic controllers (NPLCs) based on Internet protocols replace devices that use proprietary protocols. Information captured by edge devices on the factory floor is secure and accessible from any location in real time, opening the communication gateway both vertically (connecting machines across the factory and enabling the instant availability of data to stakeholders within operational silos) and horizontally (with one framework for the entire supply chain, across departments, business units, global factory locations and other markets). End-to-end security and privacy solutions in IoT space require agile, context-aware and scalable components with mechanisms that are both fluid and adaptive. The convergence of IT (information technology) and OT (operational technology) makes security and privacy by default a new important element where security is addressed at the architecture level, across applications and domains, using multi-layered distributed security measures. Blockchain is transforming industry operating models by adding trust to untrusted environments, providing distributed security mechanisms and transparent access to the information in the chain. Digital technology platforms are evolving, with IoT platforms integrating complex information systems, customer experience, analytics and intelligence to enable new capabilities and business models for digital business.
The Ocean Economy In 2030
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Author : OECD
language : en
Publisher: OECD Publishing
Release Date : 2016-04-27
The Ocean Economy In 2030 written by OECD and has been published by OECD Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-27 with categories.
This report explores the growth prospects for the ocean economy, its capacity for future employment creation and innovation, and its role in addressing global challenges. Special attention is devoted to the emerging ocean-based industries.
Families In An Era Of Increasing Inequality
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Author : Paul R. Amato
language : en
Publisher: Springer
Release Date : 2014-10-07
Families In An Era Of Increasing Inequality written by Paul R. Amato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Social Science categories.
The widening gap between the rich and the poor is turning the American dream into an impossibility for many, particularly children and families. And as the children of low-income families grow to adulthood, they have less access to opportunities and resources than their higher-income peers--and increasing odds of repeating the experiences of their parents. Families in an Era of Increasing Inequality probes the complex relations between social inequality and child development and examines possibilities for disrupting these ongoing patterns. Experts across the social sciences track trends in marriage, divorce, employment, and family structure across socioeconomic strata in the U.S. and other developed countries. These family data give readers a deeper understanding of how social class shapes children's paths to adulthood and how those paths continue to diverge over time and into future generations. In addition, contributors critique current policies and programs that have been created to reduce disparities and offer suggestions for more effective alternatives. Among the topics covered: Inequality begins at home: the role of parenting in the diverging destinies of rich and poor children. Inequality begins outside the home: putting parental educational investments into context. How class and family structure impact the transition to adulthood. Dealing with the consequences of changes in family composition. Dynamic models of poverty-related adversity and child outcomes. The diverging destinies of children and what it means for children's lives. As new initiatives are sought to improve the lives of families and children in the short and long term, Families in an Era of Increasing Inequality is a key resource for researchers and practitioners in family studies, social work, health, education, sociology, demography, and psychology.