Le Cahier Transmath Dalgorithmique Cycle 4 5e 4e 3e

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Proof Technology in Mathematics Research and Teaching

Author : Gila Hanna
Publisher : Springer Nature
ISBN 13 : 3030284832
Total Pages : 374 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Proof Technology in Mathematics Research and Teaching by : Gila Hanna

Download or read book Proof Technology in Mathematics Research and Teaching written by Gila Hanna and published by Springer Nature. This book was released on 2019-10-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.

Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe

Author : Lesley B. Cormack
Publisher : Springer
ISBN 13 : 3319494309
Total Pages : 205 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe by : Lesley B. Cormack

Download or read book Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe written by Lesley B. Cormack and published by Springer. This book was released on 2017-03-15 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners (those who know by doing) and scholars (those who know by thinking). These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new methods, new subjects of enquiry, and new social structures of natural philosophy and science. The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest.

Math Made Visual

Author : Claudi Alsina
Publisher : MAA
ISBN 13 : 9780883857465
Total Pages : 202 pages
Book Rating : 4.8/5 (574 download)

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Book Synopsis Math Made Visual by : Claudi Alsina

Download or read book Math Made Visual written by Claudi Alsina and published by MAA. This book was released on 2006-07-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

Developing Research in Mathematics Education

Author : Tommy Dreyfus
Publisher :
ISBN 13 : 9781138080270
Total Pages : 0 pages
Book Rating : 4.0/5 (82 download)

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Book Synopsis Developing Research in Mathematics Education by : Tommy Dreyfus

Download or read book Developing Research in Mathematics Education written by Tommy Dreyfus and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This field-spanning book will set out the broad advances in knowledge which have accumulated in the 21st century through the sustained exchange of ideas and collaboration between mathematics education researchers, considering both european and global perspectives. It is split in to three main sections focusing on content domains and processes, aspects of mathematics teaching and learning, and linguistic and social perspectives, and concludes with two lively international discussion chapters. Each section will include coverage of recent developments, current status and future outlook of global research making this book a fascintaing compendium of state of the art mathematical knowledge.

Transmitting Knowledge

Author : Sachiko Kusukawa
Publisher : Oxford University Press, USA
ISBN 13 : 019928878X
Total Pages : 292 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Transmitting Knowledge by : Sachiko Kusukawa

Download or read book Transmitting Knowledge written by Sachiko Kusukawa and published by Oxford University Press, USA. This book was released on 2006 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The period between the fifteenth and the middle of the seventeenth centuries saw a great many changes and innovations in scientific thinking. These were communicated to various publics in diverse ways; not only through discursive prose and formal notations, but also in the form of instruments and images accompanying texts. The collected essays of this volume examine the modes of transmission of this knowledge in a variety of contexts. The schematic representation of instruments is examined in the case of the 'navicula' (a versatile version of a sundial) and the 'squadro' (a surveying instrument); the new forms of illustration of plants and the human body are investigated through the work of Fuchs and Vesalius; theories of optics and of matter are discussed in relation to the illustrations which accompany the texts of Ausonio and Descartes. The different diagrammatic strategies adopted to explain the complex medical theory of the latitude of health are charted through the work of medieval and sixteenth-century physicians; Kepler's use of illustration in his handbook of cosmology is placed in the context of book production and Copernican propaganda. The conception of astronomical instruments as either calculating devices or as cosmological models is examined in the case of Tycho Brahe and others. A study is devoted to the multiple functions of frontispieces and to the various readerships for which they were conceived. The papers in the volume are all based on new research, and they constitute together a coherent and convergent set of case studies which demonstrate the vitality and inventiveness of early modern natural philosophers, and their awareness of the media available to them for transmitting knowledge.

International Perspectives on the Teaching and Learning of Geometry in Secondary Schools

Author : Patricio Herbst
Publisher : Springer
ISBN 13 : 331977476X
Total Pages : 383 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis International Perspectives on the Teaching and Learning of Geometry in Secondary Schools by : Patricio Herbst

Download or read book International Perspectives on the Teaching and Learning of Geometry in Secondary Schools written by Patricio Herbst and published by Springer. This book was released on 2018-04-27 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.

Applications of Computer Algebra

Author : Ilias S. Kotsireas
Publisher : Springer
ISBN 13 : 3319569325
Total Pages : 513 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Applications of Computer Algebra by : Ilias S. Kotsireas

Download or read book Applications of Computer Algebra written by Ilias S. Kotsireas and published by Springer. This book was released on 2017-07-26 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

How Round Is Your Circle?

Author : John Bryant
Publisher : Princeton University Press
ISBN 13 : 1400837952
Total Pages : 345 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis How Round Is Your Circle? by : John Bryant

Download or read book How Round Is Your Circle? written by John Bryant and published by Princeton University Press. This book was released on 2011-02-28 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

Technology in Mathematics Teaching

Author : Gilles Aldon
Publisher : Springer
ISBN 13 : 3030197417
Total Pages : 335 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Technology in Mathematics Teaching by : Gilles Aldon

Download or read book Technology in Mathematics Teaching written by Gilles Aldon and published by Springer. This book was released on 2019-07-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises chapters featuring a state of the art of research on digital technology in mathematics education. The chapters are extended versions of a selection of papers from the Proceedings of the 13th International Conference on Technology in Mathematics Teaching (ICTMT-13), which was held in Lyon, France, from July 3rd to 6th. ICTMT-13 gathered together over one hundred participants from twenty countries sharing research and empirical results on the topical issues of technology and its potential to improve mathematics teaching and learning. The chapters are organised into 4 themed parts, namely assessment in mathematics education and technology, which was the main focus of the conference, innovative technology and approaches to mathematics education, teacher education and professional development toward the technology use, and mathematics teaching and learning experiences with technology. In 13 chapters contained in the book, prominent mathematics educators from all over the world present the most recent theoretical and practical advances on these themes This book is of particular interest to researchers, teachers, teacher educators and other actors interested in digital technology in mathematics education.

The Archimedes Codex

Author : Reviel Netz
Publisher : Weidenfeld & Nicolson
ISBN 13 : 1780221983
Total Pages : 307 pages
Book Rating : 4.7/5 (82 download)

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Book Synopsis The Archimedes Codex by : Reviel Netz

Download or read book The Archimedes Codex written by Reviel Netz and published by Weidenfeld & Nicolson. This book was released on 2011-10-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The story of the amazing discovery of Archimedes' lost works Drawings and writings by Archimedes, previously thought to have been destroyed, have been uncovered beneath the pages of a 13th-century monk's prayer book. These hidden texts, slowly being retrieved and deciphered by scientists, show that Archimedes' thinking (2,200 years ago) was even ahead of Isaac Newton in the 17th century. Archimedes discovered the value of Pi, he developed the theory of specific gravity and made steps towards the development of calculus. Everything we know about him comes from three manuscripts, two of which have disappeared. The third, currently in the Walters Art Museum, is a palimpsest - the text has been scraped off, the book taken apart and its parchment re-used, in this case as a prayer book. William Noel, the project director, and Reviel Netz, a historian of ancient mathematics, tell the enthralling story of the survival of that prayer book from 1229 to the present, and examine the process of recovering the invaluable text underneath as well as investigating into why that text is so important.