Visualization And Mathematics
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Visualization And Mathematics
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Author : H.-C. Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Visualization And Mathematics written by H.-C. Hege 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 2012-12-06 with Mathematics categories.
Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.
Visualization And Mathematics Iii
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Author : Hans-Christian Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Visualization And Mathematics Iii written by Hans-Christian Hege 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 2013-11-11 with Psychology categories.
A collection of state-of-the-art presentations on visualization problems in mathematics, fundamental mathematical research in computer graphics, and software frameworks for the application of visualization to real-world problems. Contributions have been written by leading experts and peer-refereed by an international editorial team. The book grew out of the third international workshop ‘Visualization and Mathematics’, May 22-25, 2002 in Berlin. The variety of topics covered makes the book ideal for researcher, lecturers, and practitioners.
Visualization In Mathematics Reading And Science Education
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Author : Linda M. Phillips
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Visualization In Mathematics Reading And Science Education written by Linda M. Phillips 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 2010-09-02 with Science categories.
Science education at school level worldwide faces three perennial problems that have become more pressing of late. These are to a considerable extent interwoven with concerns about the entire school curriculum and its reception by students. The rst problem is the increasing intellectual isolation of science from the other subjects in the school curriculum. Science is too often still taught didactically as a collection of pre-determined truths about which there can be no dispute. As a con- quence, many students do not feel any “ownership” of these ideas. Most other school subjects do somewhat better in these regards. For example, in language classes, s- dents suggest different interpretations of a text and then debate the relative merits of the cases being put forward. Moreover, ideas that are of use in science are presented to students elsewhere and then re-taught, often using different terminology, in s- ence. For example, algebra is taught in terms of “x, y, z” in mathematics classes, but students are later unable to see the relevance of that to the meaning of the universal gas laws in physics, where “p, v, t” are used. The result is that students are c- fused and too often alienated, leading to their failure to achieve that “extraction of an education from a scheme of instruction” which Jerome Bruner thought so highly desirable.
Reading For Evidence And Interpreting Visualizations In Mathematics And Science Education
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Author : Stephen P. Norris
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17
Reading For Evidence And Interpreting Visualizations In Mathematics And Science Education written by Stephen P. Norris 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 2012-09-17 with Education categories.
CRYSTAL—Alberta was established to research ways to improve students’ understanding and reasoning in science and mathematics. To accomplish this goal, faculty members in Education, Science, and Engineering, as well as school teachers joined forces to produce a resource bank of innovative and tested instructional materials that are transforming teaching in the K-12 classroom. Many of the instructional materials cross traditional disciplinary boundaries and explore contemporary topics such as global climate change and the spread of the West Nile virus. Combined with an emphasis on the use of visualizations, the instructional materials improve students’ engagement with science and mathematics. Participation in the CRYSTAL—Alberta project has changed the way I think about the connection between what I do as a researcher and what I do as a teacher: I have learned how to better translate scientific knowledge into language and activities appropriate for students, thereby transforming my own teaching. I also have learned to make better connections between what students are learning and what is happening in their lives and the world, thereby increasing students’ interest in the subject and enriching their learning experience.
Visualizing Mathematics
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Author : Kelly S. Mix
language : en
Publisher: Springer
Release Date : 2018-12-07
Visualizing Mathematics written by Kelly S. Mix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Education categories.
This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. Among the topics included: From intuitive spatial measurement to understanding of units. Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit. What processes underlie the relation between spatial skill and mathematics? Learning with and from drawing in early years geometry. Communication of visual information and complexity of reasoning by mathematically talented students. Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education.
Visualization Explanation And Reasoning Styles In Mathematics
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Author : P. Mancosu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Visualization Explanation And Reasoning Styles In Mathematics written by P. Mancosu 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 2006-03-30 with Mathematics categories.
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Mathematics And Art
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Author : Claude P. Bruter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Mathematics And Art written by Claude P. Bruter 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 2013-04-17 with Mathematics categories.
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.
Enhancing Mathematics Understanding Through Visualization The Role Of Dynamical Software
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Author : Habre, Samer
language : en
Publisher: IGI Global
Release Date : 2013-05-31
Enhancing Mathematics Understanding Through Visualization The Role Of Dynamical Software written by Habre, Samer and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-31 with Education categories.
Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a students understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.
Mathematical Visualization
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Author : H.-C. Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mathematical Visualization written by H.-C. Hege 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 2013-03-09 with Mathematics categories.
Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.
Visualizing Mathematics With 3d Printing
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Author : Henry Segerman
language : en
Publisher: JHU Press
Release Date : 2016-10-04
Visualizing Mathematics With 3d Printing written by Henry Segerman and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-04 with Mathematics categories.
The first book to explain mathematics using 3D printed models. Winner of the Technical Text of the Washington Publishers Wouldn’t it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book’s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.