Mathematical Visualization
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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.
Mathematical Principles For Scientific Computing And Visualization
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Author : Gerald Farin
language : en
Publisher: CRC Press
Release Date : 2008-10-21
Mathematical Principles For Scientific Computing And Visualization written by Gerald Farin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-21 with Computers categories.
This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coo
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.
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 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.
Mathematical Visualization
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Author : H.-C. Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-10-20
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 1998-10-20 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.
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.
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.
Handbook Of Research On The Psychology Of Mathematics Education
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Author : Angel Gutiérrez
language : en
Publisher: Sense Publishers
Release Date : 2006
Handbook Of Research On The Psychology Of Mathematics Education written by Angel Gutiérrez and has been published by Sense Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Education categories.
Compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation in 1976. The first three sections summarize cognitively-oriented research on learning and teaching specific content areas, transversal areas, and based on technology-rich environments. The fourth section is devoted to the research on social, affective, cultural and cognitive aspects of mathematics education. The fifth section includes two chapters summarizing the PME research on teacher training and professional life of mathematics teachers.
Mathematical Foundations Of Scientific Visualization Computer Graphics And Massive Data Exploration
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Author : Torsten Möller
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12
Mathematical Foundations Of Scientific Visualization Computer Graphics And Massive Data Exploration written by Torsten Möller 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 2009-06-12 with Computers categories.
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.