Visualization And Mathematics Iii

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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.

Mathematical Visualization aims at an abstract framework for fundamen tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers' own work and will further strenghten the development of the field of Mathe matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

Visualization And Mathematics Iii

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Author : Hans-Christian Hege
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-23

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 2003-06-23 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 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.

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:
Release Date : 2014-01-15

Visualization And Mathematics Iii written by Hans-Christian Hege and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

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.

Mathematics And Art

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Author : Claude Bruter
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-21

Mathematics And Art written by Claude 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 2002-08-21 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.

Visualization In Teaching And Learning Mathematics

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Author : Walter Zimmermann
language : en
Publisher: MAA Press
Release Date : 1991

Visualization In Teaching And Learning Mathematics written by Walter Zimmermann and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

The twenty papers in the book give an overview of research analysis, practical experience, and informed opinion about the role of visualization in teaching and learning mathematics, especially at the undergraduate level. Visualization, in its broadest level. Visualization, in its broadest sense, is as old as mathematics, but progress in computer graphics has generated a renaissance of interest in visual representations and visual thinking in mathematics.

Topology Based Methods In Visualization

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Author : Helwig Hauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25

Topology Based Methods In Visualization written by Helwig Hauser 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 2007-06-25 with Computers categories.

This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It contains a survey of the state-of-the-art, as well original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in its subject.

Gpu Based Interactive Visualization Techniques

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Author : Daniel Weiskopf
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-13

Gpu Based Interactive Visualization Techniques written by Daniel Weiskopf 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 2006-10-13 with Mathematics categories.

This book presents efficient visualization techniques, a prerequisite for the interactive exploration of complex data sets. High performance is demonstrated as a process of devising algorithms for the fast graphics processing units (GPUs) of modern graphics hardware. Coverage includes parallelization on cluster computers with several GPUs, adaptive rendering methods, and non-photorealistic rendering techniques for visualization.