Mathematical Visualization

Author : H.-C. Hege,K. Polthier
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642591952

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Visualization and Mathematics by H.-C. Hege,K. Polthier Pdf

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.

Author : H.-C. Hege,K. Polthier
Publisher : Springer Science & Business Media
Page : 398 pages
File Size : 48,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662035672

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Mathematical Visualization by H.-C. Hege,K. Polthier Pdf

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.

Author : P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 40,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9781402033353

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Visualization, Explanation and Reasoning Styles in Mathematics by P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen Pdf

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.

Author : Gerald Farin,Dianne Hansford
Publisher : CRC Press
Page : 296 pages
File Size : 41,6 Mb
Release : 2008-10-21
Category : Mathematics
ISBN : 9781568813219

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Mathematical Principles for Scientific Computing and Visualization by Gerald Farin,Dianne Hansford Pdf

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 coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

Author : Henry Segerman
Publisher : JHU Press
Page : 201 pages
File Size : 47,9 Mb
Release : 2016-10-04
Category : Mathematics
ISBN : 9781421420363

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Visualizing Mathematics with 3D Printing by Henry Segerman Pdf

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.

Author : Linda M. Phillips,Stephen P. Norris,John S. Macnab
Publisher : Springer Science & Business Media
Page : 112 pages
File Size : 45,5 Mb
Release : 2010-09-02
Category : Science
ISBN : 9789048188161

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Visualization in Mathematics, Reading and Science Education by Linda M. Phillips,Stephen P. Norris,John S. Macnab Pdf

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.

Author : Torsten Möller,Bernd Hamann,Robert D. Russell
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 53,9 Mb
Release : 2009-06-12
Category : Computers
ISBN : 9783540499268

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Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration by Torsten Möller,Bernd Hamann,Robert D. Russell Pdf

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.

Author : Hans-Christian Hege,Konrad Polthier
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 53,5 Mb
Release : 2013-11-11
Category : Psychology
ISBN : 9783662051054

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Visualization and Mathematics III by Hans-Christian Hege,Konrad Polthier Pdf

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.

Author : Habre, Samer
Publisher : IGI Global
Page : 298 pages
File Size : 51,7 Mb
Release : 2013-05-31
Category : Education
ISBN : 9781466640511

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Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software by Habre, Samer Pdf

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 student’s 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.

Author : Claude P. Bruter
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 45,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662049099

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Mathematics and Art by Claude P. Bruter Pdf

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.

Author : Kelly S. Mix,Michael T. Battista
Publisher : Springer
Page : 378 pages
File Size : 46,7 Mb
Release : 2018-12-07
Category : Education
ISBN : 9783319987675

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Visualizing Mathematics by Kelly S. Mix,Michael T. Battista Pdf

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.

Author : James S. Tanton
Publisher : Unknown
Page : 128 pages
File Size : 47,9 Mb
Release : 2016-08-13
Category : Electronic
ISBN : 1629973297

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The Power of Mathematical Visualization by James S. Tanton Pdf

Author : Elena Zudilova-Seinstra,Tony Adriaansen,Robert van Liere
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 47,5 Mb
Release : 2008-12-17
Category : Computers
ISBN : 9781848002692

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Trends in Interactive Visualization by Elena Zudilova-Seinstra,Tony Adriaansen,Robert van Liere Pdf

II Challenges in Data Mapping Part II deals with one of the most challenging tasks in Interactive Visualization, mapping and teasing out information from large complex datasets and generating visual representations. This section consists of four chapters. Binh Pham, Alex Streit, and Ross Brown provide a comprehensive requirement analysis of information uncertainty visualizations. They examine the sources of uncertainty, review aspects of its complexity, introduce typical models of uncertainty, and analyze major issues in visualization of uncertainty, from various user and task perspectives. Alfred Inselberg examines challenges in the multivariate data analysis. He explains how relations among multiple variables can be mapped uniquely into ?-space subsets having geometrical properties and introduces Parallel Coordinates meth- ology for the unambiguous visualization and exploration of a multidimensional geometry and multivariate relations. Christiaan Gribble describes two alternative approaches to interactive particle visualization: one targeting desktop systems equipped with programmable graphics hardware and the other targeting moderately sized multicore systems using pack- based ray tracing. Finally, Christof Rezk Salama reviews state-of-the-art strategies for the assignment of visual parameters in scientific visualization systems. He explains the process of mapping abstract data values into visual based on transfer functions, clarifies the terms of pre- and postclassification, and introduces the state-of-the-art user int- faces for the design of transfer functions.

Author : Walter Zimmermann,Steve Cunningham,Mathematical Association of America. Committee on Computers in Mathematics Education
Publisher : MAA Press
Page : 246 pages
File Size : 47,7 Mb
Release : 1991
Category : Mathematics
ISBN : UCSC:32106010742622

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Visualization in Teaching and Learning Mathematics by Walter Zimmermann,Steve Cunningham,Mathematical Association of America. Committee on Computers in Mathematics Education Pdf

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.

Author : Lars Linsen,Hans Hagen,Bernd Hamann
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 49,7 Mb
Release : 2007-12-27
Category : Medical
ISBN : 9783540726302

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Visualization in Medicine and Life Sciences by Lars Linsen,Hans Hagen,Bernd Hamann Pdf

Visualization technology is becoming increasingly important for medical and biomedical data processing and analysis. The interaction between visualization and medicine is one of the fastest expanding fields, both scientifically and commercially. This book discusses some of the latest visualization techniques and systems for effective analysis of such diverse, large, complex, and multi-source data.