Organizer: Jonathan M Borwein · Canadian Mathematical Society
Co-Organizer: José F Rodrigues · University of Lisbon
This symposium intends to present some of these exciting developments and tools for mathematical communication and computation, with an emphasis on distributed computing and advanced visualization.
Jonathan M Borwein · CECM · Simon Fraser University
In our information dominated society the favoured modes of information presentation are shifting away from primarily verbal modes and placing more emphasis on visual information presentation. As a result, a better understanding of information visualization is becoming essential as is extending graphic representation by the inclusion of different sensory modalities (movement, sound, tactile processes) within the visualization process thus enhancing interpretation and meaning.
(28.5M)
Video-based Hypermedia for Communicating Mathematics I
Teresa Chambel and José F Rodrigues · University of Lisbon
Visualization of the representation of ideas, principles or problems by images has always been an essential aid in communicating mathematical concepts. The combination of video and computer animation is a powerful visualization tool that grabs the viewer's attention, capitalizes on the viewer's intuition, portrays a large quantity and diversity of information in a brief period of time, and conveys mathematics in a rich cultural context.
Video-based hypermedia technology greatly enhances this tool, by providing flexible interactive mechanisms that integrate and navigate different types of mediavideo, animation, and tex in ways that can be adapted to a great variety of learning styles and situations.
In this first part, we present and discuss the main concepts involved in the communication and learning of mathematics with video-baased hypermedia spaces, and show some examples.
(1.9M)
Konrad Polthier · Technical University Berlin
The internet will soon provide enough bandwidth to enable true collaboration of researchers on joint interactive experiments including online visualization. Mathematical webservices are set up at different locations offering an unprecedented wealth of computational resources and databases. How will these facilities change the way of mathematical research?
In education and communication, for example, electronic blackboards allow the seamless integration of distributed numerical software experiments and interactive visualization with standard university courses while at the same time allowing the transmission the course to remote location. Is mathematical software prepared to satisfy these needs?
This talk will show several fascinating new developments and applications in mathematical research.
Jonathan M Borwein · CECM · Simon Fraser University
This presentation focusses on collaboration and visualization in the context of distributed and grid computing.
(14.8M)
Video-based Hypermedia for Communicating Mathematics II
José F Rodrigues · University of Lisbon
The combination of video and computer animation, as a powerful visualization tool that portrays a large quantity and diversity of information in a brief period of time, with text conveys mathematics in a richer and more stimulating cultural context. We show with examples how video based hypermedia technology greatly enhances this tool, by providing flexible interactive mechanisms that integrate and navigate different types of mediavideo, animation, and text in ways that can be adapted to a great variety of learning styles and situations.
Using the video and workbook materials from 'The Story of Pi', produced by Project MATHEMATICS!, as well as other films, further enhanced by interactive links to a rich variety of related source materials, we present concrete examples of visual communication of mathematical concepts and objects.
(7M)
Robert G Scharein · SFU CoLab and NewMIC
We present a new too, coKnotPlot, designed for remote collaboration in mathematical knot theory. coKnotPlot is an extension of the full featured knot theory software package, KnotPlot, which was designed for use by a single user on a standard desktop computer. coKnotPlot extends KnotPlot's display and interaction methodes to include immersive virtual reality using the CAVElib ™ VR library. This allows for full stereoscopic 3D visualization and interaction techniques using a six degree of freedom handheld 'wand' device.
Since knots are the primal 3D technology, we find that interacting with them in this environment is much more natural than via the limited interface provided by most computers. Another enhancement to KnotPlot (the 'co' part of 'coKnotPlot'), allows (two or more) knot theorists to collaborate simultaneously at a distance, while sharing the same data set. In its simplest configuration, one user interacts with coKnotPlot much as they would if they were using KnotPlot; the knot geometry data, viewpoint, and other (co)KnotPlot state is communicated using a TCP/IP socket to the remote user(s), driving their machine(s) in a 'master-slave' relationship. In addition, 'annotation' information can be sent to the remote user(s) to direct their attention to a particular item of interest. We have a simple protocol to 'hand over' control to another user.
coKnotPlot is designed to work in situations where the computers used by the participants have widely differing capabilities, so it is necessary to have reasonable default behavior for less visually rich or interaction limited computing environments. since we are still investigating the possibilities of remote collaboration, we support several different interaction protocols, some less 'polite' than the previously mentioned method. Other approaches permit users to take control at any time, or even for everyone to have simultaneous control (imagine a 'tug-of-war'). Experiments are on-going involving real knot theorists to see which of the different approaches is most useful for actual research problems.
We will conclude our presentation with a demonstration of coKnotPlot in action (modulo no Internet problems), working across two continents, using two different computing environments (a local laptop computer and the Immersive Media Laboratory at NewMIC).
(3.2M)
(The 'Making of' MESH – a New Mathematical Video).
Beau Janzen · Los Angeles and Konrad Polthier · Technical University Berlin
This talk is a companion to 'Online Visualization and Mathematical Web Services: I'. In recent years mathematical videos have become an increasingly important and widely available tool for mathematical education and research. MESH is a new fully computer generated video which introduces polyhedral meshes and shows their role in geometry, numerics and computer graphics including some latest techniques.
MESH targets a broad mathematically interested audience. The talk gives technical background information on the development phases of the video, on the mathematical topics, and the integration of mathematical visualizations with high-end animation environments.
For more information, please contact Jonathan Borwein.