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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...

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...

Visualization research aims to provide insight into large, complicated data sets and the phenomena behind them. While there are di?erent methods of reaching this goal, topological methods stand out for their solid mathem- ical foundation, which guides the algorithmic analysis and its presentation. Topology-based methods in visualization have been around since the beg- ning of visualization as a scienti?c discipline, but they initially played only a minor role. In recent years, interest in topology-basedvisualization has grown andsigni?cantinnovationhasledto...

This book contains 13 peer-reviewed papers resulting from the second workshop on "Topology-Based Methods in Visualization", held 2007 in Grimma near Leipzig, Germany. It presents the state of the art of topology-based visualization research.