Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
In geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines. Problems of counting the features of arrangements have been studied in discrete geometry, and computational geometers have found algorithms for the efficient construction of arrangements.
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.
The Alan T. Waterman Award, named after Alan Tower Waterman, is the United States's highest honorary award for scientists no older than 40, or no more than 10 years past receipt of their Ph.D. It is awarded on a yearly basis by the National Science Foundation. In addition to the medal, the awardee receives a grant of $1,000,000 to be used at the institution of their choice over a period of five years for advanced scientific research.
Kurt Mehlhorn is a German theoretical computer scientist. He has been a vice president of the Max Planck Society and is director of the Max Planck Institute for Computer Science.
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.
Joseph O'Rourke is the Spencer T. and Ann W. Olin Professor of Computer Science at Smith College and the founding chair of the Smith computer science department. His main research interest is computational geometry.
János Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.
Kenneth Lee Clarkson is an American computer scientist known for his research in computational geometry. He is a researcher at the IBM Almaden Research Center, and co-editor-in-chief of Discrete and Computational Geometry and of the Journal of Computational Geometry.
David Galer Kirkpatrick is a Professor Emeritus of computer science at the University of British Columbia. He is known for the Kirkpatrick–Seidel algorithm and his work on polygon triangulation, and for co-inventing α-shapes and the β-skeleton. He received his PhD from the University of Toronto in 1974.
In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel (1983). The alpha-shape associated with a set of points is a generalization of the concept of the convex hull, i.e. every convex hull is an alpha-shape but not every alpha shape is a convex hull.
Emmerich (Emo) Welzl is a computer scientist known for his research in computational geometry. He is a professor in the Institute for Theoretical Computer Science at ETH Zurich in Switzerland.
Franz Aurenhammer is an Austrian computational geometer known for his research in computational geometry on Voronoi diagrams, straight skeletons, and related structures. He is a professor in the Institute for Theoretical Computer Science of Graz University of Technology.
Dmitry Feichtner-Kozlov is a Russian-German mathematician.
Tamal Krishna Dey is an Indian mathematician and computer scientist specializing in computational geometry and computational topology. He is a professor at Purdue University.
Yusu Wang is a Chinese computer scientist and mathematician who works as a professor at the Halıcıoğlu Data Science Institute at the University of California, San Diego. Her research concerns computational geometry and computational topology, including results on discrete Laplace operators, curve simplification, and Fréchet distance.
In geometry, the zone theorem is a result that establishes the complexity of the zone of a line in an arrangement of lines.
