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In mathematics, a cyclic polytope, denoted C(n, d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd, where n is greater than d. These polytopes were studied by Constantin Carathéodory, David Gale, Theodore Motzkin, Victor Klee, and others. They play an important role in polyhedral combinatorics: according to the upper bound theorem, proved by Peter McMullen and Richard Stanley, the boundary Δ(n,d) of the cyclic polytope C(n,d) maximizes the number fi of i-dimensional faces among all simplicial spheres of dimension d − 1 with n vertices.
Károly Bezdek is a Hungarian-Canadian mathematician. He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada. Also he is a professor of mathematics at the University of Pannonia in Veszprém, Hungary. His main research interests are in geometry in particular, in combinatorial, computational, convex, and discrete geometry. He has authored 3 books and more than 130 research papers. He is a founding Editor-in-Chief of the e-journal Contributions to Discrete Mathematics (CDM).
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Lectures in Geometric Combinatorics is a textbook on polyhedral combinatorics. It was written by Rekha R. Thomas, based on a course given by Thomas at the 2004 Park City Mathematics Institute, and published by the American Mathematical Society and Institute for Advanced Study in 2006, as volume 33 of their Student Mathematical Library book series.
Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra. It was written by Branko Grünbaum, with contributions from Victor Klee, Micha Perles, and G. C. Shephard, and published in 1967 by John Wiley & Sons. It went out of print in 1970. A second edition, prepared with the assistance of Volker Kaibel, Victor Klee, and Günter M. Ziegler, was published by Springer-Verlag in 2003, as volume 221 of their book series Graduate Texts in Mathematics.
Roswitha Blind is a German mathematician, specializing in convex geometry, discrete geometry, and polyhedral combinatorics, and a politician and organizer for the Social Democratic Party of Germany in Stuttgart.
References
- 1 2 "Mohamed Omar". Mathematically Gifted & Black. Retrieved 2020-06-10.
- ↑ Omar, Mohamed (2007). "Combinatorial Approaches To The Jacobian Conjecture". Thesis.
- ↑ "UC Davis Mathematics - Degree Recipients". University of California Davis - Mathematics Department. Archived from the original on 2019-09-26. Retrieved 2020-06-10.
- ↑ Omar, Mohamed (2011). "Applications of Convex and Algebraic Geometry to Graphs and Polytopes". Dissertation.
- 1 2 3 "Omar, Mohamed | College News". Harvey Mudd College. Retrieved 2020-06-10.
- ↑ "Testimonials". Bridge to Enter Advanced Mathematics. Retrieved 2020-06-10.
- ↑ "Mathcamp 2012 Staff". www.mathcamp.org. Retrieved 2020-06-10.
- ↑ "Mathematics Foundation of America". 2018-07-01. Archived from the original on 2018-07-01. Retrieved 2020-06-10.
- ↑ Klawe, Maria. "Why We Need More Students Of Color In Math Enrichment Programs". Forbes. Retrieved 2020-06-10.
- ↑ Lamb, Evelyn. "Mohamed Omar's Favorite Theorem". Scientific American Blog Network. Retrieved 2020-06-10.
- ↑ "Donut". donut.caltech.edu. Retrieved 2020-06-10.
- ↑ "Mohamed Omar, Alder Award 2018 | Mathematical Association of America". www.maa.org. Retrieved 2020-06-10.
- ↑ "2020 Inaugural Class of Karen EDGE Fellows".
- ↑ "Mohamed Omar Awarded Inaugural Claytor-Gilmer Fellowship" (PDF). Notices of the American Mathematical Society. 68: 2000.
