discrete geometry
san francisco state university
universidad de los andes
federico ardila
2010
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The following is a list of books and other resources that you might find helpful. I have most of these in my office, in case you want to borrow them.
Our main sources for the course are:
o Lectures on polytopes / Gunter Ziegler
o Computing the continuous discretely : integer-point enumeration in polyhedra / Matthias Beck, Sinai Robins.
o Lecfure notes on hyperplane arrangements / Richard Stanley
A great way to learn about recent developments and find open problems is to visit the math arXiv, where many researchers post their papers before they are officially published. You can search for any keywords that interest you.
Some other related books:
o Oriented matroids / A. Bjorner, M. Las Vergnas, B. Sturmfels, N. White, G. Ziegler.
o An introduction to convex polytopes / Arne Bronsted.
o Regular complex polytopes / H. S. M. Coxeter.
o Triangulations / J. De Loera, J. Rambau, F. Santos.
o Handbook of discrete and computational geometry / edited by Jacob E. Goodman and Joseph O'Rourke.
o Polytopes : combinatorics and computation / Gil Kalai, Gunter M. Ziegler, editors.
o Lectures on discrete geometry / Jiri Matousek.
o Combinatorial optimization / A. Schrijver
o Abstract regular polytopes / Peter McMullen, Egon Schulte.
o Grobner bases and convex polytopes / Bernd Sturfmels
o The cube -- a window to convex and discrete geometry / Chuanming Zong.
Some books focusing mostly on 2 and 3 dimensions:
o Research problems in discrete geometry / Peter Brass, William Moser, Janos Pach.
o Combinatorial geometry / Janos Pach, Pankaj K. Agarwal.
o An adventure in multidimensional space : the art and geometry of polygons, polyhedra, and polytopes / Koji Miyazaki.