CIS 610, Fall 2003

Advanced Geometric Methods in Computer Science

Some Slides and Notes

• Questions, Motivations, Problems
• Basics on Affine spaces I (slides)
• Basics on Affine spaces II, Convex Sets, a first look (slides)
• Convex sets: A deeper look (slides) (NEW!)
• Convex sets, Polyhedra and Polytopes: A deeper look (Notes) (ps) (pdf) (NEW!)
• Euclidean Geometry (Gram-Schmidt) I (slides)
• Euclidean Geometry (linear isometries, The Groups O(n), SO(n), QR-decomposition, the Cartan-Dieudonne' theorem) II (slides)
• Euclidean Geometry (linear isometries, QR by Householder matrices, affine isometries, the Groups Is(n), SE(n), fixed points, Cartan-Dieudonne' thm for rigid motions, flips) III (slides)
• Euclidean Geometry (Orientation, angles, volume forms, cross products) IV (slides)
• Euclidean Geometry (Quaternions and rotations in SO(3) and SO(4)) V (slides)
• Polyhedra and Polytopes: A deeper look (slides) (NEW!)

• Zvi Har'el's web site
• The Uniform Polyhedra (web site)
• Polyhedra Collection (Bulatov web site)
• Encyclopedia of Polyhedra (George Hart web site)
• George Hart's web site
• Paper models of polyhedra
• Polyhedra
• Polyhedra Pastimes
• Unfolding Polyhedra
• Tom Getty's Polyhedra

• Voronoi Diagrams (slides)
• Hermitian Spaces (slides)
• Isometries of Hermitian Spaces and Hilbert Spaces (notes) (NEW!)
• Clifford algebras, Clifford groups, and the groups Pin and Spin (notes) (ps) (pdf) (NEW!)
• Spectral Theorems (Symmetric, Skew-Symmetric, Normal matrices) (slides)
• Polar Form and SVD (slides)
• Least squares, Pseudo-inverses, Minimization of quadratic functions using Lagrange multipliers
• Lie Groups and Lie Algebras, the exponential map, part I
• Lie Groups and Lie Algebras, the exponential map, part II
• Notes on Group Actions, Manifolds, Lie Groups and Lie Algebras (NEW!)
• Bibliography (from book))
• Basic Linear Algebra, Determinants