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)
 Convex sets, Polyhedra and Polytopes: A deeper look (Notes)
(ps)
(pdf)

Euclidean Geometry (GramSchmidt) I (slides)

Euclidean Geometry (linear isometries, The Groups O(n), SO(n),
QRdecomposition, the CartanDieudonne' theorem) II (slides)

Euclidean Geometry (linear isometries,
QR by Householder matrices,
affine isometries, the Groups Is(n), SE(n),
fixed points, CartanDieudonne' 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)

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)

Clifford algebras, Clifford groups, and the groups
Pin and Spin (notes)
(ps)
(pdf)

Spectral Theorems (Symmetric, SkewSymmetric, Normal matrices) (slides)

Polar Form and SVD (slides)

Least squares, Pseudoinverses, 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

Bibliography (from book))

Basic Linear Algebra, Determinants