CIS 700, Spring 2002

More Advanced Geometric Methods in Computer Science

Some Slides and Notes

• Hermitian Spaces (slides)
• 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
• Differential geometry of curves, osculating circles, curvature, osculating plane, etc., part I
• Differential geometry of curves, normal plane, rectifying plane, torsion, Frenet frame, etc., part II
• Differential geometry of curves, more on Frenet frames of nD curves, part III (ps) (pdf)
• Differential geometry of surfaces, tangent plane, normal, first fundamental form, part I (ps) (pdf)
• Differential geometry of surfaces, normal curvature, second fundamental form, geodesic curvature, Christoffel symbols, part II (ps) (pdf)
• Differential geometry of surfaces, principal curvatures, Gaussian curvature, mean curvature, part III (ps) (pdf)
• Differential geometry of surfaces, The Gauss map, the Dupin indicatrix, the Theorema Egregium of Gauss, part IV (ps) (pdf)
• Differential geometry of surfaces, lines of curvature, geodesic torsion, asymptotic lines, part V (ps) (pdf)
• Differential geometry of surfaces, geodesic lines, local Gauss-Bonnet theorem, covariant derivatives, part VI, VII (ps, part VI) (pdf)
• Covariant derivatives, parallel vector fields, parallel transports, geodesics revisited, part VII (ps)
• Isometries of Hermitian Spaces and Hilbert Spaces (notes)
• Clifford algebras, Clifford groups, and the groups Pin and Spin (notes) (ps) (pdf)
• Bibliography (from book))
• Basic Linear Algebra (Appendix 1)
• Determinants (Appendix 2)