CIS 515, Fall 2016

Some Course Notes and Slides

Notes

  • ** Basics of Algebra and Analysis (manuscript) (html)
  • ** Fundamentals of Linear Algebra and Optimization; Some Notes (pdf)
  • ** Applications of Scientific Computation; EAS205, Some Notes (pdf)
  • ** Spectral Theory of Unsigned and Signed Graphs
    Applications to Graph Clustering: a Survey (pdf)
  • ** Logarithms and Square Roots of Real Matrices (pdf)
  • ** Chapters 1, 2, 3 on Mathematical Reasoning and Logic, functions, relations, from "Discrete Mathematics, Second Edition:" (pdf)
  • ** Chapter 5 from GMA (2nd edition); Basics of Projective Geometry (pdf)
  • ** Chapter 9 from GMA (2nd edition); The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf)
  • ** Chapter 10 from GMA (2nd edition); Dirichlet-Voronoi Diagrams and Delaunay Triangulations (pdf)

    Slides

  • ** Some Matlab code
  • bezier-parabola (m)
  • bezier-cubic (m)
  • bezier function, degree 2 (m)
  • bezier function, degree 3 (m)
  • Lemniscate (m)
  • Solving a triangular system by backsubstitution, v1 (m)
  • Solving a triangular system by backsubstitution, v2 (m)
  • Solving a triangular system; some examples (m)
  • Computes a point on a curve using de Casteljau's algorithm (m)
  • Linear (affine!) interpolation (m)
  • To display the construction of a point using de Casteljau's algorithm (m)
  • Running de Casteljau's algorithm; examples (m)
  • The Steiner Roman surface (m)

  • ** Problems, Questions and Motivations; Vector Spaces, Bases, Linear Maps   (slides, pdf)
  • ** Matrices and Linear Maps   (slides, pdf)
  • ** Direct Sums, Affine Maps, The Dual Space, Duality   (slides, pdf)
  • ** Gaussian, LU, and Choleski Decompositions   (slides, pdf)
  • ** Determinants and Applications   (slides, pdf)
  • ** Determinants "a la Michael Artin"   (slides, pdf)
  • ** Normed spaces and matrix norms; condition number of a matrix   (slides, pdf)
  • ** Eigenvectors and Eigenvalues   (slides, pdf)
  • ** Iterative Methods for Solving Linear Systems   (slides, pdf)
  • ** Euclidean Spaces   (slides, pdf)
  • ** QR-Decomposition for Arbitrary Matrices   (slides, pdf)
  • ** Basics of Hermitian Geometry   (slides, pdf)
  • ** Spectral Theorems in Euclidean and Hermitian Spaces   (slides, pdf)
  • ** Introduction to the Finite Elements Method   (slides, pdf)
  • ** Singular Value Decomposition (SVD) and Polar Form   (slides, pdf)
  • ** Applications of SVD and Pseudo-Inverses   (slides, pdf)
  • ** Quadratic Optimization Problems   (slides, pdf)

    Slides on the spectral theory of unsigned and signed graphs
    with applications to graph clustering

  • ** Graphs and graph Laplacians   (slides, pdf)
  • ** Spectral Graph Drawing   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; 2 clusters   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; K clusters   (slides, pdf)
  • ** Graph Clustering using Normalized Cuts; Finding a discrete solution   (slides, pdf)
  • ** Signed Graphs ;   (slides, pdf)
  • ** Graph Clustering Using Ratio Cuts   (slides, pdf)
  • ** Appendix; Rayleigh Ratios, Rayleigh-Ritz Theorem, Courant-Fischer Theorem   (slides, pdf)

    Other slides

  • ** Rotation Logic (talk given at the Robotics Symposium, Sept. 27, 2013) (slides, pdf)
  • ** Dirichlet-Voronoi Diagrams and Delaunay Triangulations (pdf)
  • ** The Quaternions and the Spaces S^3, SU(2), SO(3), and RP^3 (pdf)

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    published by:

    Jean Gallier