# 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)

Back to Gallier Homepage