CIS 515, Fall 2015
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)
iterate1
(m)
iterate2
(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" (from EAS205)  
(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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