I have created this course (a flyer for Fall 2022) with lecture notes from my recent offerings available below. Not all of them are covered in a single offering. Hopefully, you will find some of them useful. (The notes on several topics have been cited often in research papers by others.)

1. Projective geometry
   • Homogeneous coordinates (pdf)
   • Plücker coordinates (pdf)
   • Homogeneous transformations (pdf)
   • Perspective projection (pdf)
   • Classification of projections (pdf)
2. Rotations 
   • Rotations in the space (pdf)
   • Quaternions (pdf)
   • Dual quaternions (pdf)
3. Solution of systems of equations
   • Solution of linear equations (pdf)
   • Singular value decomposition (pdf)
   • Solution of nonlinear equations (pdf)
   • Polynomial evaluation (pdf)
   • Polynomial interpolation (pdf)
   • Roots of polynomials (pdf)
   • Roots of a polynomial system (pdf)
4. Differential geometry
   • Curves (pdf)
   • Curvature (pdf)
   • Closed curves and space curves (pdf)
   • Arbitrary-speed curves (pdf)
   • Algebraic curves (pdf)
   • Surfaces (pdf)
   • Surface curves and fundamental forms (pdf)
   • Principal curvatures (pdf)
   • Gaussian and mean curvatures (pdf)
   • Geodesics (pdf)
5. Data fitting and approximation
   • Least squares method (pdf)
   • Nonlinear least squares (pdf)
   • Fourier series (pdf)
   • Fast Fourier transform (pdf)
6. Estimation
   • Probability (pdf)
   • Recursive least squares (pdf)
   • Kalman filtering (pdf)
7. Optimization
   • Linear programming (pdf)
   • The Simplex method (pdf)
   • Nonlinear optimization (pdf)
   • Lagrange multipliers (pdf)
   • Calculus of variations (pdf)
   • Variational problems (pdf)