Mathematics for Robotics

1 Course Unit

This course is an introductory graduate level applied mathematics course for robotics. The topics to be covered in the course include: Derivatives and Ordinary Differential Equations (e.g. gradients, Jacobians, Hessians, and Taylor expansions), Linear Algebra (e.g., vector spaces, orthogonal bases, projection theorem, least squares, matrix factorizations, vector and matrix calculus, norms, matrix decompositions, and spectral analysis), Optimization Theory (e.g., convergent sequences, contraction mappings, Newton Raphson algorithm, local vs global convergence in nonlinear optimization, convexity, linear and quadratic programs), and Probabilities and Information Theory (e.g., Kalman filters and underlying probabilistic concepts and Gaussian Process Regression). Prerequisite: Students are expected to have basic matrix algebra (e.g., matrix addition, multiplication, inversion, rank, and computing eigenvalues and eigenvectors), basic statistics and probability theory (e.g., computing means, variances, and conditional probabilities), simple properties of complex numbers (e.g., addition, multiplication, magnitude, and direction), basic programming (e.g., plotting, manipulation of arrays, writing for and while loops, or finding help). 1 Course Unit