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Introduces affine varieties and covers morphisms between them and their coordinate rings.
Covers the concept of affine transformations in functions, including shifting and compressing functions.
Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.
Covers Gaussian random variables, affine transformations, and linear systems driven by Gaussian noise in multivariable control.
Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.
On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.
Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.
Explores data augmentation as a key regularization method in deep learning, covering techniques like translations, rotations, and artistic style transfer.
Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.
