Nonlinear Algebra
The toolbox of linear algebra is often not sufficient to meet the nonlinear world. Polynomials offer a natural generalization. The course offers participants hands-on investigations (via both proofs and coding) of wide classes of algebraic optimization problems and algebraic inverse problems, coming from various fields of engineering (robotics, computer vision, deep learning, etc).
The course covers: Overview of the necessary background in algebra/algebraic geometry. Solving polynomial systems with symbolic and numeric methods, optimization over semi-algebraic sets, tensor geometry, metric algebraic geometry. Applications of the theory to solve problems within engineering, machine learning, data science, AI.
Besides the strict requirements for eligibility, the knowledge from the course Mathematics III - Abstract Algebra (MM5020) is beneficial, but not strictly necessary.
The course consists of one module.
Teaching Format
Instruction consists of lectures and exercises sessions, and laboratories.
Assessment
Assessment takes place through written exam and written and oral presentation of the laboratory project.
