Algebraic and Geometric Methods in Engineering and Physics — 1^{st} Semester 2023/2024
AnnouncementsThe final grades are now available (see side bar). If you want to take a look at your graded exams come to my office at your convenience. SyllabusTopics of algebra and applications: Groups, rings and fields. Group actions. Representations of finite groups. Applications: RSA algorith in information security and vibrations of symmetric structures using representations of finite groups. Topics of geometry and topology and applications: Metric spaces and topological spaces. Simplicial complexes and homology. Manifolds, tensor fields and differential forms. Riemannian manifolds. Lie derivatives and symmetry group of a tensor field. Aplications: data science and persitent homology, fluid mechanics. Lie algebras, Lie groups and applications: Lie groups and Lie algebras. Lie group actions on manifolds. Representations of complex semisimple Lie algebras. Aplications: cosmological models, particle physics and theories of unification. BibliographyWe will use these lecture notes, which will be updated as the course progresses. See the bibliography in the notes for more references. Grading PolicyHomework: Makes up 50% of the grade. Late homework will not be accepted. Final exam: Makes up 50% of the grade. Can be retaken if necessary. Homework
Essays
ExamsYou can see more exams on the course webpages from previous years: |