Polyhedral group

Algebraic and Geometric Methods in Engineering and Physics — 1st Semester 2024/2025




Lecturer: José Natário
Email: jnatar@math.tecnico.ulisboa.pt
Office: Mathematics Building, 4th floor, room 4.29
Classes: Tuesdays and Wednesdays at 10:00 in classrooms E5 and Q4.7
Office Hours:  Drop by my office or send me an email


Announcements

Homework 10 is due on December 4.



Syllabus

Topics 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.



Bibliography

We will use these lecture notes, which will be updated as the course progresses. See the bibliography in the notes for more references.

See also the abbreviated lectures notes.



Grading Policy

Homework: 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

  • Homeworks 13 and 14 will jointly be a two-page (excluding figures), computer-typed essay on some application of Algebra, Geometry or Topology to Engineering or Physics. You can find examples of such applications here and here.



Exams

You can see more exams on the course webpages from previous years:
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