Algebraic and Geometric Methods in Engineering and Physics — 1^st Semester 2023/2024

Announcements

Homework 9 is due on November 29.

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 suggestions of such applications here and here.

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.

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

• Homework 1 (due on September 20)
• Homework 2 (due on September 27)
• Homework 3 (due on October 4)
• Homework 4 (due on October 11)
• Homework 5 (due on October 18)
• Homework 6 (due on October 25)
• Homework 7 (due on November 15)
• Homework 8 (due on November 22)
• Homework 9 (due on November 29)

Exams

• Exam 1

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

• 2020/2021
• 2019/2020