Academic Team
Course Content
Type: Optional– PEC Track – 1st Trimester
This course provides a solid foundation in the key mathematical tools used in modern theoretical physics, with a focus on differential geometry, group theory, and probability & statistics. Students will not only learn the theory but also apply these methods to real physical problems and data analysis. Emphasis is placed on mathematical reasoning, problem-solving, and collaborative work.
Main Topics
- Differential Geometry – Manifolds, tensor algebra, vector bundles, connections, curvature, Riemannian geometry, and basics of manifold topology.
- Group Theory – Lie groups and algebras, representation theory, classification of algebras, and applications to symmetries in physics (Poincaré, Lorentz, internal symmetries).
- Probability & Statistics – Probability distributions, estimators, hypothesis testing, Bayesian statistics, and Monte Carlo simulations.
Reading List
Group Theory:
1) H. Georgi: “Lie Algebras in Particle Physics”,
2) H.F. Jones: “Groups, Representations and Physics”
3) J.F. Cornwell: “Group Theory in Physcis”, Vols. 1,2
Differential Geometry:
1) Nash, Sen: “Topology and Geometry for Physicists”
2) M. Nakahara: “Geometry, Topology and Physics”
Teaching Plan Information
Course Schedule
