Course

1. Introduction to Mathematica. (1a) Exercises: Graphs and movies with Mathematica

Functional Derivatives, Gamma and Zeta

Functional Derivatives and Green's Functions

Path Integrals and Distributions

Irreducible representation of SU(N) and Young Tableau

Classification of all semi-simple Lie algebra

Contact geometry: Hamiltonian mechanics revised, Example of field theory: Vibrations of a string

All the irreducible representation of SU(2)

Canonical transformations, Noether's theorem, Hidden symmetry of Kepler motion, Nambu mechanics

Structure constants, Adjoint Representation of Lie algebra

Constraints, Symplectic geometry, Hamilton's equations revised

From quantum mechanics to Lie groups, Representation of groups, Important Lie group examples

Hamilton-Jacobi theory, Integrable  systems