A rigorous construction of the definition of symplectic manifolds, portraying the most significant properties ensuing, particularly in their connections to Hamiltonian and Lagrangian systems. [7 pgs]

A self-contained presentation of Lagrangian and Hamiltonian mechanics [9 pgs]

A succint overview of Quantum Mechanics presenting foundational concepts of the theory and an introduction to its mathematical formalism [6 pgs]