Classical and Quantum Mechanics introduces advanced concepts in classical mechanics and then links these to the theory of quantum mechanics. This course begins with introducing the concepts of degrees of freedom and least action. Subsequent topics include Lagrangians and Hamiltonians, Legendre transformations and Poisson brackets, with a focus on solving example problems from various branches of physics. Building on this knowledge, the concept of quantum theory is introduced, including wave and matrix mechanics, operators and observables. Example problems are solved for one-dimensional potentials and time evolution of finite state systems.

The topics covered are essential prerequisites for advanced studies in physics. This course will approach the subjects with a high level of mathematical rigour in order to give students a solid grounding in the mathematical tools used in advanced physics, including at a postgraduate level.