Mathematical Physics

Classical mechanics is the study of the motion of macroscopic bodies under the influence of forces. You will understand Newtonian, Lagrangian, and Hamiltonian formulations, enabling you to model and solve the dynamics of particles, rigid bodies, and oscillating systems.

Electrodynamics is the study of the interactions between electric charges, currents, and electromagnetic fields. You will understand Maxwell's equations, electromagnetic waves, and radiation, enabling you to analyze physical phenomena ranging from simple circuits to relativistic particle dynamics.

General relativity is the geometric theory of gravitation developed by Albert Einstein. Learners will understand how mass and energy curve spacetime, governing the motion of cosmic bodies, gravitational waves, and the physics of black holes.

Hamiltonian mechanics reformulates classical mechanics using phase space and conservation laws. Learners will understand how to model complex physical systems, apply Hamilton's equations, and transition from classical physics to quantum mechanics.

Quantum field theory combines classical field theory, special relativity, and quantum mechanics. Learners will understand the mathematical framework governing subatomic particles, quantum fields, and the fundamental forces of the Standard Model.

Quantum mechanics is the study of physical phenomena at the atomic and subatomic scales. Learners will understand wave-particle duality, the Schrödinger equation, quantum states, and how to calculate probabilities for physical observables.

Special relativity is the physics of objects moving at speeds approaching the speed of light. Learners will understand time dilation, length contraction, Lorentz transformations, and the equivalence of mass and energy.

Statistical mechanics applies probability theory to large assemblies of microscopic particles. Learners will understand how macroscopic thermodynamic properties, like temperature and entropy, emerge from the microscopic states of individual atoms and molecules.

String theory is a theoretical framework where point-like particles are replaced by one-dimensional vibrating strings. Learners will understand how this model attempts to unify quantum mechanics with general relativity into a single theory.

Symplectic geometry is the branch of differential geometry that studies symplectic manifolds. Learners will understand the mathematical structure of phase spaces, classical mechanics, and the geometric formulation of Hamiltonian systems.