This project presents a rigorous derivation of the Einstein field equations using the principle of stationary action. Starting from the Einstein Hilbert action, I carefully vary both the Ricci scalar and the metric determinant.

The derivation includes full proofs of key identities such as the Palatini identity and Jacobi’s formula, along with a precise treatment of divergence terms and boundary contributions.

This project explores the visualization of finite cyclic groups and their direct products using MATLAB. Subgroup structures, Cayley tables, and geometric patterns are visualized to reveal algebraic structure.

The work emphasizes how visual representations can support intuition and structural understanding in abstract algebra.

This reading project studies hyperbolic geometry on the upper half plane, including conformal maps, horocycles, and Busemann cocycles.

The project also examines the action of Fuchsian groups and the construction of Dirichlet domains, emphasizing geometric and dynamical perspectives.