My minor in mathematics focuses on rigorous proof, abstraction, and structural thinking. Through complex analysis, topology, and other advanced coursework, I strengthened my ability to navigate formal systems and construct precise arguments. Mathematics functions as the language in which the laws of physics are formulated and understood.
This graduate-level course emphasized rigorous proof, analytic structure, and the behavior of functions in the complex plane. Through topics such as contour integration, analytic continuation, and conformal mapping, I developed a deeper understanding of how local properties determine global structure. The course strengthened my ability to construct precise arguments within abstract frameworks.
This graduate-level course, aligned with Ph.D.-level qualifying standards, focused on approximation theory, error analysis, and computational methods for solving mathematical problems. Emphasis was placed on stability, convergence, and the structural behavior of algorithms. The course reinforced the connection between theoretical mathematics and practical computation.
Linear algebra provided the structural language for understanding transformations, vector spaces, and eigenvalue problems that arise throughout physics and applied mathematics. The course emphasized rigorous reasoning together with concrete computational tools such as matrix decompositions and spectral analysis. Topics included linear transformations, eigenvalues and eigenvectors, diagonalization, and the role of vector spaces in modeling dynamical systems. These ideas later connected directly to stochastic processes and Markov chains, where matrix structure governs the long-term behavior of probabilistic systems.