A growing ecosystem of interconnected courses designed for research students.
A foundational course introducing the fundamentals of differential calculus. We will discuss concepts such as limits, derivatives and their respective rules.
Go to Differential Calculus →A foundational course introducing the fundamentals of integral calculus. We will discuss concepts such as Riemann sums, integration and their respective rules.
Go to Integral Calculus →A foundational course introducing first- and second-order ODEs, linearity, homogeneity, separability, and solution techniques. This course provides the conceptual backbone for PDEs, dynamical systems, and operator theory.
Go to ODE Course →An introduction to randomness, distributions, expectation, variance, independence, sampling, and inference. These ideas support data science, stochastic modeling, and uncertainty quantification.
Go to Probability & Statistics Course →A structural view of vector spaces, linear transformations, eigenvalues, eigenvectors, and matrix decompositions. This course underpins nearly every other course in the ecosystem.
Go to Linear Algebra Course →A study of diffusion, waves, and potential theory through separation of variables, Fourier methods, and eigenfunction expansions. Strongly linked to ODEs and functional analysis.
Go to PDE Course →An applied course on discretization, stability, convergence, and numerical simulation of fluid flows. Builds on PDEs, linear algebra, and numerical analysis.
Go to CFD Course →A rigorous exploration of normed spaces, operators, spectra, and infinite-dimensional analysis. Essential for modern PDE theory, operator-theoretic modeling, and advanced research.
Go to Functional Analysis Course →A foundational course introducing set theory, constructive proof and proof by contradiction.
Go to Mathematical Proof Course →A foundational course introducing the fundamentals of measure theory.
Go to Measure Theory Course →A foundational course introducing the fundamentals of quantum mechanics.
Go to Quantum Mechanics Course →A foundational course introducing the fundamentals of quantum mechanics.
Go to Topology Course →A foundational course introducing the fundamentals of complex analysis.
Go to Complex Analysis Course →A foundational course introducing the fundamentals of real analysis.
Go to Real Analysis Course →