**Random Sampling**: Uniform Random Sampling on common shapes**Spectral Methods 101**: Intro to spectral methods, specifically Chebyshev collocation method. Multi domain methods. Nonlinear problems**MPI on windows with MINGW**: Instructions to setup an MPI compiler and runtime on windows using mingw for C,C++ and fortran**Introduction to Multigrid methods**: The Multigrid method in two dimensions. The V cycle algorithm. Full Multigrid algorithm. Using V cycle as a preconditioner in Python**Mixed C/Fortran Programming**: A few code examples demonstrating mixed C and Fortran programming. I will cover how to call a C function from Fortran and how to call a Fortran function in C.