In this presentation, we will demonstrate the utilization of some common applied mathematics techniques in the field of computational quantum chemistry.   First, we will show how simple matrix diagonalization techniques are used in the Hueckel molecular orbital theory for predicting the stability of aromatic molecules, and in the computation of absorption spectra of chromophores.   Next, we will explain why integrals over Gaussian functions are commonly used in quantum chemistry calculations, and how the fast multipole moment algorithm can accelerate these calculations.  Finally, we will  present a number of topics in the quantum chemistry methodology development that might benefit from borrowing more advanced techniques from the applied mathematics community.