Abstract: Scientific Machine Learning (SciML) is an emerging research area that applies machine learning techniques to solve scientific computing problems, such as numerically solving forward and inverse problems associated with partial differential equations (PDEs). In this accessible talk, I will present the main SciML techniques and discuss how they can be applied to problems in numerical analysis. In particular, I will introduce physics-informed neural networks which, unlike traditional deep neural networks, have greater interpretability and can be verified and validated for use in critical domains. I will present examples of how SciML can be applied in epidemiology to predict disease spread, and discuss emerging research topics in this area related to learning operators associated with PDEs. With this talk, I aim to evidence the relevance of SciML techniques for a modern training in Applied Mathematics.