These lecture notes accompany a refresher course in applied mathematics with a focus on numerical concepts (Part I), numerical linear algebra (Part II), numerical analysis, Fourier series and Fourier transforms (Part III), and differential equations (Part IV). Several numerical projects for group work are provided in Part V. In these projects, the tasks are threefold: mathematical modeling, algorithmic design, and implementation. Therein, it is important to draw interpretations of the obtained results and provide measures (Parts I-IV) how to build confidence into numerical findings such intuition, error analysis, convergence analysis, and comparison to manufactured solutions. Both authors have been jointly teaching over several years this class and bring in a unique mixture of their respective teaching and research fields.