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 fivefold: mathematical modeling, algorithmic design, implementation, presenting scientific findings, and learning how to interpret those results in order to draw scientific conclusions. Therefore, we provide measures (Parts I-IV) how to build confidence into numerical findings such as 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.