The successful completion of the foundational mathematics course largely depends on the ability to solve the assigned exercises effectively. However, this requires a level of professionalism that students must gradually develop. This book aims to support them in this process. It provides models in the form of detailed sample solutions to typical problems from analysis and linear algebra. Additionally, it offers guidance on understanding, practicing, and reflecting on essential strategies and techniques. The book strives to present complete solution paths, including the generation of ideas and possible alternatives. In the exercise section, it trains students to toggle between condensed and detailed sample solutions.