The biggest stumbling block in the first semesters of a computer science or engineering degree for many students is mathematics. The initially unfamiliar mathematical notation and the consistent way of justifying a statement through proof often feel like stepping into a new, previously unknown world. This guide aims to help and support students during their first semesters. The presentation is oriented towards the fundamental needs of the new bachelor's and master's programs and bridges across the actual subject lectures. In particular, it aims to facilitate the cross-linking of knowledge regarding specific computer science topics.