Textbook: Mathematics in strokes: An introduction to probability theory
Digitization has triggered massive growth in data. As a result, the competent handling of data is becoming increasingly important in more and more sectors of the economy and society. The necessary statistical know-how has its roots in probability theory, which defines elementary concepts that are indispensable for developing appropriate data literacy. Unfortunately, the literature in this area is very formal and difficult to understand for beginners.
As an alternative, this book introduces a visual language of probability theory. This provides graphical access to the otherwise very formal mathematical concepts. However, this should not be confused with visualizations of data by conventional diagrams, which are mostly limited to display frequencies. Instead, the new visual language maps the underlying concepts themselves to the diagrammatic level, and in this way, is suitable for self-study. Numerous examples explain diagrammatically the foundations of set theory, which are essential for probability theory, as well as multi-stage and mixed experiments, discrete and continuous distributions, significance tests as well as the concepts of dependency, conditionality, and much more.
Despite their diversity, all these concepts are represented in a unified framework. This makes dependencies among them explainable and the student can fall back on a uniform approach when dealing with a wide variety of questions: constructing a diagram that represents the task at hand, extending the diagram depending on problems to be solved, and eventually, deriving the solution from that diagram. This approach allows the reader of this textbook to gain basic insights into the analysis of uncertain data, because those diagrams lead to a new mental idea of data and their relationships.