The existing Computer Algebra Systems (like “MathLab”, “Mathematica”, and similar applications) are designed for professional mathematicians and engineers. They do not support at all, or only partially support dynamical interactions with graphical models. In any case, these tools require some mastery of nontrivial and cumbersome programming syntax (for example, Mathematica)—an obvious obstacle for the inexperienced learners of mathematics. The uniform non-formulaic interface for manipulating with virtual graphical models is lacking in the traditional Computer Algebra Systems. On the other hand, the popular dynamic geometry applications (like “Geometer’s SketchPad” or “Cinderella”) are limited by their 2D-nature.
“VisuMatica”, a comprehensive software package for visualizing and investigating mathematics, is designed to fill in this educational niche.
In the paper, we aim to show how VisuMatica can handle virtual experiments in the intricate universe of multi-valued functions. Difficulties in grasping the concept of multivalued functions partially are due to the lack of adequate tools for their visualization. We present templates of visual models and interactive activities that could help students to explore the universe of multi-valued functions and to study the topology of Riemann surfaces.