  Mathematical concepts and tools have shaped the field of visualization in
fundamental ways and played a key role in the development of a large variety of
visualization techniques. In this chapter, we sample the visualization
literature to provide a taxonomy of the usage of mathematics in visualization,
and to identify a fundamental set of mathematics that should be taught to
students as part of an introduction to contemporary visualization research.
Within the scope of this chapter, we are unable to provide a full review of all
mathematical foundations of visualization; rather, we identify a number of
concepts that are useful in visualization, explain their significance, and
provide references for further reading.
