The term field designates a variety of different, closely related concepts in mathematics and physics that have been carried over into everyday language to designate a context or region of influence. In geometry a field is a function that is defined (i.e., has values) at every point of a manifold (smooth continuous surface). Similarly, in physics a field (e.g., an electric, magnetic, or gravitational field) is a function describing a physical quantity (e.g., electric, magnetic, or gravitational influence or forces) at all points of a region of space and time. Sometimes the region that is under the influence of an electric, magnetic, gravitational, or other source or agent is also referred to as a field. A similar and almost equivalent definition of a field in physics, especially in contemporary physics, is as a continuous dynamical system, or a dynamical system with infinite degrees of freedom. Fields are essential to the...