  In 2008, Lomonaco and Kauffman introduced a knot mosaic system to define a
quantum knot system. A quantum knot is used to describe a physical quantum
system such as the topology or status of vortexing that occurs on a small scale
can not see. Kuriya and Shehab proved that knot mosaic type is a complete
invariant of tame knots. In this article, we consider the mosaic number of a
knot which is a natural and fundamental knot invariant defined in the knot
mosaic system. We determine the mosaic number for all eight-crossing or fewer
prime knots. This work is written at an introductory level to encourage other
undergraduates to understand and explore this topic. No prior of knot theory is
assumed or required.
