Over the last two centuries there has been an explosion in our knowledge of the global underwater environment. This understanding of the world's oceans and seas has been accomplished by a variety of methods, including the use of both manned and unmanned (i.e., robotic) vehicles. When people use any of these modern methods to explore the undersea realm, they must, in one way or another, use a mathematical description of the under-sea environment in order to be successful. For example, scuba divers must be aware of such quantities as the depth below the surface and the total time they can remain submerged. Each of these quantities is expressed as a number: for example, depth in feet and total dive time in minutes. The use and application of mathematics is therefore an essential part of undersea exploration.

Oceanography is the branch of earth science concerned with...