In science and engineering, a successful attack on a problem will usually lead to some equations that have to be solved. There are many types of such equations: differential equations, linear or polynomial equations or inequalities, recurrences, equations in groups, tensor equations, etc. In principle, there are two ways of solving such equations: approximately or exactly. Numerical analysis is a well-developed field that provides highly successful mathematical methods and computer software to compute approximate solutions.

Computer algebra is a more recent area of computer science, where mathematical tools and computer software are developed for the exact solution of equations.

Why use approximate solutions at all if we can have exact solutions? The answer is that in many cases an exact solution is not possible. This may have various reasons: for certain (simple) ordinary differential equations, one can prove that no closed form solution (of a specified type) is possible. More important are questions of efficiency: any system of linear equations, say with rational coefficients, can be solved exactly, but for the huge linear systems that arise in meteorology, nuclear physics, geology or other areas of science, only approximate solutions can be computed efficiently. The exact methods, run on a supercomputer, would not yield answers within a few days or weeks (which is not really acceptable for weather prediction).