Since the first computers were built researchers have been interested in having these machines do symbol manipulations and
make exact
calculations. Early examples include computing the cosets of finitely presented group (1953) and symbolic integration (1961). It is clear that what we do formally as scientists and mathematicians is manipulate symbols and make exact calculations. Essentially factoring a polynomial is an exercise in symbol
manipulation. Donald Knuth and Peter Bendix in their seminal paper from 1967 formalize algebraic symbol manipulation in a precise manner such that it can be done on the computer. In this talk we will consider symbolic computations within the context of applications from engineering and science. In particular, aspect from computational group theory will be highlighted.