**By Thomas Becker,**

__Gröbner Bases: A Computational Approach to Commutative Algebra__

The origins of the mathematics in this book date back than two thousand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Euclid The word algorithm as well as the key word algebra in the title of this book come from the name and the work of the ninth century scientist Mohammed ibThe origins of the mathematics in this book date back than two thousand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Euclid The word algorithm as well as the key word algebra in the title of this book come from the name and the work of the ninth century scientist Mohammed ibn Musa al Khowarizmi, who was born in what is now Uzbekistan and worked in Baghdad at the court of Harun al Rashid s son The word algorithm is actually a westernization of al Khowarizmi s name, while algebra derives from al jabr, a term that appears in the title of his book Kitab al jabr wa l muqabala, where he discusses symbolic methods for the solution of equations This close connection between algebra and algorithms lasted roughly up to the beginning of this century until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid s time, namely, the axiomatic method.

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