Download E-books Gröbner Bases: A Computational Approach to Commutative Algebra (Graduate Texts in Mathematics) (v. 141) PDF

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By Thomas Becker

The origins of the maths during this publication date again greater than thou­ sand years, as may be obvious from the truth that probably the most vital algorithms provided right here bears the identify of the Greek mathematician ecu­ clid. The note "algorithm" in addition to the foremost observe "algebra" within the identify of this e-book come from the identify and the paintings of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who used to be born in what's now Uzbek­ istan and labored in Baghdad on the court docket of Harun al-Rashid's son. The observe "algorithm" is absolutely a westernization of al-Khowarizmi's identify, whereas "algebra" derives from "al-jabr," a time period that looks within the identify of his publication Kitab al-jabr wa'l muqabala, the place he discusses symbolic tools for the answer of equations. This shut connection among algebra and al­ gorithms lasted approximately as much as the start of this century; until eventually then, the first target of algebra was once the layout of optimistic tools for fixing equations via symbolic alterations. throughout the moment 1/2 the 19th century, a brand new line of suggestion started to input algebra from the area of geometry, the place it were winning when you consider that Euclid's time, specifically, the axiomatic technique.

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