By Serge A. Lang
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We have now been excited about numbers--and top numbers--since antiquity. One extraordinary new path this century within the examine of primes has been the inflow of principles from likelihood. The target of this ebook is to supply insights into the major numbers and to explain how a chain so tautly decided can comprise any such amazing volume of randomness.
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Additional resources for Cyclotomic fields II
10 It is an early treatise on what we now call “algebra”, that name coming from the term al-jabr in the title. The phrase al-jabr wa’l-muqabala translates literally as “restoration and confrontation”, or more loosely as “balancing an equation”. Scholars today usually refer to this book as “al-Khwārizmī’s Algebra”. In Algebra, al-Khwārizmī developed a systematic approach to solving linear and quadratic equations, providing a comprehensive account of solving polynomial equations up to the second degree.
But not until another thousand years had passed did Pisa begin to rise to the prominence it enjoyed when Leonardo was born. Travelers today who approach Pisa by train from Florence notice that as they near their destination, the beautiful rolling hills of the Chianti wine region give way to a large flat plain, which stretches beyond Pisa to the sea. After heavy rains, the land here floods regularly, a lasting reminder of why Pisa had become a port in the first place: This modern-day floodplain is where, in Roman times and earlier, Pisa’s harbor used to be.
Pisa, along with Italy’s other maritime cities, Genoa to the north and Venice on the northeastern coast, dominated the trade, and their ships sailed constantly from one Mediterranean port to another. 1 Evidence of Pisa’s origins stretches back almost two thousand years BCE, when it served as a transit port for Greek and Phoenician trade to and from Gaul. Later, the Romans also used it as a port. But not until another thousand years had passed did Pisa begin to rise to the prominence it enjoyed when Leonardo was born.