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P-adic numbers. --- Banach spaces. --- Analytic functions.

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p-adic numbers --- Lie, Groupes de --- Nombres p-adiques

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In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab­ stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor­ ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.

p-adic numbers --- Numbers, p-adic --- Number theory --- p-adic analysis --- P-adic numbers. --- p-adic numbers. --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Theorie des nombres --- P-adiques

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p-adic numbers --- Banach spaces --- Analytic functions --- Nombres P-adiques --- Banach, Espaces de --- Fonctions analytiques

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p-adic numbers --- Nombres p-adiques --- Valuation theory. --- Valuations, Théorie des --- Nombres, Théorie des