Universitext: P-Adic Numbers: An Introduction (Paperback)

Fernando Quadros Gouvea
Springer
 9783540629115
3-540-62911-4

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.

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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.