(Ebook) p-adic Numbers: An Introduction: Third Edition by Fernando Q. Gouvêa ISBN 9783030472948, 9783030472955, 3030472949, 3030472957

(Ebook) p-adic Numbers: An Introduction: Third Edition by Fernando Q. Gouvêa ISBN 9783030472948, 9783030472955, 3030472949, 3030472957

Main subject categories: • Number theory • p-adic numbers • Analysis • AlgebraMathematics Subject Classification (2010): • 11S80 Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.) • 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory • 12J25 Non-Archimedean valued fields • 13F30 Valuation ringsIn the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, abstract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic corners 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 play a 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 numbers have shown up in other areas of mathematics, and even in physics.