p-adic Numbers
An Introduction
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Beschreibung
p-adic numbers are of great theoretical importance in number
theory, since they allow the use of the language of analysis
to study problems relating toprime numbers and diophantine
equations. Further, they offer a realm where one can do
things that are very similar to classical analysis, but
with results that are quite unusual. The book should be of
use to students interested in number theory, but at the same
time offers an interesting example of the many connections
between different parts of mathematics.
The book strives to be understandable to an undergraduate
audience. Very little background has been assumed, and the
presentation is leisurely. There are many problems, which
should help readers who are working on their own (a large
appendix with hints on the problem is included).
Most of all, the book should offer undergraduates exposure
to some interesting mathematics which is off the beaten
track. Those who will later specialize in number theory,
algebraic geometry, and related subjects will benefit more
directly, but all mathematics students can enjoy the book.
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating to prime numbers and diophantine equations. This book is an informal elementary introduction. Using minimal prerequisites, it introduces the reader to the p-adic numbers and analogues of the real numbers, and explores some of their properties. The book strives to be understandable to an undergraduate audience and offers interesting mathematics that is somewhat off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects, will benefit more directly, but all mathematics students can enjoy the book.
Autor*in
Fernando Q. Gouvea
Themen in »p-adic Numbers«
Rack calculus completions diophantine equation diophantine equations equation local fields mathematics metric spaces non-archimedian analysis number theory p-adic analysis p-adic numbers presentation prime number