European Mathematical Society - american mathematical society, providence: student mathematical library, vol. 37
https://euro-math-soc.eu/publisher/american-mathematical-society-providence-student-mathematical-library-vol-37
enp-adic Analysis Compared with Real
https://euro-math-soc.eu/review/p-adic-analysis-compared-real
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>The courses of p-adic (non-Archimedean) analysis seldom find a place in the undergraduate curriculum and often run separately from the classical (Archimedean) one with sporadic references to mutual differences. This book tries to introduce the reader to the first one making use of his/her familiarity with the classical counterpart and an intuitive experience from number theory and topology. The book starts with the construction of p-adic numbers based on the completion process of the field of rationals by replacing the Euclidean distance by a p-adic one. Then it continues with a study of their basic arithmetic and algebraic properties and a comparison of the topology of the field p-adic numbers, where p is a prime, with the field of real numbers (e.g. the strong triangle inequality, that balls are clopen, and the condition for the convergence of series). </p>
<p>The analytic highlights of the book are formed by elements of the analysis in the field of p-adic numbers and the basics of the calculus of p-adic functions. The reader will also find here some non-standard topics for undergraduate courses, including totally disconnected spaces, the Baire Category Theorem, and isometries of compact metric spaces. There are a large number of useful exercises and this makes the book more readable for advanced undergraduate or postgraduate students who want to learn something about p-adic numbers. In fact, many of them extend or complement the presented theory and some of them complete the proofs of results appearing in the text. Due to the role of p-adic numbers in many branches of mathematics and physics the book gives a good impetus to students to study the “p-adic worlds” more deeply. This role of the book is not only supported by carefully selected material but also by the fact that it is written in a very lively and lucid style.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">spor</div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/s-katok" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">s. katok</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/american-mathematical-society-providence-student-mathematical-library-vol-37" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">american mathematical society, providence: student mathematical library, vol. 37</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2007</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-8218-4220-1</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">USD 23</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/46-functional-analysis" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">46 Functional analysis</a></li></ul></span>Fri, 30 Sep 2011 15:47:36 +0000Anonymous39789 at https://euro-math-soc.eu