The book gives an introduction to
$p$-adic numbers from the point of view of number theory,
topology, and analysis. Compared to other books on the subject, its
novelty is both a particularly balanced approach to these three points
of view and an emphasis on topics accessible to undergraduates. In
addition, several topics from real analysis and elementary topology
which are not usually covered in undergraduate courses (totally
disconnected spaces and Cantor sets, points of discontinuity of maps
and the Baire Category Theorem, surjectivity of isometries of compact
metric spaces) are also included in the book. They will enhance the
reader's understanding of real analysis and intertwine the real and
$p$-adic contexts of the book.
The book is based on an advanced undergraduate course given by the
author. The choice of the topic was motivated by the internal beauty
of the subject of $p$-adic analysis, an unusual one in the
undergraduate curriculum, and abundant opportunities to compare it
with its much more familiar real counterpart. The book includes a
large number of exercises. Answers, hints, and solutions for most of
them appear at the end of the book. Well written, with obvious care
for the reader, the book can be successfully used in a topic course or
for self-study.
Readership
Undergraduate and graduate students interested in
$p$-adic numbers.
