Welcome to diophantine analysis - an area of number theory in which
we attempt to discover hidden treasures and truths within the
jungle of numbers by exploring rational numbers. Diophantine
analysis comprises two different but interconnected domains -
diophantine approximation and diophantine equations. This highly
readable book brings to life the fundamental ideas and theorems
from diophantine approximation, geometry of numbers, diophantine
geometry and $p$-adic analysis. Through an engaging style, readers
participate in a journey through these areas of number theory. Each
mathematical theme is presented in a self-contained manner and is
motivated by very basic notions. The reader becomes an active
participant in the explorations, as each module includes a sequence
of numbered questions to be answered and statements to be verified.
Many hints and remarks are provided to be freely used and
enjoyed.Each module then closes with a Big Picture Question that
invites the reader to step back from all the technical details and
take a panoramic view of how the ideas at hand fit into the larger
mathematical landscape. This book enlists the reader to build
intuition, develop ideas and prove results in a very user-friendly
and enjoyable environment. Little background is required and a
familiarity with number theory is not expected. All that is needed
for most of the material is an understanding of calculus and basic
linear algebra together with the desire and ability to prove
theorems. The minimal background requirement combined with the
author's fresh approach and engaging style make this book enjoyable
and accessible to second-year undergraduates, and even advanced
high school students. The author's refreshing new spin on more
traditional discovery approaches makes this book appealing to any
mathematician and/or fan of number theory.
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