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This book serves as an introduction to number theory at the
undergraduate level, emphasizing geometric aspects of the subject.
The geometric approach is exploited to explore in some depth the
classical topic of quadratic forms with integer coefficients, a
central topic of the book. Quadratic forms of this type in two
variables have a very rich theory, developed mostly by Euler,
Lagrange, Legendre, and Gauss during the period 1750-1800. In this
book their approach is modernized by using the splendid
visualization tool introduced by John Conway in the 1990s called
the topograph of a quadratic form. Besides the intrinsic interest
of quadratic forms, this theory has also served as a stepping stone
for many later developments in algebra and number theory. The book
is accessible to students with a basic knowledge of linear algebra
and arithmetic modulo $n$. Some exposure to mathematical proofs
will also be helpful. The early chapters focus on examples rather
than general theorems, but theorems and their proofs play a larger
role as the book progresses.
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