This textbook illuminates the field of discrete mathematics with
examples, theory, and applications of the discrete volume of a
polytope. The authors have weaved a unifying thread through basic
yet deep ideas in discrete geometry, combinatorics, and number
theory. We encounter here a friendly invitation to the field of
"counting integer points in polytopes," and its various connections
to elementary finite Fourier analysis, generating functions, the
Frobenius coin-exchange problem, solid angles, magic squares,
Dedekind sums, computational geometry, and more. With 250 exercises
and open problems, the reader feels like an active participant.
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