num_pages: 244
description: 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.
language: English
title: Computing the Continuous Discretely: Integer-point Enumeration in Polyhedra
publisher: Springer