Includes bibliographical references (p. [211]-220) and index.
PART I. THE ESSENTIALS OF DISCRETE VOLUME COMPUTATIONS. -- The coin-exchange problem of Frobenius -- A gallery of discrete volumes -- Counting lattice points in polytopes: the Ehrhart theory -- Reciprocity -- Face numbers and the Dehn-Sommerville relations in Ehrhartian terms -- Magic squares -- PART II. BEYOND THE BASICS. -- Finite Fourier analysis -- Dedekind sums -- The decomposition of a polytope into its cones -- Euler-Maclaurin summation in R[superscript]d -- Solid angles -- A discrete version of Green's theorem using elliptic functions -- Appendix: Triangulations of polytopes.