* The spanning number and the independence number of a subset of an abelian group * A formula related to the Frobenius problem in two dimensions * One bit world * Use of Padé approximation in spline construction * Interactions between number theory and operator algebras in the study of Riemann zeta function (d'apres Bost-Connes and Connes) * A hyperelliptic curve with real multiplication of degree two * Humbert's conic model and the Kummer surface * Arithmeticity and theta correspondence of an orthogonal group * Morphis heights and periodic points * The elementary proof of the prime number theorem: An historical perspective * Additive bases representations and the Erdös-Túran conjecture * The boundary structure of the sumset in Z^2 * On NTU's in function fields * Continued fractions and quadratic irrationals * The inverse problem for representation functions of additive bases * On the ubiquity of Sidon sets