Many texts emphasize generality and abstract principles at the expense of concreteness; this text remedies that common mistake, stressing formal manipulations, intuitive appeal, and ingenuity. A two-volume treatment in a single binding, it supplements standard mathematics courses, employing physical analogies, encouraging problem formulation, and supplying problem-solving methods. Since it addresses topics of varying complexity—from number-multiplication games and other recreational mathematics to the zeros of the Riemann zeta function and the presumed transcendence of Euler's constant—this volume can be used by readers of every background. Beginners will find it a source of useful techniques and subjects not usually taught in standard courses. They'll also discover connections between seemingly unrelated aspects of mathematics. Experienced mathematicians can rely upon the book as a source of problems and information on branches beyond their specialties. Other professionals—theoretical physicists and chemists, engineers, numerical analysts, and computer scientists—will also consider it a valuable reference.