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.