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Ever wonder just what a million of something means? How about a billion? Or a trillion? Marvelosissimo the mathematical magician can teach you! How Much is a Million? knocks complex numbers down to size in a fun, humorous way, helping children conceptualize a…

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Why was the number of Hardy's taxi significant? Why does Graham's number need its own notation? How many grains of sand would fill the universe? What is the connection between the Golden Ratio and sunflowers? All these questions and a host more are answered in…

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During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson…

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The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and…

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This book deals with the number-theoretic properties of almost all real numbers. It brings together many different types of result never covered within the same volume before, thus showing interactions and common ideas between different branches of the subject.…

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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers…

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In the first two lectures, there is a very brief description of the early history, as well as a selection of a few of the more representative recent results. In the lectures which follow, I examine in succession the main theories connected with the problem. The…

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Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in…

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This book is the first comprehensive treatise of the transcendence theory of Mahler functions and their values. Recently the theory has seen profound development and has found a diversity of applications. The book assumes a background in elementary field theory,…

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From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American…

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This selection of expository essays by Paulo Ribenboim should be of interest to mathematicians from all walks. Ribenboim, a highly praised author of several popular titles, writes each essay in a light and humorous language without secrets, making them thoroughly…