In studying mathematics, one can encounter surprises, whether in results that seem astonishing or in proofs that lead down unexpected paths. Over his career, the author came across many such gems. This book includes his favorites and invites readers to experience the same sense of wonder they inspired in him.Here are results about number theory, Euclidean geometry, trigonometry, algebra, and infinite series, with stories from the history of mathematics added to the mix. There are t...

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway to higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth. Now with a new preface by the author, this book documents the evolution of calculus from a pow...