Beyond infinity An expedition to the outer limits of mathematics

Beyond Infinity is a delightful book that is full of examples intended to give those readers who are math-phobic a sense of "the outer limits of mathematics." Cheng, a scientist in residence at the School of the Art Institute of Chicago, focuses on the term infinity, which can often refer to an element that is vague and/or somewhat mysterious. The author explores the many ins and outs of the concept from a mathematical perspective. In doing so, Cheng uses many intuitively clear examples rather than restricting the discussion to abstract mathematical approaches. Overall, the book is completely self-contained. This is a general interest book, which could reside in a mathematical library collection; it could also find a home in non-mathematical collections. The book is incredibly readable and will be appropriate for readers in middle school through adulthood. Unfortunately, the text does not contain a reference section or suggestions for further reading. Summing Up: Recommended. Lower-division undergraduates and general readers. --Donald Z. Spicer, University System of Maryland

Cheng (How to Bake?), a scientist in residence at the School of the Art Institute of Chicago and honorary fellow at Sheffield University, tackles some difficult concepts in this superb study of the mathematics of infinity. Beginning with the definition of infinity, Cheng moves through myriad mind-bending inquiries, including what the smallest infinity is, how to compare different infinities, whether you can subtract from infinity, and whether you can make an infinite number of cookies with a finite amount of dough. For each, she provides the mathematics behind the often counterintuitive answers. Cheng works hard at making these concepts accessible, employing menus and music playlists, among other things, to frame the challenging mathematical proofs. Acknowledging the difficulties the proofs present, Cheng wisely provides readers with reasonably accessible equations, useful graphics, and entertaining and straightforward explanations. Contemplating infinity is not trivial, even when following the lead of a writer as talented as Cheng, and readers will have to stop and wrestle with such recondite concepts as surjective and injective functions, harmonics, and factorials. Cheng's enthusiasm for mathematics is infectious and readers curious about the mathematics of infinity will find her to be a worthy guide. Agent: George Lucas, Inkwell. (Mar.) © Copyright PWxyz, LLC. All rights reserved.