Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. Many PWWs date back to classical Greece, ancient China, and medieval Europe and the Middle East. This third collection of PWWs follows a coherent structure, with proofs being arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integers and integer sums; and infinite series and other topics. They are intended primarily for the enjoyment of the reader; however, teachers will want to use them with students at many levels, including high school courses from algebra through precalculus and calculus, college level courses in number theory, combinatorics, and discrete mathematics, and pre-service and in-service courses for teachers.

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Roger B. Nelsen was born in Chicago, Illinois. He received his BA in mathematics from DePauw University, Indiana in 1964 and his PhD in mathematics from Duke University, North Carolina in 1969. Nelson was elected to Phi Beta Kappa and Sigma Xi, and taught mathematics and statistics at Lewis and Clark College, Portland for forty years before his retirement in 2009. His previous books include Proofs without Words (1993), An Introduction to Copulas (1999, 2nd edition 2006), Proofs without Words II (2000), Math Made Visual (with Claudi Alsina, 2006), When Less Is More (with Claudi Alsina, 2009), Charming Proofs (with Claudi Alsina, 2010), The Calculus Collection (with Caren Diefenderfer, 2010), Icons of Mathematics (with Claudi Alsina, 2011), College Calculus (with Michael Boardman, 2015), A Mathematical Space Odyssey (with Claudi Alsina, 2015) and Cameos for Calculus (2015).

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