Calculus teachers recognize this book as the leading resource among the reform projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. This edition uses all strands of the "Rule of Four" ― graphical, numeric, symbolic/algebraic, and verbal/applied presentations ― to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique.

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Deborah J. Hughes Hallett is a mathematician who works as a professor of mathematics at the University of Arizona. Her expertise is in the undergraduate teaching of mathematics. She has also taught as Professor of the Practice in the Teaching of Mathematics at Harvard University, and continues to hold an affiliation with Harvard as Adjunct Professor of Public Policy in the John F. Kennedy School of Government.

Hughes Hallett earned a bachelor's degree in mathematics from the University of Cambridge in 1966, and a master's degree from Harvard in 1976. She worked as a preceptor and senior preceptor at Harvard from 1975 to 1991, as an instructor at the Middle East Technical University in Ankara, Turkey from 1981 to 1984, and as a faculty member at Harvard from 1986 to 1998. She served as Professor of the Practice in the Teaching of Mathematics at Harvard from 1991 to 1998. She moved to Arizona in 1998, and took on her adjunct position at the Kennedy School in 2001.

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