Beyond the Quadratic Formula

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MAA, Oct 10, 2013 - Mathematics - 228 pages
The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial’s coefficients can be used to obtain detailed information on its roots. A closing chapter offers glimpses into the theory of higher-degree polynomials, concluding with a proof of the fundamental theorem of algebra. The book also includes historical sections designed to reveal key discoveries in the study of polynomial equations as milestones in intellectual history across cultures. Beyond the Quadratic Formula is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.

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About the author (2013)

Ronald Irving has been a Professor of Mathematics at the University of Washington since 1981, prior to which he held postdoctoral positions at Brandeis University, the University of Chicago, and the University of California, San Diego. He became chair of the University of Washington's mathematics department in 2001, Divisional Dean of Natural Sciences in 2002, and Interim Dean of Arts and Sciences in 2006. In 2003, Irving joined the Board of Governors of the Astrophysical Research Consortium and continues to serve as the secretary-treasurer of the consortium. Since 2010, he has been a member of the external board of the Burke Museum of Natural History and Culture, one of Washington's state museums and a part of the University of Washington. Irving is a member of the Mathematical Association of America and the American Mathematical Society.

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