Pell’s Equation (Problem Books in Mathematics) - Softcover

Über die Autorin bzw. den Autor

Ed Barbeau is professor emeritus at the University of Toronto. Dr. Barbeau is a life member of the MAA, the AMS, and the CMS, and has served all three societies on various committees, particularly having to do with mathematics education. He has published a number of books directed to students of mathematics and their teachers, including "Polynomials" (Springer), "Pell's Equation" (Springer). Ed Barbeau has frequently given talks and workshops at professional meetings and in schools, has worked with high school students preparing for Olympiad competitions and has on five occasions accompanied the Canadian team to the International Mathematical Olympiad. He is currently associate editor in charge of the Fallacies, Flaws and Flimflam column in the College Mathematics Journal and education editor for the Notes of the Canadian Mathematical Society. He is a former chairman of the Education Committee of the Canadian Mathematical Society. Honors include the Fellowship of the Ontario Institutefor Studies in Education, the David Hilbert Award from the World Federation of National Mathematics Competitions and the Adrien Pouliot Award from the Canadian Mathematical Society.

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 Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic number fields. The history of this equation is long and circuitous, and involved a number of different approaches before a definitive theory was found. There were partial patterns and quite effective methods of finding solutions, but a complete theory did not emerge until the end of the eighteenth century.

The topic is motivated and developed through sections of exercises which allow the student to recreate known theory and provide a focus for their algebraic practice. There are also several explorations that encourage the reader to embark on their own research. Some of these are numerical and often require the use of a calculator or computer. Others introduce relevant theory that can be followed up on elsewhere, or suggest problems that the reader may wish to pursue. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Edward Barbeau is Professor of Mathematics at the University of Toronto. He has published a number of books directed to students of mathematics and their teachers, including Polynomials (Springer 1989), Power Play (MAA 1997), Fallacies, Flaws and Flimflam (MAA 1999) and After Math (Wall & Emerson, Toronto 1995).