Arithmetical Wonderland - Andrew Liu

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Résumé :
Arithmetical Wonderland is intended as an unorthodox mathematics textbook for students in elementary education, in a contents course offered by a mathematics department. The scope is deliberately restricted to cover only arithmetic, even though geometric elements are introduced whenever warranted. For example, what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid is showcased. Many students find mathematics somewhat daunting. It is the author'...

Biographie:
Andrew Liu is a Professor Emeritus of the University of Alberta in Edmonton, Canada. He has a doctorate in mathematics as well as a professional diploma after degree in elementary education. Over his career, he had primary responsibility within the Department of Mathematical and Statistical Sciences for designing and teaching the lone course offered to students in elementary education. He acted as the deputy leader of the USA team and the leader of the Canadian team in the International Mathematical Olympiad and ran a mathematical circle for junior high school students, which he did for thirty-two years. He has authored ten other books prior to this volume, four of which were published by the Mathematical Association of America. He was also a winner of the Deborah and Franklin Teppo-Haimo Award.

Sommaire:
s belief that much of that is caused not by the subject itself, but by the language of mathematics. In this book, much of the discussion is in dialogues between Alice, of Wonderland fame, and the twins Tweedledum and Tweedledee who hailed from Through the Looking Glass.

The boys are learning High Arithmetic or Elementary Number Theory from Alice, and the reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language. Nevertheless, the book has considerable depth. It examines many arcane corners of the subject, and raises rather unorthodox questions. For instance, Alice tells the twins that six divided by three is two only because of an implicit assumption that division is supposed to be fair, whereas fairness does not come into addition, subtraction or multiplication. Some topics often not covered are introduced rather early, such as the concepts of divisibility and congruence....