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Arithmetical Wonderland

Andrew C. F. Liu


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, we showcase what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid.

Many students find mathematics somewhat daunting. It is our 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.

Great care is exercised in limiting the number of results labeled Theorems. This focuses the attention of the students on what is really important. Notation is introduced sparingly and with great care. It should be mentioned that one of the highlights of the book is the new notations for greatest common divisor and least (positive) common multiple. We leave it to the reader to look this up.

Introduction

Contents

Electronic ISBN:  9781614441199

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