**Classroom Resource Materials**

Volume: 48;
2015;
223 pp;
Hardcover

**Print ISBN: 978-0-88385-789-2
Product Code: CLRM/48**

List Price: $50.00

AMS Member Price: $37.50

MAA Member Price: $37.50

**Electronic ISBN: 978-1-61444-119-9
Product Code: CLRM/48.E**

List Price: $50.00

AMS Member Price: $37.50

MAA Member Price: $37.50

# Arithmetical Wonderland

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*Andy Liu*

MAA Press: An Imprint of the American Mathematical Society

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'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.

# Table of Contents

## Arithmetical Wonderland

- Cover cov11
- Half title i2
- Copyright ii3
- Title iii4
- Series page iv5
- Contents vii8
- Preface to a Preliminary Edition ix10
- Introduction xi12
- 0 Review of Arithmetic 116
- 1 Divisibility 2742
- 2 Congruence 4560
- 3 Common Divisors and Multiples 6580
- 4 Linear Diophantine Equations 91106
- 5 Prime Factorizations 115130
- 6 Rational and Irrational Numbers 133148
- 7 Numeration Systems 155170
- Appendix: A Legacy of Martin Gardner 183198
- Solution to Odd-numbered Exercises 185200
- Index 221236
- About the Author 225240