Hardcover ISBN:  9780883857892 
Product Code:  CLRM/48 
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eBook ISBN:  9781614441199 
Product Code:  CLRM/48.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857892 
eBook: ISBN:  9781614441199 
Product Code:  CLRM/48.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 
Hardcover ISBN:  9780883857892 
Product Code:  CLRM/48 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781614441199 
Product Code:  CLRM/48.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857892 
eBook ISBN:  9781614441199 
Product Code:  CLRM/48.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 

Book DetailsClassroom Resource MaterialsVolume: 48; 2015; 223 pp
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

Chapters

0. Review of Arithmetic

1. Divisibility

2. Congruence

3. Common Divisors and Multiples

4. Linear Diophantine Equations

5. Prime Factorizations

6. Rational and Irrational Numbers

7. Numeration Systems


Additional Material

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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.

Chapters

0. Review of Arithmetic

1. Divisibility

2. Congruence

3. Common Divisors and Multiples

4. Linear Diophantine Equations

5. Prime Factorizations

6. Rational and Irrational Numbers

7. Numeration Systems