Arithmetical wonderland / Andrew C.F. Liu, University of Alberta.
Material type:
TextSeries: Classroom resource materials (Unnumbered)Publisher: Washington, DC : Mathematical Association of America, [2015]Copyright date: ©2015Description: xiii, 225 pages : illustrations ; 26 cmContent type: - text
- unmediated
- volume
- 9780883857892
- 0883857898
| Item type | Home library | Collection | Call number | Materials specified | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|---|---|
Adult Book
|
Main Library | NonFiction | 513 L783 | Available | 33111009230216 |
Enhanced descriptions from Syndetics:
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.
Includes index.
Review of arithmetic -- Divisibility -- Congruence -- Common divisors and multiples -- Linear diophantine equations -- Prime factorizations -- Rational and irrational numbers -- Numeration systems.
Many students find mathematics a daunting subject. Yet, in this unorthodox textbook, Liu brings a whole new clarity to arithmetic, making it a perfect resource for any budding teacher. With everyday language, even for formal proofs, students are carried along an accessible mathematical adventure by characters from the well-loved novels Alice in Wonderland and Through the Looking-Glass. At the same time, the book's prime focus on arithmetic allows the exploration of often uncovered topics, such as the concepts of divisibility and congruence as well as Diophantine equations. In eight chapters, Liu covers a range of topics from basic arithmetic to the Euclidean algorithm. Each chapter also includes a wealth of exercises catering to students of every level. As Liu has been noted for his 'unique ability to present difficult concepts in a clear and logical manner', Arithmetical Wonderland is an essential classroom resource.