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## Details

Material Type: | Internet resource |
---|---|

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
G M Phillips |

ISBN: | 9780387255286 0387255281 |

OCLC Number: | 60964661 |

Description: | xiv, 240 pages : illustrations ; 25 cm |

Contents: | 1 Squares 1 -- 1.1 Square and Triangular Numbers 1 -- 1.2 Pythagoras's Theorem 17 -- 1.3 The Equation a[superscript 2] + b[superscript 2] = c[superscript 2] 24 -- 1.4 Sum of Two Squares 29 -- 1.5 Complex Numbers 32 -- 2 Numbers, Numbers Everywhere 43 -- 2.1 Different Bases 43 -- 2.2 Congruences 51 -- 2.3 Continued Fractions 56 -- 2.4 The Euclidean Algorithm 67 -- 2.5 Infinity 72 -- 3 Fibonacci Numbers 81 -- 3.1 Recurrence Relations 81 -- 3.2 Fibonacci and Lucas Numbers 85 -- 3.3 The Golden Section 94 -- 4 Prime Numbers 101 -- 4.2 The Distribution of Primes 104 -- 4.3 Large Primes 111 -- 4.4 The Riemann Hypothesis 120 -- 5 Choice and Chance 127 -- 5.1 Arrangements and Permutations 127 -- 5.2 Binomial Coefficients 138 -- 5.3 Probability 146 -- 6 Geometrical Constructions 151 -- 6.1 Ruler and Compasses 151 -- 6.2 Unsolvable Problems 163 -- 6.3 Properties of the Triangle 168 -- 6.4 Coordinate Geometry 174 -- 6.5 Regular Polyhedra 183 -- 7 The Algebra of Groups 195 -- 7.2 Groups 201 -- 7.3 Subgroups 208 -- 7.4 Permutation Groups 215 -- 7.5 Further Material 218 -- 7.6 Groups of Small Order 224 -- 7.7 Dihedral and Polyhedral Groups 229. |

Responsibility: | George Phillips. |

More information: |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews:"The title of this book is an aphorism known by many concerned with the education of mathematicians, at many different levels. It is appropriate at all levels from primary school children `investigating' to postgraduates generating and attempting to solve new problems. ... The suggested audience is senior students in high school, students just beginning mathematics at university, and general readers no longer formally studying mathematics ... . The content and style of the book matches this quite well and realistically." (John Baylis, The Mathematical Gazette, Vol. 91 (520), 2007)"In this book, the author develops some (easy) mathematical concepts, which are suitable for high school students or non-mathematicians disciplines ... . Each of the seven chapters is an invitation to learn new mathematical concepts. ... The book is carefully written and a pleasure to read. ... It is ... an excellent prize to honor high school students for some extraordinary work in mathematics." (Alexander Pott, Zentralblatt MATH, Vol. 1140, 2008) Read more...

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