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This resource volume is an enlargement as well as an update of the previous edition. The book aims to introduce the reader to over 100 different families of positive integers. A brief historical note accompanies the descriptions and examples of several of the families together with a mix of routine exercises and problems as well as some thought provokers to solve. Number Treasury3 especially aims to stimulate further study beyond the scope of the introductory treatment given in the book. The emphasis in Number Treasury3 is on doing not proving. However, the reader is directed to think critically about situations, to provide explanations, to make generalizations, and to formulate conjectures. To engage the reader from the start, the book begins with a set of rich Investigations. These are standalone activities that represent each of the chapters of the book.
A Perfect Number of Investigations 28 = 1 + 2 + 4 + 7 + 14
Numbers Based on Divisors and Proper Divisors
Plane Figurate Numbers
Solid Figurate Numbers
More Prime Connections
Digital Patterns and Noteworthy Numbers
More Patterns and Other Interesting Numbers
Readership: Secondary and intermediate classroom teacher and tertiary mathematics education instructor; undergraduates whose interest is in teaching mathematics at the pre-tertiary level and the segment of the general public for whom mathematics might be a hobby.
Differs from other books that treat numbers (formally or informally) because it contains numerous exercises and problems, detailed examples for the reader to follow, and the narrative is kept to a minimum
Has broad appeal for different audiences
Is a gateway to families of positive integers which leads and encourages the reader to go beyond the book to deeper study of the topics presented