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## Details

Additional Physical Format: | ebook version : |
---|---|

Document Type: | Book |

All Authors / Contributors: |
John Meier; Derek Alan Smith |

ISBN: | 9781107128989 1107128986 |

OCLC Number: | 992743788 |

Description: | xv, 324 pages ; 26 cm. |

Contents: | Let's play! -- Discovering and presenting mathematics – Sets -- The integers and the fundamental theorem of arithmetic – Functions – Relations – Cardinality -- The real numbers -- Probability and randomness -- Algebra and symmetry – Projects -- Appendix A. Solutions, answers, or hints to in-text exercises – Index -- Bibilography. |

Series Title: | Cambridge mathematical textbooks. |

Responsibility: | John Meier, Lafayette College, PA, USA, Derek Smith, Lafayette College, PA, USA. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

'Wonderful list of topics, entertaining presentation, well-chosen problems - this is the way I want my grandchildren to engage with the beauty of mathematics. Too many students enter college with tools from calculus but no concept of how mathematicians think, and hardly any exposure to sets, logic, numbers, groups, or probability. How can we expect them to decide about continuing with mathematics, without a glimpse of the wonders ahead? A marvelous world lies at your students' doorstep, and Exploring Mathematics makes them players, not just observers, in that world. You'll want all your math majors, and perhaps your computer science majors as well, to have this experience.' Peter Winkler, Dartmouth College, New Hampshire 'Meier and Smith have written a wonderful introduction to higher mathematics, showing both the thrill of abstraction and the beauty in discovering proofs.' Tom Garrity, Williams College, Massachusetts 'I think that this is an excellent book. It is playful and serious at the same time. The book takes the unusual step of explaining not just mathematical topics but also what math is about and how to do it. The book is full of interesting topics, exercises, and examples. I think that this book could really fire up the imagination of a student wanting to get a start in real mathematics.' Richard Schwartz, Brown University, Rhode Island 'The biggest step in studying mathematics is learning to write proofs. After calculus, students discover that truth is not a matter of a calculation, but a careful argument, juggling concepts within formal logic. Exploring Mathematics is a guide to this new level. Rich with exercises and projects, the book provides a well-grounded introduction to proof. 'Then the fun begins'. The reader participates by doing what mathematicians do, experimenting, formulating conjectures, exploring foundations for the basis of a proof. This book engages the reader fully to reach the goal of learning to fashion real mathematics. A valuable addition to every undergraduate library.' John McCleary, Vassar College, New York Advance praise: 'Wonderful list of topics, entertaining presentation, well-chosen problems - this is the way I want my grandchildren to engage with the beauty of mathematics. Too many students enter college with tools from calculus but no concept of how mathematicians think, and hardly any exposure to sets, logic, numbers, groups, or probability. How can we expect them to decide about continuing with mathematics, without a glimpse of the wonders ahead? A marvelous world lies at your students' doorstep, and Exploring Mathematics makes them players, not just observers, in that world. You'll want all your math majors, and perhaps your computer science majors as well, to have this experience.' Peter Winkler, Dartmouth College, New Hampshire Advance praise: 'Meier and Smith have written a wonderful introduction to higher mathematics, showing both the thrill of abstraction and the beauty in discovering proofs.' Tom Garrity, Williams College, Massachusetts Advance praise: 'I think that this is an excellent book. It is playful and serious at the same time. The book takes the unusual step of explaining not just mathematical topics but also what math is about and how to do it. The book is full of interesting topics, exercises, and examples. I think that this book could really fire up the imagination of a student wanting to get a start in real mathematics.' Richard Schwartz, Brown University, Rhode Island Advance praise: 'The biggest step in studying mathematics is learning to write proofs. After calculus, students discover that truth is not a matter of a calculation, but a careful argument, juggling concepts within formal logic. Exploring Mathematics is a guide to this new level. Rich with exercises and projects, the book provides a well-grounded introduction to proof. 'Then the fun begins'. The reader participates by doing what mathematicians do, experimenting, formulating conjectures, exploring foundations for the basis of a proof. This book engages the reader fully to reach the goal of learning to fashion real mathematics. A valuable addition to every undergraduate library.' John McCleary, Vassar College, New York Read more...

*User-contributed reviews*