With puzzles involving coins, postage stamps, and other commonplace items, this book challenges readers to account for perplexing mathematical phenomena. Although sufficiently complex to capture the essential features of mathematical discovery, the elementary methods and solutions permit focus on the way the material is explored. Complete solutions.
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Editorial Reviews
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`All aspiring mathematicians should work through this inspiring book ... This is a marvellous account of beginning with a problem/challenge, of negotiating numbers and doodling diagrams to become familiar with what aspects are important/unimportant, of using mathematical knowledge, of searching for patterns, of making predictions, of checking, of realising frustration, of the reward for perseverance, of seeing the complex become simple, of explaining and proving results, and of final triumph and pleasure. The author is to be congratulated for not only writing such an account, but for writing it with clarity, wit and enthusiasm.' Mathematical Review
`This is not a book about mathematics but about doing mathematics. The explicit aim of the author is to guide the reader in thinking about, and mentally investigating a mathematical problem. In this sense the real content of the book is not contained in the book itself. The reader has to use the presented text, the hints, the exercises and so on for developing subjective experience with, and expertise in, formulating hypotheses, finding proofs, checking hypotheses and many other valuable cognitive techniques. To attain this goal different problems are presented and the process of solution is documented in a very detailed and exemplary way . . . Mathematics could be much more attractive and valuable if teachers would make use of problems like those presented here and - even more important - would implement a teaching style in accordance with this presentation.' Zentrallblatt fur Mathematik
`All aspiring mathematicians should work through this inspiring book ... This is a marvellous account of beginning with a problem/challenge, of negotiating numbers and doodling diagrams to become familiar with what aspects are important/unimportant, of using mathematical knowledge, of searching for patterns, of making predictions, of checking, of realising frustration, of the reward for perseverance, of seeing the complex become simple, of explaining and proving results, and of final triumph and pleasure. The author is to be congratulated for not only writing such an account, but for writing it with clarity, wit and enthusiasm.' Mathematical Gazette --This text refers to an alternate Paperback edition.
`This is not a book about mathematics but about doing mathematics. The explicit aim of the author is to guide the reader in thinking about, and mentally investigating a mathematical problem. In this sense the real content of the book is not contained in the book itself. The reader has to use the presented text, the hints, the exercises and so on for developing subjective experience with, and expertise in, formulating hypotheses, finding proofs, checking hypotheses and many other valuable cognitive techniques. To attain this goal different problems are presented and the process of solution is documented in a very detailed and exemplary way . . . Mathematics could be much more attractive and valuable if teachers would make use of problems like those presented here and - even more important - would implement a teaching style in accordance with this presentation.' Zentrallblatt fur Mathematik
`All aspiring mathematicians should work through this inspiring book ... This is a marvellous account of beginning with a problem/challenge, of negotiating numbers and doodling diagrams to become familiar with what aspects are important/unimportant, of using mathematical knowledge, of searching for patterns, of making predictions, of checking, of realising frustration, of the reward for perseverance, of seeing the complex become simple, of explaining and proving results, and of final triumph and pleasure. The author is to be congratulated for not only writing such an account, but for writing it with clarity, wit and enthusiasm.' Mathematical Gazette --This text refers to an alternate Paperback edition.
About the Author
A. Gardiner, Department of Mathematics, University of Birmingham.
--This text refers to an alternate
Paperback
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1 of 1 people found the following review helpful:
4.0 out of 5 stars
A good primer of basic mathematical puzzles, solutions provided,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Discovering Mathematics: The Art of Investigation (Dover Books on Mathematics) (Paperback)
Mathematics is the act of investigating what happens when you set down a set of objects, a set of rules on what you can do with the objects and then do things following those rules. Sometimes we put forward educated guesses as to what our result will be and at other times we simply just do what we can do to see what happens.
Discovering mathematics is nothing more than doing these things and in this book, Gardiner starts with some simple games that are easy to analyze. In the next section, a generalized three-digit number is selected, the three digits reversed and the process is repeated. List of self-referential sentences such as "This sentence uses thirty symbols." are analyzed next. Further topics involve geometric figures, an extensive section involving more flipping of the digits in the positions of a number, simple recurrence relations, classic jug and postage stamp problems, solving linear equations and coinage problems. Large numbers of additional exercises are given at the end of the chapters and hints followed by solutions are also included. This book should be considered more a primer on mathematics than a book on mathematics. The problems are more in the area of mathematically based puzzles rather than what we would consider "pure" math problems. Nevertheless, it is a good source of quick problems for classes in mathematics for education majors or classes in algebra near or at the level of precalculus.
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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