Discovering Mathematics: The Art of Investigation (Dover Books on Mathematics)
`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 out of print or unavailable edition of this title.