Discovering Mathematics: The Art of Investigation - Hardcover

Gardiner, A.

Hardcover

ISBN 10: 0198532822 ISBN 13: 9780198532828

Publisher: Oxford University Press, 1987

Synopsis

One of the most striking characteristics of mathematics is that thoughtful and persistent mathematical analysis often provokes totally unexpected insights into what may at first have looked like an uninteresting or intractable problem. This book gives students an opportunity to discover the nature and process of mathematics by developing their ability to investigate problems without relying on the standardized methods usually taught. The techniques required are elementary, allowing the student to concentrate on the way the material is explored and developed, and on the strategies for addressing questions whose answers are not immediately obvious. The book will challenge high school and college mathematics students as well as interested general readers.

About this title

About the Author:

A. Gardiner is affiliated with the University of Birmingham, UK.

Review:

`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

About this edition

• Publisher: Oxford University Press
• Publication date: 1987
• ISBN 10: 0198532822
• ISBN 13: 9780198532828
• Binding: Hardcover
• Edition number: 1
• Number of pages: 220