Techniques of Problem Solving

Rating:
Summary: Chatty introduction to reasoning and problem-solving
Review: I like lots of pieces of this book, and I definitely approve of the general approach (it's meant to be an introduction to the key ideas of mathematical reasoning -- the translation of problems into mathematical terms, a collection of useful techniques along with a sense of when each might be appropriate, and a broad collection of problems for students to practice on to develop their own personal sense of the toolkit.).

Most of the book requires little or no mathematical knowledge beyond high school algebra and geometry. In fact, in the preface, the author says: "this book has minimal prerequisites. Certainly no calculus is required...this is intended to be a book on reasoning more than a book on mathematics per se." Of course, on page 103 he also says: "...we all have some exposure to solid geometry through our calculus course and our real variable course..." so go figure.

The book is a bit chattier than I personally like -- it sometimes reads like an only slightly edited transcript of a lecture. This may be unavoidable: describing the thought processes of problem-solving is hard enough to do orally and almost impossible to do in typeset words.

With a few exceptions, the approaches taken are sensible and coherent. The collections of exercises are pretty good, on the whole (though there aren't any snazzy induction problems to compare with those in, say, the book Mathematical Circles (Fomin, et al).

This may not be the ONE book on problem-solving to give to an interested student (that's probably Paul Zeitz's book "the Art and Craft of Problem Solving"), but it is readable and engaging.

Rating:
Summary: Chatty introduction to reasoning and problem-solving
Review: I like lots of pieces of this book, and I definitely approve of the general approach (it's meant to be an introduction to the key ideas of mathematical reasoning -- the translation of problems into mathematical terms, a collection of useful techniques along with a sense of when each might be appropriate, and a broad collection of problems for students to practice on to develop their own personal sense of the toolkit.).

Most of the book requires little or no mathematical knowledge beyond high school algebra and geometry. In fact, in the preface, the author says: "this book has minimal prerequisites. Certainly no calculus is required...this is intended to be a book on reasoning more than a book on mathematics per se." Of course, on page 103 he also says: "...we all have some exposure to solid geometry through our calculus course and our real variable course..." so go figure.

The book is a bit chattier than I personally like -- it sometimes reads like an only slightly edited transcript of a lecture. This may be unavoidable: describing the thought processes of problem-solving is hard enough to do orally and almost impossible to do in typeset words.

With a few exceptions, the approaches taken are sensible and coherent. The collections of exercises are pretty good, on the whole (though there aren't any snazzy induction problems to compare with those in, say, the book Mathematical Circles (Fomin, et al).

This may not be the ONE book on problem-solving to give to an interested student (that's probably Paul Zeitz's book "the Art and Craft of Problem Solving"), but it is readable and engaging.