Techniques of Problem Solving [Paperback]

Steven G. Krantz (Author)

Book Description

Publication Date: November 13, 1996 | ISBN-10: 082180619X | ISBN-13: 978-0821806197

Winner of the CHOICE Outstanding Academic Book Award for 1997! The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to ... translate verbal discussions into analytical data. learn problem-solving methods for attacking collections of analytical questions or data. build a personal arsenal of internalized problem-solving techniques and solutions. become "armed problem solvers", ready to do battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a "Challenge Problem" is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is available.

Editorial Reviews

Review

"Krantz has collected a thoroughly engaging arsenal of problems and problem-solving techniques. Most scientists will want to have a copy for personal reference and for the mental stimulation that it provides. It is well written in a style that encourages the reader to become actively involved ... a myriad of fascinating related problems are provided. After a delightful introductory chapter, the chapters are primarily organized around specific techniques and their applicability in areas such as geometry, logic, recreational math, and counting. The book is written in a linear fashion that makes it advisable to tackle problems in sequential order ... would be an excellent tool for teaching novices to read some mathematics." ---- CHOICE Magazine

"The book will help students to: translate verbal discussions into analytical data; learn problem-solving methods for attacking collections of analytical questions or data; build a personal arsenal of solutions and internalized problem solving techniques; become "armed problem solvers", ready to do battle with a variety of puzzles in different areas of life." ---- Zentralblatt für Didaktik der Mathematik

"It may be an enjoyable task for high school undergraduate mathematics students, their teachers, and people interested in the field to read the book and to learn from it by working on the challenging ideas which are provided throughout the text." ---- Zentralblatt MATH

Product Details

• Paperback: 465 pages
• Publisher: American Mathematical Society (November 13, 1996)
• Language: English
• ISBN-10: 082180619X
• ISBN-13: 978-0821806197
• Product Dimensions: 9.9 x 6.8 x 1.1 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 2.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,838,028 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

16 of 17 people found the following review helpful:

3.0 out of 5 stars Chatty introduction to reasoning and problem-solving, June 20, 2000

By 

Theodore M. Alper (Palo Alto, CA USA) - See all my reviews
(REAL NAME)   

This review is from: Techniques of Problem Solving (Paperback)

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.

2 of 10 people found the following review helpful:

1.0 out of 5 stars garbage, September 15, 2007

By 

reader - See all my reviews

This review is from: Techniques of Problem Solving (Paperback)

One thing an author should never do is to
stray outside his field of expertise. In
the present case we have someone who is not
a problem solver laying waste to a beautiful
and elegant subarea of mathematics.
The solutions to many problems are so poor as
to defy description. The main technique seems
to be 'bludgeon it into submission' [witness the
section on counting].
Don't waste your money on this piece of garbage.