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Techniques of Problem Solving
Steven G. Krantz, Washington University, St. Louis, MO

1997; 465 pp; softcover
ISBN-10: 0-8218-0619-X
ISBN-13: 978-0-8218-0619-7
List Price: US$42
Member Price: US$33.60
Order Code: TPS
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See also:

Solutions Manual for Techniques of Problem Solving - Luis Fernandez and Haedeh Gooransarab

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.

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Advanced high school and undergraduate mathematics students with a modest level of mathematical and/or analytical sophistication; teachers of these students. General mathematical audience.


"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."


"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

"Steven Krantz is a teacher, scholar, and artist. How else could he have written a book that not only introduces students to many of the great problems of mathematics, but also informs them about the process of solving these problems? Although many books include collections of intriguing problems, Techniques of Problem Solving uses clear development and lucid explanations to guide students through the process of problem solving. The text gives compelling examples that capture students' interest and encourages them to work problems at the end of the chapter ... Although the book would be excellent for a senior-level capstone course in mathematics, it would also appeal to advanced lower-division or strong high school students as well. [T]his superb book connects the worlds of great mathematical problems with effective classroom instruction."

-- The Mathematics Teacher

"[Krantz] exposes, and analyzes in detail, the solutions of various types of mathematical and logical problems. The choices of problems solved is very varied indeed, both in content and level of sophistication. Traditional `recreational' problems are well represented."

-- The Mathematical Gazette

Table of Contents

  • Basic concepts (Chapter 1)
  • A deeper look at geometry (Chapter 2)
  • Problems involving counting (Chapter 3)
  • Problems of logic (Chapter 4)
  • Recreational math (Chapter 5)
  • Algebra and analysis (Chapter 6)
  • A miscellany (Chapter 7)
  • Real life (Chapter 8)
  • Bibliography
  • Index
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