Softcover ISBN:  9780821806197 
Product Code:  TPS 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470412241 
Product Code:  TPS.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9780821806197 
eBook: ISBN:  9781470412241 
Product Code:  TPS.B 
List Price:  $108.00 $83.50 
MAA Member Price:  $97.20 $75.15 
AMS Member Price:  $86.40 $66.80 
Softcover ISBN:  9780821806197 
Product Code:  TPS 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470412241 
Product Code:  TPS.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9780821806197 
eBook ISBN:  9781470412241 
Product Code:  TPS.B 
List Price:  $108.00 $83.50 
MAA Member Price:  $97.20 $75.15 
AMS Member Price:  $86.40 $66.80 

Book Details1997; 465 ppMSC: Primary 00Winner 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 problemsolving methods for attacking collections of analytical questions or data.
 build a personal arsenal of internalized problemsolving 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 endofchapter exercises is available.
ReadershipAdvanced high school and undergraduate mathematics students with a modest level of mathematical and/or analytical sophistication; teachers of these students. General mathematical audience.

Table of Contents

Front Cover

TABLE OF CONTENTS

PREFACE

ACKNOWLEDGEMENTS

Chapter 1 Basic Concepts

1.1 Introductory Remarks

1.2 A First Problem

1.3 How to Count

1.4 The Use of Induction

1.5 Problems of Logic

1.6 Issues of Parity

EXERCISES for Chapter 1

Chapter 2 A Deeper Look at Geometry

2.1 Classical Planar Geometry

2.2 Analytic Geometry

2.3 Miscellaneous and Exotic Geometry Problems

2.4 Solid Geometry

EXERCISES for Chapter 2

Chapter 3 Problems Involving Counting

3.1 Elementary Problems in Probability

3.2 More Sophisticated Problems in Probability

3.3 More on Counting

3.4 The Classical Marriage Problem and Related Ideas

EXERCISES for Chapter 3

Chapter 4 Problems of Logic

4.1 Straight Logic

4.2 Games

4.3 Tracing Routes, and Learning from Parity

4.4 Mysterious Arithmetic Problems

4.5 Surprises

EXERCISES for Chapter 4

Chapter 5 Recreational Math

5.1 Magic Squares and Related Ideas

5.2 Problems Involving Weighings

EXERCISES for Chapter 5

Chapter 6 Algebra and Analysis

6.1 A Little Algebra

6.2 Inequalities

6.3 Trigonometry and Related Ideas

EXERCISES for Chapter 6

Chapter 7 A Miscellany

7.1 Crossing the River and Similar Exercises

7.2 Things That Are Impossible

EXERCISES for Chapter 7

Chapter 8 Real Life

8.0 Introductory Remarks

8.1 Everyday Objects

8.2 Some Case Studies

8.3 Statistics

EXERCISES for Chapter 8

Bibliography

Index

Solutions to OddNumbered Problems

Preface

Chapter 1 Basic Concepts

Chapter 2 A Deeper Look at Geometry

Chapter 3 Problems Involving Counting

Chapter 4 Problems of Logic

Chapter 5 Recreational Math

Chapter 6 Algebra and Analysis

Chapter 7 A Miscellany

Chapter 8 Real Life

Back Cover


Additional Material

Reviews

Krantz has collected a thoroughly engaging arsenal of problems and problemsolving 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 
The book will help students to: translate verbal discussions into analytical data; learn problemsolving 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 seniorlevel capstone course in mathematics, it would also appeal to advanced lowerdivision 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


RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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 problemsolving methods for attacking collections of analytical questions or data.
 build a personal arsenal of internalized problemsolving 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 endofchapter exercises is available.
Advanced high school and undergraduate mathematics students with a modest level of mathematical and/or analytical sophistication; teachers of these students. General mathematical audience.

Front Cover

TABLE OF CONTENTS

PREFACE

ACKNOWLEDGEMENTS

Chapter 1 Basic Concepts

1.1 Introductory Remarks

1.2 A First Problem

1.3 How to Count

1.4 The Use of Induction

1.5 Problems of Logic

1.6 Issues of Parity

EXERCISES for Chapter 1

Chapter 2 A Deeper Look at Geometry

2.1 Classical Planar Geometry

2.2 Analytic Geometry

2.3 Miscellaneous and Exotic Geometry Problems

2.4 Solid Geometry

EXERCISES for Chapter 2

Chapter 3 Problems Involving Counting

3.1 Elementary Problems in Probability

3.2 More Sophisticated Problems in Probability

3.3 More on Counting

3.4 The Classical Marriage Problem and Related Ideas

EXERCISES for Chapter 3

Chapter 4 Problems of Logic

4.1 Straight Logic

4.2 Games

4.3 Tracing Routes, and Learning from Parity

4.4 Mysterious Arithmetic Problems

4.5 Surprises

EXERCISES for Chapter 4

Chapter 5 Recreational Math

5.1 Magic Squares and Related Ideas

5.2 Problems Involving Weighings

EXERCISES for Chapter 5

Chapter 6 Algebra and Analysis

6.1 A Little Algebra

6.2 Inequalities

6.3 Trigonometry and Related Ideas

EXERCISES for Chapter 6

Chapter 7 A Miscellany

7.1 Crossing the River and Similar Exercises

7.2 Things That Are Impossible

EXERCISES for Chapter 7

Chapter 8 Real Life

8.0 Introductory Remarks

8.1 Everyday Objects

8.2 Some Case Studies

8.3 Statistics

EXERCISES for Chapter 8

Bibliography

Index

Solutions to OddNumbered Problems

Preface

Chapter 1 Basic Concepts

Chapter 2 A Deeper Look at Geometry

Chapter 3 Problems Involving Counting

Chapter 4 Problems of Logic

Chapter 5 Recreational Math

Chapter 6 Algebra and Analysis

Chapter 7 A Miscellany

Chapter 8 Real Life

Back Cover

Krantz has collected a thoroughly engaging arsenal of problems and problemsolving 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 
The book will help students to: translate verbal discussions into analytical data; learn problemsolving 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 seniorlevel capstone course in mathematics, it would also appeal to advanced lowerdivision 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