Want a NOOK? Explore Now
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.
In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
In this best-selling classic, George Pólya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Pólya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. How to Solve It popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages.
Pólya was one of the most influential mathematicians of the twentieth century. He made important contributions to a great variety of mathematical research: from complex analysis to mathematical physics, number theory, probability, geometry, astronomy, and combinatorics. He was also an extraordinary teacher--he taught until he was ninety--and maintained a strong interest in pedagogical matters throughout his long career. In addition to How to Solve It, he published a two-volume work on the topic of problem solving, Mathematics of Plausible Reasoning, also with Princeton.
Pólya is one of the most frequently quoted mathematicians, and the following statements from How to Solve It make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till a solution occurs to you."
| From the preface to the first printing | ||
| From the preface to the seventh printing | ||
| Preface to the second edition | ||
| "How to solve it" list | ||
| Foreword | ||
| Introduction | ||
| Pt. 1 | In the classroom | |
| 1 | Helping the student | 1 |
| 2 | Questions, recommendations, mental operations | 1 |
| 3 | Generality | 2 |
| 4 | Common sense | 3 |
| 5 | Teacher and student, imitation and practice | 3 |
| 6 | Four phases | 5 |
| 7 | Understanding the problem | 6 |
| 8 | Example | 7 |
| 9 | Devising a plan | 8 |
| 10 | Example | 10 |
| 11 | Carrying out the plan | 12 |
| 12 | Example | 13 |
| 13 | Looking back | 14 |
| 14 | Example | 16 |
| 15 | Various approaches | 19 |
| 16 | The teacher's method of questioning | 20 |
| 17 | Good questions and bad questions | 22 |
| 18 | A problem of construction | 23 |
| 19 | A problem to prove | 25 |
| 20 | A rate problem | 29 |
| Pt. II | How to solve it | |
| A dialogue | 33 | |
| Pt. III | Short dictionary of heuristic | |
| Analogy | 37 | |
| Auxiliary elements | 46 | |
| Auxiliary problem | 50 | |
| Bolzano | 57 | |
| Bright idea | 58 | |
| Can you check the result? | 59 | |
| Can you derive the result differently? | 61 | |
| Can you use the result? | 64 | |
| Carrying out | 68 | |
| Condition | 72 | |
| Contradictory | 73 | |
| Corollary | 73 | |
| Could you derive something useful from the data? | 73 | |
| Could you restate the problems? | 75 | |
| Decomposing and recombining | 75 | |
| Definition | 85 | |
| Descartes | 92 | |
| Determination, hope, success | 93 | |
| Diagnosis | 94 | |
| Did you use all the data? | 95 | |
| Do you know a related problem? | 98 | |
| Draw a figure | 99 | |
| Examine your guess | 99 | |
| Figures | 103 | |
| Generalization | 108 | |
| Have you seen it before? | 110 | |
| Here is a problem related to yours and solved before | 110 | |
| Heuristic | 112 | |
| Heuristic reasoning | 113 | |
| If you cannot solve the proposed problem | 114 | |
| Induction and mathematical induction | 114 | |
| Inventor's paradox | 121 | |
| Is it possible to satisfy the condition? | 122 | |
| Leibnitz | 123 | |
| Lemma | 123 | |
| Look at the unknown | 123 | |
| Modern heuristic | 129 | |
| Notation | 134 | |
| Pappus | 141 | |
| Pedantry and mastery | 148 | |
| Practical problems | 149 | |
| Problems to find, problems to prove | 154 | |
| Progress and achievement | 157 | |
| Puzzles | 160 | |
| Reductio ad absurdum and indirect proof | 162 | |
| Redundant | 171 | |
| Routine problem | 171 | |
| Rules of discovery | 172 | |
| Rules of style | 172 | |
| Rules of teaching | 173 | |
| Separate the various parts of the condition | 173 | |
| Setting up equations | 174 | |
| Signs of progress | 178 | |
| Specialization | 190 | |
| Subconscious work | 197 | |
| Symmetry | 199 | |
| Terms, old and new | 200 | |
| Test by dimension | 202 | |
| The future mathematician | 205 | |
| The intelligent problem-solver | 206 | |
| The intelligent reader | 207 | |
| The traditional mathematics professor | 208 | |
| Variation of the problem | 209 | |
| What is the unknown? | 214 | |
| Why proofs? | 215 | |
| Wisdom of proverbs | 221 | |
| Working backwards | 225 | |
| Pt. IV | Problems, hints, solutions | |
| Problems | 234 | |
| Hints | 238 | |
| Solutions | 242 |
Anonymous
Posted July 18, 2001
This is the classic book on problem solving. Every student of mathematics should read it and find his or her own derivative approach to solving problems using Mr. Polya's framework.
1 out of 1 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted August 6, 2008
The value of this book lies mainly in the dictionary at the back. The method for solving problems is helpful but it's discussed only briefly.
0 out of 1 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted November 6, 2008
No text was provided for this review.
Anonymous
Posted September 18, 2009
No text was provided for this review.
Overview
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.
In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, ...