Princeton University Press
How to Solve It
-
-
Preface by:
and
About this book
The bestselling book that has helped millions of readers solve any problem
A must-have guide by eminent mathematician G. Polya, How to Solve It shows 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 help you attack any problem that can be reasoned out—from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.
This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it’s not just for the classroom. Generations of readers from all walks of life have relished Polya’s brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem.
Author / Editor information
Reviews
“[How to Solve It] shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected.”—Herman Weyl, Mathematical Review
“Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher’s art.”—A. C. Schaeffer, American Journal of Psychology
“I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it.”—Scientific Monthly
“Every prospective teacher should read [How to Solve It]. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: ‘He writes a, he says b, he means c; but it should be d.’”—E. T. Bell, Mathematical Monthly
“In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let’s hope this classic will remain a source of inspiration for several generations to come.”—A. Bultheel, European Mathematical Society
Topics
-
Download PDFPublicly Available
Frontmatter
i -
Download PDFPublicly Available
From the Preface to the First Printing
v -
Download PDFPublicly Available
From the Preface to the Seventh Printing
viii -
Download PDFPublicly Available
Preface to the Second Edition
ix -
Download PDFPublicly Available
Contents
xi -
Download PDFPublicly Available
"How to Solve It" list
xvi -
Download PDFPublicly Available
Foreword
xix -
Download PDFPublicly Available
Introduction
xxv - Part I. In the Classroom
-
Download PDFRequires Authentication UnlicensedLicensed
Purpose
1 -
Download PDFRequires Authentication UnlicensedLicensed
Main divisions, main questions
5 -
Download PDFRequires Authentication UnlicensedLicensed
More examples
23 - Part II. How to Solve it
-
Download PDFRequires Authentication UnlicensedLicensed
A dialogue
33 - Part III. Short Dictionary of Heuristic
-
Download PDFRequires Authentication UnlicensedLicensed
Analogy
37 -
Download PDFRequires Authentication UnlicensedLicensed
Auxiliary elements
46 -
Download PDFRequires Authentication UnlicensedLicensed
Auxiliary problem
50 -
Download PDFRequires Authentication UnlicensedLicensed
Bolzano
57 -
Download PDFRequires Authentication UnlicensedLicensed
Bright idea
58 -
Download PDFRequires Authentication UnlicensedLicensed
Can you check the result?
59 -
Download PDFRequires Authentication UnlicensedLicensed
Can you derive the result differently?
61 -
Download PDFRequires Authentication UnlicensedLicensed
Can you use the result?
64 -
Download PDFRequires Authentication UnlicensedLicensed
Carrying out
68 -
Download PDFRequires Authentication UnlicensedLicensed
Condition
72 -
Download PDFRequires Authentication UnlicensedLicensed
Contradictory
73 -
Download PDFRequires Authentication UnlicensedLicensed
Corollary
73 -
Download PDFRequires Authentication UnlicensedLicensed
Could you derive something useful from the data?
73 -
Download PDFRequires Authentication UnlicensedLicensed
Could you restate the problem?
75 -
Download PDFRequires Authentication UnlicensedLicensed
Decomposing and recombining
75 -
Download PDFRequires Authentication UnlicensedLicensed
Definition
85 -
Download PDFRequires Authentication UnlicensedLicensed
Descartes
92 -
Download PDFRequires Authentication UnlicensedLicensed
Determination, hope, success
93 -
Download PDFRequires Authentication UnlicensedLicensed
Diagnosis
94 -
Download PDFRequires Authentication UnlicensedLicensed
Did you use all the data?
95 -
Download PDFRequires Authentication UnlicensedLicensed
Do you know a related problem?
98 -
Download PDFRequires Authentication UnlicensedLicensed
Draw a figure
99 -
Download PDFRequires Authentication UnlicensedLicensed
Examine your guess
99 -
Download PDFRequires Authentication UnlicensedLicensed
Figures
103 -
Download PDFRequires Authentication UnlicensedLicensed
Generalization
108 -
Download PDFRequires Authentication UnlicensedLicensed
Have you seen it before?
110 -
Download PDFRequires Authentication UnlicensedLicensed
Here is a problem related to yours and solved before
110 -
Download PDFRequires Authentication UnlicensedLicensed
Heuristic
112 -
Download PDFRequires Authentication UnlicensedLicensed
Heuristic reasoning
113 -
Download PDFRequires Authentication UnlicensedLicensed
If you cannot solve the proposed problem
114 -
Download PDFRequires Authentication UnlicensedLicensed
Induction and mathematical induction
114 -
Download PDFRequires Authentication UnlicensedLicensed
Inventor's paradox
121 -
Download PDFRequires Authentication UnlicensedLicensed
Is it possible to satisfy the condition?
122 -
Download PDFRequires Authentication UnlicensedLicensed
Leibnitz
123 -
Download PDFRequires Authentication UnlicensedLicensed
Lemma
123 -
Download PDFRequires Authentication UnlicensedLicensed
Look at the unknown
123 -
Download PDFRequires Authentication UnlicensedLicensed
Modern heuristic
129 -
Download PDFRequires Authentication UnlicensedLicensed
Notation
134 -
Download PDFRequires Authentication UnlicensedLicensed
Pappus
141 -
Download PDFRequires Authentication UnlicensedLicensed
Pedantry and mastery
148 -
Download PDFRequires Authentication UnlicensedLicensed
Practical problems
149 -
Download PDFRequires Authentication UnlicensedLicensed
Problems to find, problems to prove
154 -
Download PDFRequires Authentication UnlicensedLicensed
Progress and achievement
157 -
Download PDFRequires Authentication UnlicensedLicensed
Puzzles
160 -
Download PDFRequires Authentication UnlicensedLicensed
Reductio ad absurdum and indirect proof
162 -
Download PDFRequires Authentication UnlicensedLicensed
Redundant
171 -
Download PDFRequires Authentication UnlicensedLicensed
Routine problem
171 -
Download PDFRequires Authentication UnlicensedLicensed
Rules of discovery
172 -
Download PDFRequires Authentication UnlicensedLicensed
Rules of style
172 -
Download PDFRequires Authentication UnlicensedLicensed
Rules of teaching
173 -
Download PDFRequires Authentication UnlicensedLicensed
Separate the various parts of the condition
173 -
Download PDFRequires Authentication UnlicensedLicensed
Setting up equations
174 -
Download PDFRequires Authentication UnlicensedLicensed
Signs of progress
178 -
Download PDFRequires Authentication UnlicensedLicensed
Specialization
190 -
Download PDFRequires Authentication UnlicensedLicensed
Subconscious work
197 -
Download PDFRequires Authentication UnlicensedLicensed
Symmetry
199 -
Download PDFRequires Authentication UnlicensedLicensed
Terms, old and new
200 -
Download PDFRequires Authentication UnlicensedLicensed
Test by dimension
202 -
Download PDFRequires Authentication UnlicensedLicensed
The future mathematician
205 -
Download PDFRequires Authentication UnlicensedLicensed
The intelligent problem-solver
206 -
Download PDFRequires Authentication UnlicensedLicensed
The intelligent reader
207 -
Download PDFRequires Authentication UnlicensedLicensed
The traditional mathematics professor
208 -
Download PDFRequires Authentication UnlicensedLicensed
Variation of the problem
209 -
Download PDFRequires Authentication UnlicensedLicensed
What is the unknown?
214 -
Download PDFRequires Authentication UnlicensedLicensed
Why proofs?
215 -
Download PDFRequires Authentication UnlicensedLicensed
Wisdom of proverbs
221 -
Download PDFRequires Authentication UnlicensedLicensed
Working backwards
225 - Part IV. Problems, Hints, Solutions
-
Download PDFRequires Authentication UnlicensedLicensed
Problems
234 -
Download PDFRequires Authentication UnlicensedLicensed
Hints
238 -
Download PDFRequires Authentication UnlicensedLicensed
Solutions
242