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Tables of Contents for How to Solve It
Chapter/Section Title
Page #
Page Count
From the Preface to the First Printing
v
From the Preface to the Seventh Printing
viii
Preface to the Second Edition
ix
"How to Solve It" list
xvi
Foreword
xix
Introduction
xxv
PART I. IN THE CLASSROOM
Purpose
1. Helping the student
1
1
2. Questions, recommendations, mental operations
1
1
3. Generality
2
1
4. Common sense
3
1
5. Teacher and student. Imitation and practice
3
2
Main divisions, main questions
6. Four phases
5
1
7. Understanding the problem
6
1
8. Example
7
1
9. Devising a plan
8
2
10. Example
10
2
11. Carrying out the plan
12
1
12. Example
13
1
13. Looking back
14
2
14. Example
16
3
15. Various approaches
19
1
16. The teacher's method of questioning
20
2
17. Good questions and bad questions
22
1
More examples
18. A problem of construction
23
2
19. A problem to prove
25
4
20. A rate problem
29
PART II. HOW TO SOLVE IT
A dialogue
33
4
PART III. SHORT DICTIONARY OF HEURISTIC
Analogy
37
9
Auxiliary elements
46
4
Auxiliary problem
50
7
Bolzano
57
1
Bright idea
58
1
Can you check the result?
59
2
Can you derive the result differently?
61
3
Can you use the result?
64
4
Carrying out
68
4
Condition
72
1
Contradictory
73
1
Corollary
73
1
Could you derive something useful from the data?
73
2
Could you restate the problem?
75
1
Decomposing and recombining
75
10
Definition
85
7
Descartes
92
1
Determination, hope, success
93
1
Diagnosis
94
1
Did you use all the data?
95
3
Do you know a related problem?
98
1
Draw a figure
99
1
Examine your guess
99
4
Figures
103
5
Generalization
108
2
Have you seen it before?
110
1
Here is a problem related to yours and solved before
110
2
Heuristic
112
1
Heuristic reasoning
113
1
If you cannot solve the proposed problem
114
1
Induction and mathematical induction
114
7
Inventor's paradox
121
1
Is it possible to satisfy the condition?
122
1
Leibnitz
123
1
Lemma
123
1
Look at the unknown
123
6
Modern heuristic
129
5
Notation
134
7
Pappus
141
7
Pedantry and mastery
148
1
Practical problems
149
5
Problems to find, problems to prove
154
3
Progress and achievement
157
3
Puzzles
160
2
Reductio ad absurdum and indirect proof
162
9
Redundant
171
1
Routine problem
171
1
Rules of discovery
172
1
Rules of style
172
1
Rules of teaching
173
1
Separate the various parts of the condition
173
1
Setting up equations
174
4
Signs of progress
178
12
Specialization
190
7
Subconscious work
197
2
Symmetry
199
1
Terms, old and new
200
2
Test by dimension
202
3
The future mathematician
205
1
The intelligent problem-solver
206
1
The intelligent reader
207
1
The traditional mathematics professor
208
1
Variation of the problem
209
5
What is the unknown?
214
1
Why proofs?
215
6
Wisdom of proverbs
221
4
Working backwards
225
9
PART IV. PROBLEMS, HINTS, SOLUTIONS
Problems
234
4
Hints
238
4
Solutions
242