How to solve it : a new aspect of Mathematical method

By:

Polya, G

Publication details: New York ISHI Press International 2009Description: xxi,253pISBN:

9784871878302

Subject(s):

DDC classification:

510 POL

Contents:

Contents 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 Introduction xix PART I. IN THE CLASSROOM Purpose 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 Main divisions main questions 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 More examples 18. A problem of construction 23 19. A problem to prove 25 20. A rate problem 29 PART II. HOW TO SOLVE IT A dialogue 33 PART 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 Contradictoryt 73 Corollary 73 Could you derive something useful from the data? 73 Could you restate the problem? 75 Decomposing and recombining 75 Definition 85 Descartes 92 Determination,hope success 93 Diagnosis 94 Did you use all the data ? 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 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 Redundantt 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 PART IV. PROBLEMS,HINTS,SOLUTIONS Problems 234 Hints 238 Solutions 242

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	CEPT Library	Faculty of Architecture	510 POL	Available		021529

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Contents
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
Introduction xix
PART I. IN THE CLASSROOM
Purpose
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
Main divisions main questions
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
More examples
18. A problem of construction 23
19. A problem to prove 25
20. A rate problem 29
PART II. HOW TO SOLVE IT
A dialogue 33
PART 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
Contradictoryt 73
Corollary 73
Could you derive something useful from the data? 73
Could you restate the problem? 75
Decomposing and recombining 75
Definition 85
Descartes 92
Determination,hope success 93
Diagnosis 94
Did you use all the data ?
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
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
Redundantt 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
PART IV. PROBLEMS,HINTS,SOLUTIONS
Problems 234
Hints 238
Solutions 242

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