How to Solve It: A New Aspect of Mathematical Method / Edition 2

How to Solve It: A New Aspect of Mathematical Method / Edition 2

by G. Polya, George Polya
     
 

ISBN-10: 0691023565

ISBN-13: 9780691023564

Pub. Date: 11/01/1971

Publisher: Princeton University Press

In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof on 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.  See more details below

Overview

In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof on 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.

Product Details

ISBN-13:
9780691023564
Publisher:
Princeton University Press
Publication date:
11/01/1971
Series:
Princeton Science Library Series
Edition description:
Older Edition
Pages:
288
Product dimensions:
5.18(w) x 8.00(h) x 0.61(d)

Table of Contents

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. 1In the classroom
1Helping the student1
2Questions, recommendations, mental operations1
3Generality2
4Common sense3
5Teacher and student, imitation and practice3
6Four phases5
7Understanding the problem6
8Example7
9Devising a plan8
10Example10
11Carrying out the plan12
12Example13
13Looking back14
14Example16
15Various approaches19
16The teacher's method of questioning20
17Good questions and bad questions22
18A problem of construction23
19A problem to prove25
20A rate problem29
Pt. IIHow to solve it
A dialogue33
Pt. IIIShort dictionary of heuristic
Analogy37
Auxiliary elements46
Auxiliary problem50
Bolzano57
Bright idea58
Can you check the result?59
Can you derive the result differently?61
Can you use the result?64
Carrying out68
Condition72
Contradictory73
Corollary73
Could you derive something useful from the data?73
Could you restate the problems?75
Decomposing and recombining75
Definition85
Descartes92
Determination, hope, success93
Diagnosis94
Did you use all the data?95
Do you know a related problem?98
Draw a figure99
Examine your guess99
Figures103
Generalization108
Have you seen it before?110
Here is a problem related to yours and solved before110
Heuristic112
Heuristic reasoning113
If you cannot solve the proposed problem114
Induction and mathematical induction114
Inventor's paradox121
Is it possible to satisfy the condition?122
Leibnitz123
Lemma123
Look at the unknown123
Modern heuristic129
Notation134
Pappus141
Pedantry and mastery148
Practical problems149
Problems to find, problems to prove154
Progress and achievement157
Puzzles160
Reductio ad absurdum and indirect proof162
Redundant171
Routine problem171
Rules of discovery172
Rules of style172
Rules of teaching173
Separate the various parts of the condition173
Setting up equations174
Signs of progress178
Specialization190
Subconscious work197
Symmetry199
Terms, old and new200
Test by dimension202
The future mathematician205
The intelligent problem-solver206
The intelligent reader207
The traditional mathematics professor208
Variation of the problem209
What is the unknown?214
Why proofs?215
Wisdom of proverbs221
Working backwards225
Pt. IVProblems, hints, solutions
Problems234
Hints238
Solutions242

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