Contents
Second edition
https://archive.org/details/howtosolveit0000gpol_q4e3/mode/2up
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, p. xvi
Introduction, xix
PART I. IN THE CLASSROOM
Purpose, p. 1
Main divisions, main questions, p. 5
More examples, p. 23
PART II. HOW TO SOLVE IT, p. 33
PART III. SHORT DICTIONARY OF HEURISTIC, p. 37
Analogy--Auxiliary elements--Auxiliary problem--Bolzano--Bright idea--Can you check the result? --Can you derive the result differently? --Can you use the result?--Carrying out--Condition--Contradictory--Corollary--Could you derive something useful from the data?--Could you restate the problem?--Decomposing and recombining--Definition--Descartes--Determination, hope, success--Diagnosis--Did you use all the data?--Do you know a related problem?--Draw a figure--Examine your guess--Figures--Generalization--Have you seen it before?--Here is a problem related to yours and solved before--Heuristic--Heuristic reasoning--If you cannot solve the proposed problem--Induction and mathematical induction--Inventor's paradox--Is it possible to satisfy the condition?--Leibnitz--Lemma--Look at the unknown--Modern heuristic--Notation--Pappus--Pedantry and mastery--Practical problems--Problems to find, problems to prove--Progress and achievement--Puzzles--Reductio ad absurdum and indirect proof--Redundant--Routine problem--Rules of discovery--Rules of style--Rules of teaching--Separate the various parts of the condition--Setting up equations--Signs of progress--Specialization--Subconscious work--Symmetry--Terms, old and new--Test by dimension--The future mathematician--The intelligent problem-solver--The intelligent reader--The traditional mathematics professor--Variation of the problem--What is the unknown?--Why proofs?--Wisdom of proverbs--Working backwards
PART IV. PROBLEMS, HINTS, SOLUTIONS, p. 234
https://archive.org/details/howtosolveit0000gpol_q4e3/mode/2up
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, p. xvi
Introduction, xix
PART I. IN THE CLASSROOM
Purpose, p. 1
Main divisions, main questions, p. 5
More examples, p. 23
PART II. HOW TO SOLVE IT, p. 33
PART III. SHORT DICTIONARY OF HEURISTIC, p. 37
Analogy--Auxiliary elements--Auxiliary problem--Bolzano--Bright idea--Can you check the result? --Can you derive the result differently? --Can you use the result?--Carrying out--Condition--Contradictory--Corollary--Could you derive something useful from the data?--Could you restate the problem?--Decomposing and recombining--Definition--Descartes--Determination, hope, success--Diagnosis--Did you use all the data?--Do you know a related problem?--Draw a figure--Examine your guess--Figures--Generalization--Have you seen it before?--Here is a problem related to yours and solved before--Heuristic--Heuristic reasoning--If you cannot solve the proposed problem--Induction and mathematical induction--Inventor's paradox--Is it possible to satisfy the condition?--Leibnitz--Lemma--Look at the unknown--Modern heuristic--Notation--Pappus--Pedantry and mastery--Practical problems--Problems to find, problems to prove--Progress and achievement--Puzzles--Reductio ad absurdum and indirect proof--Redundant--Routine problem--Rules of discovery--Rules of style--Rules of teaching--Separate the various parts of the condition--Setting up equations--Signs of progress--Specialization--Subconscious work--Symmetry--Terms, old and new--Test by dimension--The future mathematician--The intelligent problem-solver--The intelligent reader--The traditional mathematics professor--Variation of the problem--What is the unknown?--Why proofs?--Wisdom of proverbs--Working backwards
PART IV. PROBLEMS, HINTS, SOLUTIONS, p. 234
Description
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.
Pages
253