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How to Solve It : a New Aspect of Mathematical Method.

By: Polya, G.
Material type: materialTypeLabelBookSeries: Princeton science library: Publisher: Princeton University Press, 2014Description: 1 online resource (288 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9781400828678; 1400828678; 9780691164076; 069116407X.Subject(s): Mathematics -- Study and teaching | Mathematics -- Problems, exercises, etc | Feminism -- Islamic countries | Feminism -- Religious aspects -- Islam | Gender identity -- Islamic countries | Islamic renewal -- Egypt -- Cairo -- Case studies | Mathematics | Mathematics -- Study and teaching | Muslim women -- Egypt -- Cairo -- Religious life -- Case studies | Women in Islam | Math�ematiques -- �Etude et enseignement | MATHEMATICS / Logic | Mathematics | Mathematics -- Study and teachingGenre/Form: Electronic books. | Problems and exercises.Additional physical formats: Print version:: How to Solve It : A New Aspect of Mathematical Method.DDC classification: 510 Online resources: Click here to access online
Contents:
Cover; Title; Copyright; 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; PART I. IN THE CLASSROOM; Purpose; 1. Helping the student; 2. Questions, recommendations, mental operations; 3� Generality; 4� Common sense; 5� Teacher and student. Imitation and practice; Main divisions, main questions; 6. Four phases; 7� Understanding the problem; 8. Example; 9. Devising a plan; 10. Example; 11. Carrying out the plan; 12. Example; 13� Looking back; 14� Example.
15� Various approaches16. The teacher's method of questioning; 17� Good questions and bad questions; More examples; 18. A problem of construction; 19. A problem to prove; 20. A rate problem; PART II. HOW TO SOLVE IT; A dialogue; PART III. SHORT DICTIONARY OF HEURISTIC; 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.
DefinitionDescartes; 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 achievementPuzzles; 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; Problems.
Summary: 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.
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Cover; Title; Copyright; 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; PART I. IN THE CLASSROOM; Purpose; 1. Helping the student; 2. Questions, recommendations, mental operations; 3� Generality; 4� Common sense; 5� Teacher and student. Imitation and practice; Main divisions, main questions; 6. Four phases; 7� Understanding the problem; 8. Example; 9. Devising a plan; 10. Example; 11. Carrying out the plan; 12. Example; 13� Looking back; 14� Example.

15� Various approaches16. The teacher's method of questioning; 17� Good questions and bad questions; More examples; 18. A problem of construction; 19. A problem to prove; 20. A rate problem; PART II. HOW TO SOLVE IT; A dialogue; PART III. SHORT DICTIONARY OF HEURISTIC; 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.

DefinitionDescartes; 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 achievementPuzzles; 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; Problems.

HintsSolutions.

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.

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