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How to Solve It A New Aspect of Mathematical Method 1st edition by Polya 9781400828678 1400828678

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Product details:

• ISBN 10:1400828678

• ISBN 13:9781400828

• Author:G. Polya

How to Solve It
A New Aspect of Mathematical Method

The bestselling book that has helped millions of readers solve any problem A must-have guide by eminent mathematician G. Polya, How to Solve It shows 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 help you attack any problem that can be reasoned out—from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know. This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it’s not just for the classroom. Generations of readers from all walks of life have relished Polya’s brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem.

How to Solve It A New Aspect of Mathematical Method 1st  Table of contents:

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 approaches
16. 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
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
Problems
Hints
Solutions

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