From the Preface to the First Printing
From the Preface to the Seventh Printing
Preface to the Second Edition
"How To Solve It" list
PART 1. IN THE CLASSROOMPurpose
- Helping the student
- Questions, recommendations, mental operations
- Common sense
- Teacher and student. Imitation and practice
- Four phases
- Understanding the problem
- Devising a plan
- Carrying out the plan
- Looking back
- Various approaches
- The teacher's method of questioning
- Good questions and bad questions
- A problem of construction
- A problem to prove
- A rate problem
PART II. HOW TO SOLVE ITA dialogue <
PART Ill. SHORT DICTIONARY OF HEURISTIC
Can you check the result?
Can you derive the result differently?
Can you use the result?
Could you derive something useful from the dat
Could you restate the problem?t
Decomposing and recombining
Determination, hope, success
Did you use all the data?
Do you know a related problem?
Draw a figuret
Examine your guess
Have you seen it before?
Here is a problem related to yours and solved before
If you cannot solve the proposed problem
Induction and mathematical induction
Is it possible to satisfy the condition?
Look at the unknown
Pedantry and mastery
Problems to find, problems to prove
Progress and achievement
Reductio ad absurdum and indirect proof
Rules of discovery
Rules of style
Rules of teaching
Separate the various parts of the condition
Setting up equations
Signs of progress
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?
Wisdom of proverbs
PART IV. PROBLEMS, HINTS, SOLUTIONS
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