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How to solve it : a new aspect of mathematical method /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
2004.
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| Edición: | Expanded Princeton Science Library edition. |
| Colección: | Princeton science library.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- pt. 1. In the classroom
- 1. Helping the student
- 2. Questions, recommendations, mental operations
- 3. Generality
- 4. Common sense
- 5. Teacher and student, imitation and practice
- 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
- 18. A problem of construction
- 19. A problem to prove
- 20. A rate problem
- pt. II. How to solve it
- A dialogue
- pt. 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 problems?
- 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
- pt. IV. Problems, hints, solutions.