Mathematics and plausible reasoning. Vol. 1 Induction and analogy in mathematics /

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pólya, George, 1887-1985
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, 1954.
Temas:
Mathematics > Philosophy.
Logic, Symbolic and mathematical.
Mathématiques > Philosophie.
Logique symbolique et mathématique.
MATHEMATICS > History & Philosophy.
Logic, Symbolic and mathematical
Mathematics > Philosophy
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover Page
  • Half-title page
  • Title page
  • Copyright page
  • Preface
  • Hints to the Reader
  • Contents
  • Chapter I: Induction
  • 1. Experience and belief
  • 2. Suggestive contacts
  • 3. Supporting contacts
  • 4. The inductive attitude
  • Examples and Comments on Chapter I.
  • Chapter II: Generalization, Specialization, Analogy
  • 1. Generalization, Specialization, Analogy, and Induction
  • 2. Generalization
  • 3. Specialization
  • 4. Analogy
  • 5. Generalization, Specialization, and Analogy
  • 6. Discovery by analogy
  • 7. Analogy and induction
  • Examples and Comments on Chapter II
  • Chapter III: Induction in Solid Geometry
  • 1. Polyhedra
  • 2. First supporting contacts
  • 3. More supporting contacts
  • 4. A severe test
  • 5. Verifications and verifications
  • 6. A very different case
  • 7. Analogy
  • 8. The partition of space
  • 9. Modifying the problem
  • 10. Generalization, specialization, analogy
  • 11. An analogous problem
  • 12. An array of analogous problems
  • 13. Many problems may be easier than just one
  • 14. A conjecture
  • 15. Prediction and verification
  • 16. Again and better
  • 17. Induction suggests deduction
  • The particular case suggests the general proof
  • 18. More conjectures
  • Examples and Comments on Chapter III
  • Chapter IV: Induction in the Theory of Numbers
  • 1. Right triangles in integers
  • 2. Sums of squares
  • 3. On the sum of four odd squares
  • 4. Examining an example
  • 5. Tabulating the observations
  • 6. What is the rule?
  • 7. On the nature of inductive discovery
  • 8. On the nature of inductive evidence
  • Examples and Comments on Chapter IV
  • Chapter V: Miscellaneous Examples of Induction
  • 1. Expansions
  • 2. Approximations
  • 3. Limits
  • 4. Trying to disprove it
  • 5. Trying to prove it
  • 6. The role of the inductive phase
  • Examples and Comments on Chapter V
  • Chapter VI: A More General Statement
  • 1. Euler
  • 2. Euler's memoir
  • 3. Transition to a more general viewpoint
  • 4. Schematic outline of Euler's memoir
  • Examples and Comments
  • Chapter VII: Mathematical Induction
  • 1. The inductive phase
  • 2. The demonstrative phase
  • 3. Examining transitions
  • 4. The technique of mathematical induction
  • Examples and Comments on Chapter VII
  • Chapter VIII: Maxima and Minima
  • 1. Patterns
  • 2. Examples
  • 3. The pattern of the tangent level line
  • 4. Examples
  • 5. The pattern of partial variation
  • 6. The theorem of the arithmetic and geometric means and its first consequences
  • Examples and Comments on Chapter VIII
  • Chapter IX: Physical Mathematics
  • 1. Optical interpretation
  • 2. Mechanical interpretation
  • 3. Reinterpretation
  • 4. Jean Bernoulli's discovery of the Brachistochrone
  • 5. Archimedes' discovery of the integral calculus
  • Examples and Comments on Chapter IX
  • Chapter X: The Isoperimetric Problem
  • 1. Descartes' inductive reasons
  • 2. Latent reasons
  • 3. Physical reasons
  • 4. Lord Rayleigh's inductive reasons

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