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How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics /

"To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically - even algorithmically - from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, in...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Byers, William, 1943-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, ©2007.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Acknowledgments
  • Introduction : Turning on the light
  • Section 1 : The light of ambiguity ch. 1
  • Ambiguity in mathematics ch. 2
  • The contradictory in mathematics ch. 3
  • Paradoxes and mathematics : infinity and the real numbers ch. 4
  • More paradoxes of infinity : geometry, cardinality, and beyond
  • Section 2 : The light as idea ch. 5. The
  • idea as an organizing principle ch. 6
  • Ideas, logic, and paradox ch. 7
  • Great ideas
  • Section 3 : The light and the eye of the beholder ch. 8. The
  • truth of mathematics ch. 9
  • Conclusion : is mathematics algorithmic or creative?
  • Notes
  • Bibliography
  • Index.