Mathematics as a Cultural SystemElsevier, 20 мая 2014 г. - Всего страниц: 194 Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a force and process. Chapter VI talks about the singularities in the evolution of mechanics, while Chapter 7 deals with the laws governing the evolution of mathematics. Chapter VIII tackles the role and future of mathematics. The book will be of great interest to readers who are curious about how mathematics relates to culture. |
Содержание
| 1 | |
Chapter II Examples of Cultural Patterns Observable in the Evolution of Mathematics | 21 |
Chapter III Historical Episodes a Laboratory for the Study of Cultural Change | 47 |
Chapter IV Potential of a Theory or Field Hereditary Stress | 66 |
Force and Process | 84 |
Chapter VI The Exceptional Individual Singularities in the Evolution of Mathematics | 105 |
Chapter VII Laws Governing the Evolution of Mathematics | 126 |
Chapter VIII Mathematics in the 20th Century Role and Future | 149 |
Footnote for the Aspiring Mathematician | 164 |
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19th century abstraction acceptance achieve algebra already analysis analytic geometry arithmetic axiomatic axioms Babylonian become calculus Cantor capacity Chapter cited classical complex numbers computer theory conceptual stress concerning considered consolidation course cultural elements cultural system Desargues Descartes diffusion discovery discussion early environmental stress especially Euclid's Elements Euclidean geometry evolution of mathematics evolved example existence Fermat fields of mathematics Girard Desargues Greek growth hereditary stress ideas important infinite instance interest intuition invention Ionian numerals L. E. J. Brouwer later mathe mathematical community mathematical concepts mathematical culture mathematical evolution mathematical logic mathematicians methods modern mathematics natural numbers natural sciences non-Euclidean geometries number theory observed occur operations patterns phenomenon philosophy physics Poncelet problems projective geometry proof proved recognized regarding remarks result Saccheri seems set theory set-theoretic social solution status subculture symbols term theorems theory of sets topology usually vector Wilder