Synthetic Differential Geometry - Further Reading

Further Reading

  • John Lane Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets (PDF file)
  • F.W. Lawvere, Outline of synthetic differential geometry (PDF file)
  • Anders Kock, Synthetic Differential Geometry (PDF file), Cambridge University Press, 2nd Edition, 2006.
  • R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Springer-Verlag, 1996.
  • Michael Shulman, Synthetic Differential Geometry


Infinitesimals
History
  • Adequality
  • Infinitesimal calculus
  • Leibniz's notation
  • Integral symbol
  • Criticism of non-standard analysis
  • The Analyst
  • The Method of Mechanical Theorems
  • Cavalieri's principle
Related branches
  • Non-standard analysis
  • Non-standard calculus
  • Internal set theory
  • Synthetic differential geometry
  • Constructive non-standard analysis
Formalizations
  • Differentials
  • Hyperreal numbers
  • Dual numbers
  • Surreal numbers
Individual concepts
  • Standard part function
  • Transfer principle
  • Hyperinteger
  • Increment theorem
  • Monad
  • Internal set
  • Levi-Civita field
  • Hyperfinite set
  • Law of Continuity
  • Overspill
  • Microcontinuity
  • Transcendental law of homogeneity
Scientists
  • Gottfried Wilhelm Leibniz
  • Abraham Robinson
  • Pierre de Fermat
  • Augustin-Louis Cauchy
  • Leonhard Euler
  • Physics
  • Engineering
  • Infinitesimal strain theory
  • Infinitesimal oscillations of a pendulum
Textbooks
  • Analyse des Infiniment Petits
  • Elementary Calculus

Read more about this topic:  Synthetic Differential Geometry

Famous quotes containing the word reading:

    “When committees gather, each member is necessarily an actor, uncontrollably acting out the part of himself, reading the lines that identify him, asserting his identity.... We are designed, coded, it seems, to place the highest priority on being individuals, and we must do this first, at whatever cost, even if it means disability for the group.”
    —Lewis Thomas (b. 1913)

    “Learning is acquired by reading books; but the much more necessary learning, the knowledge of the world, is only to be acquired by reading men, and studying all the various editions of them.”
    —Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)