1st Edition

Developments in Nonstandard Mathematics

    272 Pages
    by Chapman & Hall

    This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis.

    This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.

    The infinitesimal rule of three
    Nonstandard methods in the precalculus curruculum
    Difference quotients and smoothness
    Continuous maps with special properties
    Some nonstandard methods in geometric topology
    Delayed bifurcations in perturbed systems analysis of slow passage of Suhl-threshold
    Functional analysis and NSA
    Near-standard compact internal linear operators
    Discrete Fredholm's equations
    Nonstandard theory of generalized functions
    Representing distributions by nonstandard polynomials
    Contributions of nonstandard analysis to partial differential equations
    Loeb measure theory
    Unions of Loeb nullsets: the context
    Gredient lines and distributions of functionals in infinite dimensional Euclidean spaces
    Nonstandard flat integral representation of the free Euclidean field and a large deviation bound for the exponential interaction
    Nonstandard analysis in selective unierses
    Lattices and monads
    A neometric survey
    Long sequences and neocompact sets


    Cutland\, Nigel J; Neves\, Vitor; Oliveira\, A F; Sousa-Pinto\, Jose