TY - BOOK ID - 214582 TI - The Strength of Nonstandard Analysis AU - Berg, Imme van den. AU - Neves, Vitor. PY - 2007 SN - 128113936X 9786611139360 3211499059 3211499040 3211998926 PB - Vienna : Springer Vienna : Imprint: Springer, DB - UniCat KW - Nonstandard mathematical analysis KW - Analysis, Nonstandard mathematical KW - Mathematical analysis, Nonstandard KW - Non-standard analysis KW - Nonstandard analysis KW - Model theory KW - Global analysis (Mathematics). KW - Logic, Symbolic and mathematical. KW - Distribution (Probability theory. KW - Differential equations, partial. KW - Number theory. KW - Analysis. KW - Mathematical Logic and Foundations. KW - Probability Theory and Stochastic Processes. KW - Partial Differential Equations. KW - Number Theory. KW - History of Mathematical Sciences. KW - Number study KW - Numbers, Theory of KW - Algebra KW - Partial differential equations KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Mathematics KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Mathematical logic. KW - Probabilities. KW - Partial differential equations. KW - Mathematics. KW - History. KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Math KW - Science KW - Annals KW - Auxiliary sciences of history UR - https://www.unicat.be/uniCat?func=search&query=sysid:214582 AB - Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson’s revolutionary book Nonstandard Analysis: in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained. ER -