Foreword What a relief to find a bold book with a bold title on a subject most men won't touch with a barge pole! I don't know Mr. Pawson, but surely he is a bold man. He faced the cost of putting his "obsolete and offensive" (his own words) viewpoint into print and went ahead and did it anyway-with scholarly care, with grace and courtesy. I hope and pray that people will read and heed what he ...

This is an overview of a few possibilities that are open by model theory in applied mathematics. The most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. DOI: 10.1134/S1990478909010116 The union of functional analys...