This book is addressed to mathematicians working in analysis and itsapplications. The aim is to provide an understandable introduction to the basictheory of non... » 

This book is addressed to mathematicians working in analysis and itsapplications. The aim is to provide an understandable introduction to the basictheory of nonstandard analysis and to illuminate some of its most strikingapplications. Problems are posed in all chapters. The opening chapter of thebook presents a simplified form of the general theory that is suitable for theresults of calculus and basic real analysis. The presentation is intended tofacilitate the acquisition of basic skills in the subject so that a reader whobegins with no background in mathematical logic should find it relatively easyto continue. The book then proceeds with the full theory. Following Part Ieach chapter takes up a different field for applications beginning with agentle introduction that even nonexperts can read with profit. The remainderof each chapter is then addressed to experts showing how to use nonstandardanalysis in the search for solutions of open problems and how to obtain richnew structures that produce deep insights into the field under consideration.The particular applications discussed here are in functional analysis includingoperator theory probability theory including stochastic processes andeconomics including game theory and financial mathematics. In working throughthis book the reader should gain many new and helpful insights into theenterprise of mathematics. Audience This work will be of interest tospecialists whose work involves real functions probability theory stochasticprocesses logic and foundations. Much of the book in particular theintroductory Part I can be used in a graduate course. «