Nonstandard Methods of Analysis

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Nonstandard Methods of Analysis is concerned with the main trends in this field: infinitesimal analysis and Boolean-valued analysis. The methods that have been developed in the last 25 years are explained. Attention is paid to general principles and fundamentals of formalisms for infinitesimals, as well as to the technique of descents and ascents in a Boolean-valued universe. The book also includes various applications of non-standard methods to ordered algebraic systems, vector lattices, subdifferentials and convex programming that have been developed in recent years. The text is designed for undergraduate students, postgraduates and all researchers interested in applying non-standard methods in their work.