Manfred H. Wolff

  • It is with great pleasure that we introduce the first volume of Birkhäuser Advances in Infectious Diseases.This book series will focus on relevant t- ics of microbiology and infectious diseases with emphasis (as much as p- sible) on emerging pathogens and related diseases.The series will also stress the inter-disciplinarity of the field and include "modern" aspects such as progress and new approaches in molecular biology, clinical aspects and modern insights relevant to human and veterinary medicine. In addition, questions of epidemiology,disease management,hygiene and prevention of infectious diseases will be discussed. Emerging or recently classified pathogens are a great challenge in m- icine.Therefore we focused the first volume of this series on the outbreak of SARS.The advent of SARS is a threat for people around the globe.Our modern technologies have figuratively transformed the world into a village. It is not a problem anymore for someone or something to travel to or trade with remote parts of the world.This traffic, however, reprensents a new opportunity to spread diseases, particularly such of infectious nature from tiny villages throughout the entire world.

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    Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a `secret weapon' by those who know the technique.This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler's internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems.All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics.