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	This systematic presentation of the current status and problems of the theory and observations of gravitational lensing starts from the equations of classical electrodynamics and general relativity, and develops for the first time gravitational lens theory from first principles. Beginning with simple models and basic properties of the lens mapping, the book proceeds to more complicated recent analytical and numerical treatments, thereby highlighting the prominent role played by lensing statistics in the interpretation of high-redshift objects. A detailed description of microlensing is given. The potential role of gravitational lenses as astronomical tools, for example, in determining the masses of cosmic objects and the scale of the universe and as natural telescopes, is pointed out. On the observational side, details of several known multiple QSOs, radio rings and luminous arcs, and the difficulties of observation and verification of lens systems are summarized. The basics of catastrophe theory, to the extent that it concerns singularities of plane maps, are derived and some techniques for numerical treatment of gravitational lensing are listed. This book can be viewed both as a textbook and as a research monograph.&lt;/div&gt;
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			De wiskunde heeft de laatste tientallen jaren een vlucht genomen die daarvoor wel nauwelijks te voorzien was. Ze heeft een veelzijdige wetenschappelijke en technische ontwikkeling mogelijk gemaakt, terwijl andersom ook de behoeften van wetenschap en techniek een verdere exploratie van wiskundigen problemen noodzakelijke maakten en bevorderden. Daarnaast is het verheugend te constateren dat ook in niet–vakkringen de belangstelling voor de moderne wiskunde toeneemt. De opzet van dit boek is om enkele belangrijke fundamentele ideeën en methoden van de moderne wiskunde voor een ruim publiek begrijpelijk te maken. Uiteraard is bij een zo uitgebreid gebied een volledige behandeling van alle onderwerpen onmogelijk. De auteur heeft een keuze moeten maken, maar bij die keuze heeft hij zich laten leiden door zijn ervaring dat bepaalde onderdelen van de moderne wiskunde velen interesseren. Die ervaring heeft hij opgedaan tijdens de talrijke voordrachten gehouden voor onderwijzers en leraren in een voor mensen die in industriële functies met wiskundige begrippen en problemen worden geconfronteerd. Ter sprake komen onder andere: wiskundige inductie, diverse aspecten van het gebruik van de eigenschappen van het getal, getaltheorie, elementaire groeptheorie, ringen en velden, differentiaal– en integraalrekening, wiskundige logica en topologie. Door deze onderwerpen in een eenvoudig kader te plaatsen en met interessante voorbeelden toe te lichten is de auteur er in geslaagd ze voor velen toegankelijk te maken. Speciale wiskundige kennis wordt niet verondersteld en is daardoor is dit boek bijzonder geschikt voor belangstellenden het middelbare schoolopleiding en voor aankomende wiskundestudenten.&lt;/p&gt;
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