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                <text>verzamelingen, relaties en functies&lt;br /&gt;
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lineaire algebra, algebraïsche structuren&lt;br /&gt;
moderne meetkunde, over meetkunden&lt;br /&gt;
vernieuwingen in het wiskundeonderwijs</text>
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		 In het begin van deze eeuw ontstond onder de wiskundigen een heftig debat over de verzamelingenleer van Cantor. Zijn theorie leek de basistheorie van de gehele wiskunde te worden, maar bleek te leiden tot antinomien.&lt;br /&gt;
		Michel Combs stelt het probleem en beschrijft de belangrijkste voorgestelde oplossingen en de belangrijkste discussianten: Russell, Brouwe, Zermelo en Hilbert.&lt;/div&gt;
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		&lt;br /&gt;&lt;br /&gt;
		Zes hoofdstukken behandelen in vogelvlucht de controverses binnen de theorie van de verzamelingen met de daarbij behorende paradoxen, vier interessante beschouwingen hierop en tenslotte een discussie met de zienswijze van de auteur over het voorgaande. Een zevende rubriek geeft per voorgaand hoofdstuk naast een verduidelijking van de verschillende begrippen ook veel literatuurverwijzingen. Enkele zwart-witfiguren en tabellen geven aanvullende informatie; goede en duidelijke notatie van wiskundige formules. Het boek heeft een prettige lay-out en een goede bladspiegel. Het werk is nog steeds actueel en heeft ondanks de vele moeilijke woorden en begrippen een helder taalgebruik. Dit logisch opgebouwde boek heeft een academisch niveau en is geschikt voor hen met een goede kennis van de wiskunde; enige kennis van filosofisch denken is daarbij een pre.&lt;/div&gt;
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		 &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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