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We have investigated proof in two sets of commonly used Swedish upper secondary school mathematics textbooks. The frequency of proof items is low in each mathematical topic, even in the domain of geometry where pupils traditionally have learned proof. We explore the proof items with respect to different aspects of proof and discuss how they relate to(More)
– We investigate the cohomology of the free loop space of a one point union of a three-sphere with itself. The even dimensional subalgebra is not free and relations are presented explicitly. This algebra may also be identified as the cyclic homology of a " null algebra ". L'anneau de cohomologie de l'espace de lacets libres d'un bouquet de sphères et(More)
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