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With the arrival of the nineteenth century, a process of change guided the treatment of three basic elements in the development of mathematics: rigour, the arithmetization and the clarification of the concept of function, categorised as the most important tool in the development of the mathematical analysis. In this paper we will show how several prominent mathematicians contributed greatly to the development of these basic elements that allowed the solid underpinning of mathematics and the consideration of mathematics as an axiomatic way of thinking in which anyone can deduce valid conclusions from certain types of premises. This nineteenth century stage shares, possibly with the Heroic Age of Ancient Greece, the most revolutionary period in all history of mathematics. [ABSTRACT FROM AUTHOR]

Although emerging consensus exists that practice-based approaches to teacher preparation assist in closing the distance between university coursework and fieldwork experiences and in assuring that future teachers learn to implement innovative research-based instructional strategies, little empirical research has investigated teacher learning from this approach. This study examines the impact of a video- and practice-based course on prospective teachers' mathematics classroom practices and analysis of their own teaching. Two groups of elementary prospective teachers participated in the study-one attended the course and one did not. Findings reveal that the course assisted participants in making student thinking visible and in pursuing it further during instruction and in conducting evidence-based analyses of their own teaching. Conclusions discuss the importance of teaching these skills systematically during teacher preparation. [ABSTRACT FROM AUTHOR]

The aim of the study was to evaluate a new method for automated definition of a center lumen line in vessels in cardiovascular image data. This method, called VAMPIRE, is based on improved detection of vessel-like structures. A multiobserver evaluation study was conducted involving 40 tracings in clinical CTA data of carotid arteries to compare VAMPIRE with an established technique. This comparison showed that VAMPIRE yields considerably more successful tracings and improved handling of stenosis, calcifications, multiple vessels, and nearby bone structures. We conclude that VAMPIRE is highly suitable for automated definition of center lumen lines in vessels in cardiovascular image data. [ABSTRACT FROM AUTHOR]