Complex functions with Geogebra

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from ℂ to ℂ through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.

Context-aware framework for collaborative applications

Future pervasive environments will take into consideration not only individual user’s interest, but also social relationships. In this way, pervasive communities can lead the user to participate beyond traditional pervasive spaces, enabling the cooperation among groups and taking into account not only individual interests, but also the collective and social context. Social applications in CSCW (Computer Supported Cooperative Work) field represent new challenges and possibilities in terms of use of social context information for adaptability in pervasive environments. In particular, the research describes the approach in the design and development of a context.aware framework for collaborative applications (CAFCA), utilizing user’s context social information for proactive adaptations in pervasive environments. In order to validate the proposed framework an evaluation was conducted with a group of users based on enterprise scenario. The analysis enabled to verify the impact of the framework in terms of functionality and efficiency in real-world conditions. The main contribution of this thesis was to provide a context-aware framework to support collaborative applications in pervasive environments. The research focused on providing an innovative socio-technical approach to exploit collaboration in pervasive communities. Finally, the main results reside in social matching capabilities for session formation, communication and coordinations of groupware for collaborative activities.