The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

Technologies for engineering education

Within any discipline, teaching involves a distinctive relationship between content, pedagogical approaches and the use of technologies. In engineering education, the content includes mathematical symbolic and diagrammatic forms, traditionally taught using handwritten and talk-based approaches which have not been easily accommodated by keyboard-centric digital technologies. In 2012, a pilot project involving staff in the AUT School of Engineering was initiated to explore the use of digital pen-enabled technologies. This paper reviews educational research supporting the use of these technologies in an engineering education context and reports on findings from the project. The paper also discusses ways of integrating digital pen-enabled technologies with other developments in educational technology to enhance traditional pedagogical approaches to the teaching of engineering, and to facilitate progressive development of transformative approaches

Feynman Diagrams in Algebraic Combinatorics

We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of Lagrange-Good inversion, all in the setting of multivariable power series. We took great pains to offer a self-contained presentation that, we hope, will provide any mathematician who wishes, an easy access to the wonderland of quantum field theory.Comment: 13 diagram