Geometry in the Transition from Primary to Post-Primary

This article is intended as a kind of precursor to the document Geometry for Post-primary School Mathematics, part of the Mathematics Syllabus for Junior Certicate issued by the Irish National Council for Curriculum and Assessment in the context of Project Maths. Our purpose is to place that document in the context of an overview of plane geometry, touching on several important pedagogical and historical aspects, in the hope that this will prove useful for teachers.Comment: 19 page

AI Solutions for MDS: Artificial Intelligence Techniques for Misuse Detection and Localisation in Telecommunication Environments

This report considers the application of Articial Intelligence (AI) techniques to the problem of misuse detection and misuse localisation within telecommunications environments. A broad survey of techniques is provided, that covers inter alia rule based systems, model-based systems, case based reasoning, pattern matching, clustering and feature extraction, articial neural networks, genetic algorithms, arti cial immune systems, agent based systems, data mining and a variety of hybrid approaches. The report then considers the central issue of event correlation, that is at the heart of many misuse detection and localisation systems. The notion of being able to infer misuse by the correlation of individual temporally distributed events within a multiple data stream environment is explored, and a range of techniques, covering model based approaches, `programmed' AI and machine learning paradigms. It is found that, in general, correlation is best achieved via rule based approaches, but that these suffer from a number of drawbacks, such as the difculty of developing and maintaining an appropriate knowledge base, and the lack of ability to generalise from known misuses to new unseen misuses. Two distinct approaches are evident. One attempts to encode knowledge of known misuses, typically within rules, and use this to screen events. This approach cannot generally detect misuses for which it has not been programmed, i.e. it is prone to issuing false negatives. The other attempts to `learn' the features of event patterns that constitute normal behaviour, and, by observing patterns that do not match expected behaviour, detect when a misuse has occurred. This approach is prone to issuing false positives, i.e. inferring misuse from innocent patterns of behaviour that the system was not trained to recognise. Contemporary approaches are seen to favour hybridisation, often combining detection or localisation mechanisms for both abnormal and normal behaviour, the former to capture known cases of misuse, the latter to capture unknown cases. In some systems, these mechanisms even work together to update each other to increase detection rates and lower false positive rates. It is concluded that hybridisation offers the most promising future direction, but that a rule or state based component is likely to remain, being the most natural approach to the correlation of complex events. The challenge, then, is to mitigate the weaknesses of canonical programmed systems such that learning, generalisation and adaptation are more readily facilitated

Modelling Web Service Composition for Deductive Web Mining

Composition of simpler web services into custom applications is understood as promising technique for information requests in a heterogeneous and changing environment. This is also relevant for applications characterised as deductive web mining (DWM). We suggest to use problem-solving methods (PSMs) as templates for composed services. We developed a multi-dimensional, ontology-based framework, and a collection of PSMs, which enable to characterise DWM applications at an abstract level; we describe several existing applications in this framework. We show that the heterogeneity and unboundedness of the web demands for some modifications of the PSM paradigm used in the context of traditional artificial intelligence. Finally, as simple proof of concept, we simulate automated DWM service composition on a small collection of services, PSM-based templates, data objects and ontological knowledge, all implemented in Prolog

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques