Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Automated Theorem Proving in GeoGebra: Current Achievements

GeoGebra is an open-source educational mathematics software tool, with millions of users worldwide. It has a number of features (integration of computer algebra, dynamic geometry, spreadsheet, etc.), primarily focused on facilitating student experiments, and not on formal reasoning. Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather mature stage, we embarked on a project of incorporating and testing a number of different automated provers for geometry in GeoGebra. In this paper, we present the current achievements and status of this project, and discuss various relevant challenges that this project raises in the educational, mathematical and software contexts. We will describe, first, the recent and forthcoming changes demanded by our project, regarding the implementation and the user interface of GeoGebra. Then we present our vision of the educational scenarios that could be supported by automated reasoning features, and how teachers and students could benefit from the present work. In fact, current performance of GeoGebra, extended with automated deduction tools, is already very promising—many complex theorems can be proved in less than 1 second. Thus, we believe that many new and exciting ways of using GeoGebra in the classroom are on their way

Developing Multi-Scale Models for Water Quality Management in Drinking Water Distribution Systems

Drinking water supply systems belong to the group of critical infrastructure systems that support the socioeconomic development of our modern societies. In addition, drinking water infrastructure plays a key role in the protection of public health by providing a common access to clean and safe water for all our municipal, industrial, and firefighting purposes. Yet, in the United States, much of our national water infrastructure is now approaching the end of its useful life while investments in its replacement and rehabilitation have been consistently inadequate. Furthermore, the aging water infrastructure has often been operated empirically, and the embracement of modern technologies in infrastructure monitoring and management has been limited. Deterioration of the water infrastructure and poor water quality management practices both have serious impacts on public health due to the increased likelihood of contamination events and waterborne disease outbreaks. Water quality reaching the consumers’ taps is largely dependent on a group of physical, chemical, and biological interactions that take place as the water transports through the pipes of the distribution system and inside premise plumbing. These interactions include the decay of disinfectant residuals, the formation of disinfection by-products (DBPs), the corrosion of pipe materials, and the growth and accumulation of microbial species. In addition, the highly dynamic nature of the system’s hydraulics adds another layer of complexity as they control the fate and transport of the various constituents. On the other hand, the huge scale of water distribution systems contributes dramatically to this deterioration mainly due to the long transport times between treatment and consumption points. Hence, utilities face a considerable challenge to efficiently manage the water quality in their aging distribution systems, and to stay in compliance with all regulatory standards. By integrating on-line monitoring with real-time simulation and control, smart water networks offer a promising paradigm shift to the way utilities manage water quality in their systems. Yet, multiple scientific gaps and engineering challenges still stand in the way towards the successful implementation of such advanced systems. In general, a fundamental understanding of the different physical, chemical, and biological processes that control the water quality is a crucial first step towards developing useful modeling tools. Furthermore, water quality models need to be accurate; to properly simulate the concentrations of the different constituents at the points of consumption, and fast; to allow their implementation in real-time optimization algorithms that sample different operational scenarios in real-time. On-line water quality monitoring tools need be both reliable and inexpensive to enable the ubiquitous surveillance of the system at all times. The main objective of this dissertation is to create advanced computational tools for water quality management in water distribution systems through the development and application of a multi-scale modeling framework. Since the above-mentioned interactions take place at different length and time scales, this work aims at developing computational models that are capable of providing the best description of each of the processes of interest by properly simulating each of its underlying phenomena at its appropriate scale of resolution. Molecular scale modeling using tools of ab-initio quantum chemical calculations and molecular dynamics simulations is employed to provide detailed descriptions of the chemical reactions happening at the atomistic level with the aim of investigating reaction mechanisms and developing novel materials for environmental sensing. Continuum scale reactive-transport models are developed for simulating the spatial and temporal distributions of the different compounds at the pipe level considering the effects of the dynamic hydraulics in the system driven by the spatiotemporal variability in water demands. System scale models are designed to optimize the operation of the different elements of the system by performing large-scale simulations coupled with optimization algorithms to identify the optimal operational strategies as a basis for accurate decision-making and superior water quality management. In conclusion, the computational models developed in this study can either be implemented as stand-alone tools for simulating the fundamental processes dictating the water quality at different scales of resolution, or be integrated into a unified framework in which information from the small scale models are propagated into the larger scale models to render a high fidelity representation of these processes

Active Learning in Physics, Astronomy and Engineering with NASA’s General Mission Analysis Tool

Astrodynamics is the study of the motion of artificial satellites and spacecraft, subject to both natural and artificially induced forces. It combines celestial mechanics, attitude dynamics and aspects of positional astronomy to describe spacecraft motion and enable the planning and analysis of missions. It is of significant interdisciplinary interest with relevance to physics, astronomy and spaceflight engineering, but can be challenging to deliver in an effective, engaging manner because of the often abstract nature of some concepts, the four-dimensional nature of the problems, and the computation required to explore realistic astrodynamics behaviour. The University of Leicester has adopted NASA’s General Mission Analysis Tool as a core resource to support active learning in this subject for students at Level 6 (BSc) and Level 7 (MSc). This paper describes our approach to the implementation of GMAT as an essential element of teaching and learning in the subject