We describe an approach to automatically invent/explore new mathematical theories, with the goal of producing results comparable to those produced by humans, as represented, for example, in the libraries of the Isabelle proof assistant. Our approach is based on 'schemes', which are terms in higher-order logic. We show that it is possible to automate the instantiation process of schemes to generate conjectures and definitions. We also show how the new definitions and the lemmata discovered during the exploration of a theory can be used, not only to help with the proof obligations during the exploration, but also to reduce redundancies inherent in most theory formation systems.We implemented our ideas in an automated tool, called IsaScheme, which employs Knuth-Bendix completion and recent automatic inductive proof tools.We have evaluated our system in a theory of natural numbers and a theory of lists.

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Teaching robotics is a challenge in many universities due to the mathematics concepts used in this area. In recent years, augmented reality has improved learning in several engineering areas. In this paper, a platform for teaching robotic arm manipulation concepts is presented. e system includes a homemade robotic arm, a control system, and the RAR@pp. e RAR@pp is focused on learning robotic arm manipulation algorithms by the detection of markers in the robotic arm and displaying in real time the values based on the data obtained by the control system. Details on the design of the platform are presented, and the related results are discussed. Experimental data about the usability of the application are also shown.

This paper presents an educational mobile assistant application for type 1 diabetes patients. The proposed application is based on four mathematical models that describe the glucose-insulin-glucagon dynamics using a compartmental model, with additional equations to reproduce aerobic exercise, gastric glucose absorption by the gut, and subcutaneous insulin absorption. The medical assistant was implemented in Java and deployed and validated on several smartphones with Android OS. Multiple daily doses can be simulated to perform intensive insulin therapy. As a result, the proposed application shows the influence of exercise periods, food intakes, and insulin treatments on the glucose concentrations. Four parameter variations are studied, and their corresponding glucose concentration plots are obtained, which show agreement with simulators of the state of the art. The developed application is focused on type-1 diabetes, but this can be extended to consider type-2 diabetes by modifying the current mathematical models.

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