I am developing a new kind of digital medium, library, and learning environment for college-level mathematics called xTensiv. The project includes several components: an encyclopedic content library, a database that affords generation of feasible learning paths through the library, a 2.5D spatial embedding of the library as a surveyable landscape for efficient navigation and exploratory learning, and a suite of tools to assist learners with discovery, analysis, and study in the library.
Mathematics is not amenable to serious learning and skill acquisition from a Wiki-style encyclopedia because the mean length of a practicable learning path is much too long in this subject. On the other hand, the linear ordering of a comprehensive textbook is far longer than necessary, and is therefore inefficient for learning that is directed toward individual items chosen within the textbook.
My vision of xTensiv applies modern computing and data management to produce and manage efficient pathways toward user-determined learning targets. It exploits the topology associated with a map to expose learning targets that are feasible next steps for the learner.
In a nutshell, I aim for software that offers ‘mapping’ and ‘routing’ solutions to the problems of content discovery and efficient navigation of learning pathways, something akin to the Google Maps mapping and routing solutions for location discovery and physical navigation.
I have been developing xTensiv since 2022 at UCLA. Currently xTensiv houses over 800 pages of learning material in a web-friendly format that you can browse here, as well as a demo graphical interface (which isn’t ready for public consumption). Since my move to Charlottesville, UVA students with majors in CS, math, and business, as well as experienced area entrepreneurs, have contributed to xTensiv in many ways.