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Between 2017 and 2019, a standard Linear Algebra course from Instituto Superior T\'ecnico, University of Lisbon, used virtual learning content, mainly videos and formative assessment, delivered at the institution's MOOC platform to support…
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…
We analyze the curriculum of the early common-years of engineering in our institute using tools of statistical physics of complex networks. Naturally, a course programme is structured in a networked form (temporal dependency and…
We discuss an inquiry-based curriculum that has been developed specifically for the introductory algebra-based physics course, taking into account the needs, backgrounds, learning styles and career goals of the students in that class. The…
Aversion to mathematics is a recognised and widespread problem. Following a review of the literature on this subject, this paper presents an education program which has been developed to test the hypothesis that transferring attention from…
We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we…
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…
This article describes the authors' teaching experience in flipping the class of a basic undergraduate mathematics course Introductory Linear Algebra. We utilize a full-featured free electronic textbook, online lecture notes, an intranet…
We show how the computer algebra system OSCAR can be used to obtain topologically correct or visually pleasing drawings of real plane algebraic curves.
We guess humans start acquiring grasping skills as early as at the infant stage by virtue of two key processes. First, infants attempt to learn grasps for known objects by imitating humans. Secondly, knowledge acquired during this process…
Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years…
We consider the problem of leveraging prior experience to generate roadmaps in sampling-based motion planning. A desirable roadmap is one that is sparse, allowing for fast search, with nodes spread out at key locations such that a low-cost…
Iteratively building and testing machine learning models can help children develop creativity, flexibility, and comfort with machine learning and artificial intelligence. We explore how children use machine teaching interfaces with a team…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
If we want mathematics education to be valuable to everybody, including those who do not pursue mathematics-related careers, we need to use mathematics as a training ground for certain ways of thinking. This dissertation focuses on one…
We give explicit formulae for the logarithmic class group pairing on an elliptic curve defined over a number field. Then we relate it to the descent relative to a suitable cyclic isogeny. This allows us to connect the resulting Selmer group…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
We have designed an introductory laboratory course that engaged first-year undergraduate students in two complementary types of iteration: (1) iterative improvement of experiments through cycles of modeling systems, designing experiments,…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…