Related papers: Four Geometry Problems to Introduce Automated Dedu…
Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the…
This paper outlines a deceptively complex problem in classical mechanics which the paper names the "Falling Astronaut Problem," and it explores a method for teachers to implement this problem in an undergraduate classroom. The paper…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
The flipped classroom technique has recently been a focus of attention for many math instructors and pedagogical researchers. Although research on the subject has greatly increased in recent years, it is still debated whether the flipped…
Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by…
At the start of the higher education curriculum, the conceptualization of local approximation objects of a function requires the articulation of knowledge and skills from Functional Analysis and Topology. In the study of functions, a number…
Debugging is often a challenging and infuriating experience for secondary school students learning their first text-based programming language. Many students resort to ineffective debugging strategies, making success with solving errors…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
Students sometimes produce code that works but that its author does not comprehend. For example, a student may apply a poorly-understood code template, stumble upon a working solution through trial and error, or plagiarize. Similarly,…
In this paper we will discuss problems and techniques related to underactuated systems. We give a mathematical formulation of several problems arising from applications, review some standard and new techniques, and pose some interesting and…
Science teaching in secondary schools is often abstract for students. Even if some experiments can be conducted in classrooms, mainly for chemistry or some physics fields, mathematics is not an experimental science. Teachers have to…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…