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AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
There are various types of disability egress in world like blindness, deafness, and Physical disabilities. It is quite difficult to deal with people with disability. Learning disability (LD) is types of disability totally different from…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
Background and context: Debugging is a significant and often frustrating challenge for beginner programmers. Understanding students' debugging behaviours and strategies can help to identify common difficulties and inform approaches for…
We discuss first experiences with a new variant of self-assessment in higher mathematics education. In our setting, the students of the course have to mark a part of their homework assignments themselves and they receive the corresponding…
As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…
The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
Successful implementation of active learning strategies in the engineering classroom -- and in particular in certain subjects which are highly technological in nature such as, for instance, rocket engines and space propulsion -- means…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
In parallel to the ever-growing usage of mechanized proofs in diverse areas of mathematics and computer science, proof assistants are used more and more for education. This paper surveys previous work related to the use of proof assistants…
The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the…
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…
Information and Community Technologies (ICT) are very present in our society nowadays and particularly in the educative field. In just two decades, we have passed from a learning based, in many cases, on the master lessons to one such that…
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…