Related papers: Conceptual Mathematics via Literate Programming
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Recently, the National Research Council's framework for next generation science standards highlighted "computational thinking" as one of its "fundamental practices". 9th Grade students taking a physics course that employed the Modeling…
The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
Primitive recursion is a mature, well-understood topic in the theory and practice of programming. Yet its dual, primitive corecursion, is underappreciated and still seen as exotic. We aim to put them both on equal footing by giving a…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…
Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…
Computational thinking is a way of reasoning about the world in terms of data. This mindset channels number crunching toward an ambition to discover knowledge through logic, models and simulations. Here we show how computational cognitive…
It is well documented, and has been the topic of much research, that Computer Science courses tend to have higher than average drop out rates at third level. This is a problem that needs to be addressed with urgency but also caution. The…
Technology has helped to innovate in the teaching-learning process. Today's students are more demanding actors when it comes to the environment, they have at their disposal to learn, experiment and develop critical thinking. The area of…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
Computer-supported collaborative learning (CSCL) has been a steady topic of research since the early 1990s, and the trend has continued to this date. The basic benefits of CSCL in the classroom have been established in many fields of…
For the past several decades, programmers have been modeling things in the world with trees using hierarchies of classes and object-oriented programming (OOP) languages. In this paper, we describe a novel approach to programming, called…
This paper aims to advance the mathematical intelligence of machines by presenting the first Chinese mathematical pre-trained language model~(PLM) for effectively understanding and representing mathematical problems. Unlike other standard…
Introductory programming courses often rely on small code-writing exercises that have clearly specified problem statements. This limits opportunities for students to practice how to clarify ambiguous requirements -- a critical skill in…
Contributing to the literature on aptitude-treatment interactions between worked examples and problem-solving, this paper addresses differential learning from the two approaches when students are positioned as domain experts learning new…