Related papers: Conceptual Mathematics via Literate Programming
The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…
Mathematical documents written in LaTeX often contain ambiguities. We can resolve some of them via semantic markup using, e.g., sTeX, which also has other potential benefits, such as interoperability with computer algebra systems, proof…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
Theorists and advocates of "remixing" have suggested that appropriation can act as a pathway for learning. We test this theory quantitatively using data from more than 2.4 million multimedia programming projects shared by more than 1…
We describe a way to introduce physics high school students with no background in programming to computational problem-solving experiences. Our approach builds on the great strides made by the Modeling Instruction reform curriculum. This…
As pervasive data collection and powerful algorithms increasingly shape children's experience of the world and each other, their ability to interrogate computational algorithms has become crucially important. A growing body of work has…
This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and…
Computation has become an integral part of physics research. However, little is known about how students learn to productively use computation as a tool beyond the introductory level, especially as they transition into physics research. In…
The problems in our teaching on object-oriented programming are analyzed, and the basic ideas, causes and methods of the reform are discussed on the curriculum, theoretical teaching and practical classes. Our practice shows that these…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
We study the problem of computer-assisted teaching with explanations. Conventional approaches for machine teaching typically only provide feedback at the instance level e.g., the category or label of the instance. However, it is intuitive…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
We outline a new tool that can promote coherence within and across higher education mathematics courses by focusing on problem-solving: the Mathematical Problem-Solving Pipeline or MPSP. The MPSP can be used for teaching mathematics and…
A functional hardware description language enables students to gain a working understanding of computer systems, and to see how the levels of abstraction fit together. By simulating circuits, digital design becomes a living topic, like…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…