Related papers: Parmesan: mathematical concept extraction for educ…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models 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…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
The definition of who is or what makes a ``mathematician" is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered…
Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery…
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…
Product Data Management (PDM) aims to provide 'Systems' contributing in industries by electronically maintaining organizational data, improving data repository system, facilitating with easy access to CAD and providing additional…
Concurrent to the rapid progress in the development of neural-network based models in areas like natural language processing and computer vision, the need for creating explanations for the predictions of these black-box models has risen…
Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…
Generating a huge number of association rules reduces their utility in the decision making process, done by domain experts. In this context, based on the theory of Formal Concept Analysis, we propose to extend the notion of Formal Concept…
Recognizing handwritten mathematics is a challenging classification problem, requiring simultaneous identification of all the symbols comprising an input as well as the complex two-dimensional relationships between symbols and…
In natural language, words and phrases themselves imply the semantics. In contrast, the meaning of identifiers in mathematical formulae is undefined. Thus scientists must study the context to decode the meaning. The Mathematical Language…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical…
Machine-learning models are ubiquitous. In some domains, for instance, in medicine, the models' predictions must be interpretable. Decision trees, classification rules, and subgroup discovery are three broad categories of supervised…