Related papers: Some instructive mathematical errors
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
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…
Tools have become a mainstay of LLMs, allowing them to retrieve knowledge not in their weights, to perform tasks on the web, and even to control robots. However, most ontologies and surveys of tool-use have assumed the core challenge for…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
This study addresses the critical issue of factual inaccuracies in machine-generated text summaries, an increasingly prevalent issue in information dissemination. Recognizing the potential of such errors to compromise information…
When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…
Prior research demonstrates that performance of language models on reasoning tasks can be influenced by suggestions, hints and endorsements. However, the influence of endorsement source credibility remains underexplored. We investigate…
Google Scholar has been well received by the research community. Its promises of free, universal and easy access to scientific literature as well as the perception that it covers better than other traditional multidisciplinary databases the…
Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…
Suspense is an important tool in storytelling to keep readers engaged and wanting to read more. However, it has so far not been studied extensively in Computational Literary Studies. In this paper, we focus on one of the elements authors…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics…
Current research on bias in machine learning often focuses on fairness, while overlooking the roots or causes of bias. However, bias was originally defined as a "systematic error," often caused by humans at different stages of the research…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
How can one meaningfully make a measurement, if the meter does not conform to any standard and its scale expands or shrinks depending on what is measured? In the present work it is argued that current evaluation practices for…
Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances…
It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree…
Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt…
We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities -- (1) formulating models; (2) analysing models; and (3) fitting or comparing…
We propose a novel system, MathMistake Checker, designed to automate step-by-step mistake finding in mathematical problems with lengthy answers through a two-stage process. The system aims to simplify grading, increase efficiency, and…