Related papers: Some instructive mathematical errors
This paper describes types of errors arising in a recently proposed method of incidence estimation from prevalence data. The errors are illustrated by a simulation study about a hypothetical irreversible disease. In addition, a way of…
Assessing student handwritten scratchwork is crucial for personalized educational feedback but presents unique challenges due to diverse handwriting, complex layouts, and varied problem-solving approaches. Existing educational NLP primarily…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
Production machine learning (ML) systems fail silently -- not with crashes, but through wrong decisions. While observability is recognized as critical for ML operations, there is a lack empirical evidence of what practitioners actually…
If you want to tell people the truth, make them laugh, otherwise they'll kill you. (source unclear) Machine learning and deep learning are the technologies of the day for developing intelligent automatic systems. However, a key hurdle for…
Offline evaluation is a popular approach to determine the best algorithm in terms of the chosen quality metric. However, if the chosen metric calculates something unexpected, this miscommunication can lead to poor decisions and wrong…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
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…
Those of us who teach Mathematics for Liberal Arts (MLA) courses often underestimate the mathematical abilities of the students enrolled in our courses. Despite the fact that many of these students suffer from math anxiety and will admit to…
Large Language Models (LLMs) exhibit strong potential in mathematical reasoning, yet their effectiveness is often limited by a shortage of high-quality queries. This limitation necessitates scaling up computational responses through…
Intelligent Tutoring Systems (ITSs) often contain an automated feedback component, which provides a predefined feedback message to students when they detect a predefined error. To such a feedback component, we often resort to template-based…
Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…
Peer review and citation metrics are two means of gauging the value of scientific research, but the lack of publicly available peer review data makes the comparison of these methods difficult. Mathematics can serve as a useful laboratory…
In recent years, many studies have applied wearable devices to capture psychophysiological data from software developers. However, the current literature lacks investigations that classify the studies and point out gaps to be explored. This…
In a variety of applications, such as handwritten mathematics and diagram labelling, it is common to have symbols of many different sizes in use and for the writing not to follow simple baselines. In order to understand the scale and…
In this paper we have suggested a family of estimators for the population mean in the presence of measurement errors. Expression for the mean squared error (MSE) of the suggested family is derived. An empirical study has been carried out to…
Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical…
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…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with…