Related papers: Beginning Mathematical Writing Assignments
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
Over the past 20 years, Wikipedia has gone from a rather outlandish idea to a major reference work, with more than 60 million articles across all languages, including nearly 7 million in English [Wiki01]. Around 27,000 of these articles…
While state-of-the-art LLMs have shown poor logical and basic mathematical reasoning, recent works try to improve their problem-solving abilities using prompting techniques. We propose giving "hints" to improve the language model's…
For many students, introductory college science courses are often the only opportunity in their formal higher education to be exposed to science, shaping their view of the subject, their scientific literacy, and their attitudes towards…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
This is a draft of my textbook on mathematical analysis and the areas of mathematics on which it is based. The idea is to fill the gaps in the existing textbooks. Any remarks from readers are welcome.
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
This introduction to arithmetic coding is divided in two parts. The first explains how and why arithmetic coding works. We start presenting it in very general terms, so that its simplicity is not lost under layers of implementation details.…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
Starting from the well-known and elementary problem of inscribing the rectangle of the greatest area in an ellipse, we look at possible, gradually more and more complicated variants of this problem. Our goal is to demonstrate to an average…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
Language students are most engaged while reading texts at an appropriate difficulty level. However, existing methods of evaluating text difficulty focus mainly on vocabulary and do not prioritize grammatical features, hence they do not work…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics…
Readability assessment is the task of evaluating the reading difficulty of a given piece of text. Although research on computational approaches to readability assessment is now two decades old, there is not much work on synthesizing this…
Many instructors choose to assess their students using open-ended written exam items that require students to show their understanding of physics by solving a problem and/or explaining a concept. Grading these items is fairly time…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…