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Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…
This study examines the adaptation of the problem-solving studio to computer science education by combining it with pair programming. Pair programming is a software engineering practice in industry, but has seen mixed results in the…
Our main goal is to develop plans to increase physics enrollment. Once again we thoroughly analyze the problem from the beginning and reach the conclusion that the most appropriate starting point in this direction should be to look into…
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and…
Mathematical reasoning with algebraic and graphical representations is essential for success in physics courses. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely…
Improving modularity and reusability are two key objectives in object-oriented programming. These objectives are achieved by applying several key concepts, such as data encapsulation and inheritance. A class in an object-oriented system is…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
This paper suggests integrating one-dimensional optimization methods to tackle diverse problems, emphasizing their significance in resolving practical issues and applying mathematical principles to real-world contexts. It focuses on…
In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…
With the advent of multi-core processors and their fast expansion, it is quite clear that {\em parallel computing} is now a genuine requirement in Computer Science and Engineering (and related) curriculum. In addition to the pervasiveness…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Worked examples (solutions to typical programming problems presented as a source code in a certain language and are used to explain the topics from a programming class) are among the most popular types of learning content in programming…
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often…
The field of partial differential equations (PDEs) is vast in size and diversity. The basic reason for this is that essentially all fundamental laws of physics are formulated in terms of PDEs. In addition, approximations to these…
A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…
In a first course to classical mechanics elementary physical processes like elastic two-body collisions, the mass-spring model, or the gravitational two-body problem are discussed in detail. The continuation to many-body systems, however,…
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is…
An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…
We present the results of an experience of teaching updating dispensed to Italian high-school physics teachers to promote the application of the Cooperative Problem Solving method as an useful strategy to improve physics learning at…