Related papers: Teaching Divisibility and Binomials with Coq
Machine language acquisition is often presented as a problem of imitation learning: there exists a community of language users from which a learner observes speech acts and attempts to decode the mappings between utterances and situations.…
Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…
The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum…
In this work, we present the results of a research in which we aimed to evidence obstacles and advances in pre-service teachers' conceptualization on a subject involving elementary Quantum Mechanics. We based our analysis on the theories…
In domain theory every finite computable object can be represented by a single mathematical object instead of a set of objects, using the notion of finitary-basis. In this article we report on our effort to formalize domain theory in Coq in…
The revolutionary new field of Quantum Computing (QC) continues to gain attention in industry, academia, and government in both research and education. At educational institutions, there is a proliferation of introductory courses at various…
The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
We designed three color-coding schemes to identify related information across representations and to differentiate distinct information within a representation in slide-based instruction for calculus-based introductory mechanics. We found…
Recent advances in our understanding of the Universe have revolutionized our view of its structure, composition and evolution. However, these new ideas have not necessarily been used to improve the teaching of introductory astronomy…
We present educational material about Bell inequalities in the context of quantum computing. In particular, we provide software tools to simulate their violation, together with a guide for the classroom discussion. The material is organized…
We describe the development of a Quantum Interactive Learning Tutorial (QuILT) on quantum key distribution, a context which involves a practical application of quantum mechanics. The QuILT helps upper-level undergraduate students learn…
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…
This article describes a curricular innovation designed to help students experience authentic physics inquiry with an emphasis on computational modeling and scientific communication. The educational design centers on a new type of…
Reproducibility of computational studies is a hallmark of scientific methodology. It enables researchers to build with confidence on the methods and findings of others, reuse and extend computational pipelines, and thereby drive scientific…
We present new applications on $q$-binomials, also known as Gaussian binomial coefficients. Our main theorems determine cardinalities of certain error-correcting codes based on Varshamov-Tenengolts codes and prove a curious phenomenon…
In this work, we describe our experience in learning the use of a computer proof assistant - specifically, Lean - from scratch, through proving formulae for the solutions of polynomial equations. Specifically, in this work we characterize…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
IWIMS (WWW Interactive Multipurpose Server) offers interactive resources designed over the past 20 years for teaching in various subjects (particularly focusing on mathematics, but also in biology, chemistry, economics, languages, physics),…