Related papers: Teaching Divisibility and Binomials with Coq
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
In France, the first year of study at university is usually abbreviated L1 (for premiere annee de Licence). At Sorbonne Paris Nord University, we have been teaching an 18 hour introductory course in formal proofs to L1 students for 3 years.…
We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…
The milq approach to quantum physics for high schools focuses on the conceptual questions of quantum physics. Students should be given the opportunity to engage with the world view of modern physics. The aim is to achieve a conceptually…
We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
We present Bicoq3, a deep embedding of the B system in Coq, focusing on the technical aspects of the development. The main subjects discussed are related to the representation of sets and maps, the use of induction principles, and the…
We are investigating cognitive issues in learning quantum mechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Engaging students in teaching foundational Computer Science concepts is vital for the student's continual success in more advanced topics in the field. An idea of a series of Jupyter notebooks was conceived as a way of using Bloom's…
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…
We describe the basic notions of co-induction as they are available in the coq system. As an application, we describe arithmetic properties for simple representations of real numbers.
In this paper, we gave some properties of binomial coefficient.
In this note we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task-design that gives students the opportunity to conjecture, refute and prove. What is…
As quantum information science advances and the need for pre-college engagement grows, a critical question remains: How can young learners be prepared to participate in a field so radically different from what they have encountered before?…
This is an informal and mostly expository note describing some asymptotic behavior and qualitative properties of the q-binomial coefficients. The results are mostly not new, but the overall story we present does not seem to be well known --…