Related papers: Teaching Divisibility and Binomials with Coq
We describe the formalisation in Coq of a proof that the numbers e and $\pi$ are transcendental. This proof lies at the interface of two domains of mathematics that are often considered separately: calculus (real and elementary complex…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
In this article, we try to explain and unify standard divisibility tests found in various books. We then look at recurring decimals, and list a few of their properties. We show how to compute the number of digits in the recurring part of…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…
These few pages briefly present the way in which Activity Theory has been adopted for several years now by French researchers in didactics of mathematics and has been adapted to study the learning of school mathematics in relation with the…
There are different manners of teaching a spreadsheet program. In any case, it is intended that the teacher settles the objectives of the course and adapts them to the particular audience he/she has to deal with. This paper aims at…
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research…
The aim of this study is to construct and compose an instructional design in combinatorial learning, particularly in the concept of counting. A composed design is expected to optimize students' combinatorial-thinking skill. This research…
Divisibility tests are algorithms that can quickly decide if one integer is divisible by another. There are many tests but most are either of the trimming or summing variety. Our goals are to present Zbikowski's family of trimming tests as…
Quantum mechanics is a notoriously abstract subject, and therefore challenging to teach at pre-college and introductory college levels. Here we introduce the Bloch Cube, a hands-on educational tool which can illustrate key quantum concepts…
As the field of Quantum Computing continues to grow, so too has the general public's interest in testing some of the publicly available quantum computers. However, many might find learning all of the supplementary information that goes into…
These notes on modern cosmology were made with high school teachers and students in mind. Taking into account the lack of availability of time and classes that many teachers have nowadays in Brazil, often caused by having to comply with…
In its most general form, a `secret objective' is any inconsistency between the experimental reality and the information provided to students prior to starting work on an experiment. Students are challenged to identify the secret objectives…
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
Quantum computing is a technology that promises to offer significant advantages during the coming decades. Though the technology is still in a prototype stage, the last few years have seen many of these prototype devices become accessible…
Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates into the students a loss of interest with a consequent removal of motivation in the…
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation…
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for…