Related papers: Composite Numbers in an Arithmetic Progression
Teaching graph theory with the most adequate tools requires time and ideas. We present how an open community of teachers shares contents and ideas on an innovative platform. The objective is to get the students autonomous in their training…
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…
Curriculum learning--ordering training examples in a sequence to aid machine learning--takes inspiration from human learning, but has not gained widespread acceptance. Static strategies for scoring item difficulty rely on indirect proxy…
These are the notes of my lectures at the 1996 European Congress of Mathematicians. {} Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones.…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…
We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
Numerical analysis has no satisfactory method for the more realistic optimization models. However, with constraint programming one can compute a cover for the solution set to arbitrarily close approximation. Because the use of constraint…
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties.…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
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…
Elementary school students sometimes exhibit deplorable behaviors when faced with arithmetic problems. These behaviors may result from certain teaching practices and could be mitigated by a few actions that are relatively easy to implement…
This is a survey of old and new problems and results in additive number theory.
In this paper, we describe how we changed the structure of problem sessions in an algorithmic subject, in order to improve student confidence. The subject in question is taught to very large cohorts of (around 900) students, though our…
The aim of this paper is to present a didactical sequence that fosters the development of meanings related to fractions, conceived as numbers that can be placed on the number line. The sequence was carried out in various elementary school…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…