Related papers: Composite Numbers in an Arithmetic Progression
Good problems grab us. They invite us to find patterns, make conjectures, and prove-or perhaps disprove-a conjecture. When I first taught, I saw my work as tantalizing students with structures just beyond their reach, so that I could elicit…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients on the numerators.
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared…
Curriculum learning is a class of training strategies that organizes the data being exposed to a model by difficulty, gradually from simpler to more complex examples. This research explores a reverse curriculum generation approach that…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
The widespread establishment of computational thinking in school curricula requires teachers to introduce children to programming already at primary school level. As this is a recent development, primary school teachers may neither be…
Methods are developed for eliciting a Dirichlet prior based upon bounds on the individual probabilities that hold with virtual certainty. This approach to selecting a prior is applied to a contingency table problem where it is demonstrated…
The purpose of this paper is to introduce basic concepts that are fundamental in the examination of composite moduli, while avoiding the notoriously difficult problem of prime-factorization. We introduce a new class of numbers, called…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. Atle Selberg\cite{Selberg} gave an elementary proof of this theorem. In this article we give an alternative…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…