Related papers: An invitation to Fibonacci digits
In this article, we reflect upon our positive experiences incorporating or working on extra credit projects in algebra-based introductory physics that asked students to connect physics with humanities, social sciences, and everyday life. We…
I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness.
The study examines the relationship between Ball's magic numbers and reverses divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while…
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
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…
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
A few remarks on how mathematics quests for freedom.
We study the Fibonacci and Lucas numbers and demonstrate how identities can be constructed by investigating trivalent graphs and splitting fields.
The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…
This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…
This work reports on results from the first national study of the impact of student facilitation of informal physics outreach programs on their physics identity, sense of belonging, and essential career skill development. Drawing on results…
Shared artifacts and environments play a prominent role in shaping the collaboration between their users. This article describes this role and explains how annotations can provide a bridge between direct communication and collaboration…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…
The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the…
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…