Related papers: An invitation to Fibonacci digits
The purpose of this paper is to investigate integer sequences with exponent lifting property, a property common in Fibonacci or Lucas sequences.
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
The purpose of this paper is to demonstrate that it is possible, in principle, to obtain knowledge of the entire universe at the present time, even if the radius of the universe is much larger than the radius of the observable universe.
We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern…
The flipped classroom technique has recently been a focus of attention for many math instructors and pedagogical researchers. Although research on the subject has greatly increased in recent years, it is still debated whether the flipped…
A strong sense of classroom community is associated with many positive learning outcomes and is a critical contributor to undergraduate students' persistence in STEM, particularly for women and students of color. This chapter describes a…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…
Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are…
This short note discusses the role of syntax vs. semantics and the interplay between logic, philosophy, and language in computer science and game theory.
In many data analysis applications, there is a need to explain why a surprising or interesting result was produced by a query. Previous approaches to explaining results have directly or indirectly used data provenance (input tuples…
Understanding how to engage users is a critical question in many applications. Previous research has shown that unexpected or astonishing events can attract user attention, leading to positive outcomes such as engagement and learning. In…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
Writing assignments in any mathematics course always present several challenges, particularly in lower-level classes where the students are not expecting to write more than a few words at a time. Developed based on strategies from several…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or…
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…
The purpose of this note is to offer some partition implications of a $q$-series that is connected to the second Atkin-Garvan moment. Inequalities and relationships among the number of divisors and partitions are provided as consequences.
Each time we teach, our students communicate to us. They talk, write, and draw. How do we take in their expressions of self and mathematics? How do we listen? In this column, published in the Fall 2023 AWM Newsletter, I explore different…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.