Judy Holdener

• Kenyon College

Two special issues of PRIMUS focus on The Creation and Implementation of Effective Homework Assignments. In this introduction to Part 2, we present some of the literature surrounding best homework practices for successful student learning. We then introduce the six papers appearing in this issue, which focuses on the implementation of homework in m...

Two special issues of PRIMUS focus on The Creation and Implementation of Effective Homework Assignments. In this introduction to the first issue, we discuss the tensions facing instructors today surrounding homework design and implementation and provide an overview of recent PRIMUS articles published on the subject. Using the notion of “learning go...

Over millennia, storytelling has been an effective way of passing on information to future generations. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article we consider the role of narrative in the design and implementati...

In this article we present three group activities designed for math students: a balloon-twisting workshop, a group proof of the irrationality of π, and a game of Math Bingo. These activities have been particularly successful in building enthusiasm for mathematics and camaraderie among math faculty and students at Kenyon College.

Does your hometown have any mathematical tourist attractions such as statues, plaques, graves, the cafe where the famous conjecture was made, the desk where the famous initials are scratched, birthplaces, houses, or memorials? Have you encountered a mathematical sight on your travels? If so, we invite you to submit an essay to this column. Be sure...

There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind....

This illustration of two sums of sines and cosines shows a finger supporting a tray of glasses. The center of mass of the tray, on which the glasses are placed at the Nth roots of unity, clearly lies at the origin. This shows that the sums of real and imaginary parts are zero and these are the sums of sines and cosines of the title.

In this article, the authors present a mathematical scavenger hunt designed to motivate and excite students learning RSA cryptography in an introductory number theory course. The hunt relies on the RSA cryptosystem, in which Maple is used to encipher and decipher secret information contained within the clues.

The abundancy index of a positive integer n is defined to be the rational number I(n) = σ(n)/n, where σ is the sum of divisors function σ(n) = Σd|n- An abundancy outlaw is a rational number greater than 1 that fails to be in the image of of the map I. In this paper, we consider rational numbers of the form (σr(N) + t)/N and prove that under certain...

P. A. Weiner [ibid. 73, 307–310 (2000; Zbl 1227.11017)] proved that if the abundancy of an integer n is 5/3, then 5n is an odd perfect number. R. F. Ryan [Math. Mag. 76, No. 4, 299–301 (2003; Zbl 1051.11010)] generalized Weiner’s result by proving that if there exists a positive integer n and an odd positive integer m such that 2m-1 is a prime not...

The card game SET has attracted the attention of math and game enthusiasts alike. In this article, I present a first semester Abstract Algebra project that guides the students through an algebraic formulation of the game. There are many interesting mathematical questions that one can ask about the game, and I illustrate how the project can be used...

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section...

A turtle sequence is a word constructed from an alphabet of two letters: F, which represents the forward motion of a turtle in the plane, and L, which represents a counterclockwise turn. In this paper, we investigate such sequences and establish links between the combinatoric properties of words and the geometric properties of the curves they gener...

Results of an anchored final exam in a reformed computer-based multivariable calculus course are presented. The reformed course was taught in a computer lab using the Calculus & Mathematica materials, and the final exam was anchored to the final given in the standard calculus course.

The abundancy index of a positive integer n is defined to be the rational number I(n)=sigma(n)/n, where sigma is the sum of divisors function sigma(n)=sum_{d| n}d. An abundancy outlaw is a rational number greater than 1 that fails to be in the image of of the map I. In this paper, we consider rational numbers of the form (sigma(N)+t)/N and prove th...