For more information on the published version, visit Mathematical Association of America's (MAA) Website., Richeson, David. A-Tweeting We Will Go: Building a Professional Network with Twitter. MAA Focus 37, no. 3 (2017):...
For more information on the published version, visit MAA's (Mathematical Association of America) Website., Bowen, Jennifer, Mark Kozek, Pamela Pierce, and Jennifer Schaefer. Advice for First-Year Seminar Instructors. In...
Our research experimentally, mathematically, and computationally investigated the singularity that forms at the tip of water droplets freezing on a flat surface (Snoeijer and Brunet, AJP 2012). We designed an apparatus to...
For more information on the published version, visit Science Direct's Website., Several studies have found that students' academic achievement is as much determined by the socioeconomic composition of their school as their own...
Bryant, Sarah N., and Jennifer B. Schaefer. Becoming Successful Proof-Writers Through Peer Review, Journals, and Portfolios. In Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of Proof-Writing...
For more information on the published version, visit Mathematical Association of America's Website., This past semester I (Jennifer Schaefer) taught single-variable calculus. Like many of you, I have taught this course numerous...
We discuss connectivity properties of Julia sets of the parameterized Dixon elliptic functions. Our main result is that the connectivity locus of the parameterized Dixon sine function is the exterior of the open unit disc, and...
Published as:Koss, Lorelei. Cantor Julia Sets in a Family of Even Elliptic Functions. Journal of Difference Equations and Applications 16, no. 5-6 (2010): 675-88. For more information on the published version, visit Taylor...
D'Agostino, Susan, Sarah Bryant, Amy Buchmann, Michelle Craddock Guinn, and Leona Harris, eds. A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond. Cham: Springer, 2019., The Enhancing Diversity...
Just where is the geographic center of the United States? And where is the population center? In this article we describe how to find these and other geographic features of the U.S. The approach we take is appropriate for a...
We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant equals the area constant. He stated neither result...
In this paper we will discuss the orbits of the fixed-point group on the tori of the generalized symmetric spaces of SL2(k) where k is a finite field. Specifically, we will provide a characterization and classification of the...
This paper is concerned with binary quadratic programs (BQPs), which are among the most well-studied classes of nonlinear integer optimization problems because of their wide variety of applications. While a number of different...
Published as: Hawkins, Jane and Lorelei Koss. Connectivity Properties of Julia Sets of Weierstrass Elliptic Functions. Topology and its Applications 152, no. 1 (2005): 107-37. For more information on the published version,...
A lot of research has been spent determining the domination numbers, γ m,n, of grid graphs. But relatively little effort has been given to constructing minimum dominating sets of grid graphs. In this paper, we introduce a...
Timothy Gowers was the 2015 recipient of the Joseph Priestley Award at Dickinson College. On March 26, 2015, Gowers gave a public lecture at the college and received his award. Afterward David Richeson chatted with Gowers...
We consider the subordinate killed Brownian motion process generated by first killing Brownian motion at some boundary point on a smooth bounded domain then subordinating by a Lévy time-clock. For classes of subordinators...
Conventional farming utilizes tools such pesticides, synthetic chemical fertilizers, and herbicides, with the goal of producing large amounts of food on less land and with less labor. While these powerful mechanisms help to...
Lorelei Koss is a professor of Mathematics at Dickinson College. , Koss, Lorelei. Crowdsourcing Solutions in the Online Mathematics Classroom. International Journal of Mathematical Education in Science and Technology 53, no....
Published as:Koss, Lorelei. Differential Equations in Literature, Poetry and Film. Journal of Mathematics and the Arts 9, no. 1-2 (2015): 1-16. For more information on the published version, visit Taylor and Francis's...
Koss, Lorelei. Differential Equations in Music and Dance. Journal of Mathematics and the Arts 10, no. 1-4 (2016): 53-64., For more information on the published version, visit Taylor and Francis's Website., and This is the...
Kokichi Sugihara, a professor of engineering in Japan, has spent decades making objects look and move in seemingly impossible ways. This year Sugihara’s video Ambiguous Optical Illusion received second prize in the Neural...
We study the dynamics of a family of polynomial functions and the relationship to the dynamics of a related entire transcendental family of functions. As the degree of the polynomial approaches infinity, the polynomial...
Published as:Goldsmith, Jeff and Lorelei Koss. Dynamical Properties of the Derivative of the Weierstrass Elliptic Function. Involve 2, no. 3 (2009): 267-88.For more information on the published version, visit Mathematical...
In studying dynamical systems, we often use algebraic tools to determine the dynamical behavior of a given function. However, when working with a transcendental function such as the real Weierstrass elliptic function, ℘, we...
For more information on the published version, visit Mathematical Sciences Publisher's Website., In this paper, we investigate the dynamics of iterating the Weierstrass elliptic functions on vertical real rhombic lattices. The...
Bryant, Sarah, and Jessica Spott. The EDGE Program: 20 Years and Counting. In A Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond, edited by Susan D'Agostino, Sarah Bryant, Amy Buchmann,...
String art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting...
Published as:Hawkins, Jane, Lorelei Koss, and Janina Kotus. Elliptic Functions with Critical Orbits Approaching Infinity. Journal of Difference Equations and Applications, 16, no. 5-6 (2010): 613-30.For more information on...
In this paper, we investigate elliptic functions of the form , where is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin...
Bryant, Sarah, Christina Eubanks-Turner, Charles Moore, Sarah Reznikoff, and Josephine Yu. Equity in Mathematics Education: Five Mathematicians Reflect on the 2018 PCMI Workshop. MAA Focus 38, no. 6 (2018): 16-18....
Published as:Koss, Lorelei. Ergodic and Bernoulli Properties of Analytic Maps of Complex Projective Space. Transactions of the American Mathematical Society 354, no. 6 (2002): 2417-2459. For more information on the published...
We discuss properties of the Julia and Fatou sets of Weierstrass elliptic p functions arising from real lattices. We give sufficient conditions for the Julia sets to be the whole sphere and for the maps to be ergodic, exact,...
Published as:Barnes, Julia and Lorelei Koss. The Ergodic Theory Carnival. Mathematics Magazine, 83, no. 3 (2010): 180-90.For more information on the published version, visit Mathematical Association of America's Website....
For more information on the published version, visit Princeton University Press's Website. Euler's Gem: The Polyhedron Formula and the Birth of Topology was selected to be included in the Princeton Science Library series, a...
This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit New York Journal of Mathematics's Website., Koss, Lorelei. "Examples of...
For more information on the published version, visit Project Euclid's Website. Also see: Addendum to:A Fixed Point Theorem for Bounded Dynamical Systems'' published as:Richeson, David, and Jim Wiseman. Addendum to:A...
In this paper, we characterize and classify the orbits of the fixed-point group on the unipotent elements of the generalized symmetric spaces for inner involutions of SL3(k) and SL4(k) where k is a finite field of odd...
For more information on the published version, visit Taylor and Francis's Website., Francese, Christopher, and David Richeson. The Flaw in Euler's Proof of His Polyhedral Formula. The American Mathematical Monthly 114, no. 4...
A nematocyst is a specialized organelle within cells of jellyfish and other Cnidarians that sting. Nematocysts are also present in some single-celled protists. They contain a barbed venomous thread that accelerates faster than...
Published as:Koss, Lorelei. A Fundamental Dichotomy for Julia Sets of a Family of Elliptic Functions. Proceedings of the American Mathematical Society, 137 no. 11 (2009): 3927-3938. For more information on the published...
Symmetric spaces of Lie groups and Riemannian manifolds have been an area of study since the seminal work of Cartan in the early 19th century with applications to representation theory, geometry, and number theory. Though...
Instructors teaching empirical techniques in managerial economics or economic and business statistics courses often face a dilemma. The typical student in these classes has less mathematical sophistication than those in...
Clemons, Joshua J., and Lorelei Koss. Higher Order Elliptic Functions with Connected Julia Sets. Topology Proceedings 53 (2019): 57-72. (Article published online May 7, 2018)....
For more information on the published version, visit MAA Focus's Website., Armstrong, Alice, Sarah Bryant, Robin McCann, and Kate McGivney. How to Combat Unconcious Bias. MAA Focus April/May (2015): 10-12....
Tired of hearing people ask which area of maths is your favourite? Get one of these tattooed on your forehead and you’ll never be asked again…, For more information on the published version, visit Chalkdust Magazine's Website.,...
Many post-secondary academic institutions in the United States have a First-Year Seminar Program. These seminars are designed to support the success of new incoming first-year students by combining writing, research and active...
Forrester, Richard, and Miguel Rodriguez. An Integer Programming Approach to Crop Rotation Planning at an Organic Farm. The UMAP Journal 38, no. 4 (2018): 5-25. http://www.comap.com/product/?idx=1617, This published version...
Published as: Richeson, David, Paul Winkler, and Jim Wiseman. Itineraries of Rigid Rotations and Diffeomorphisms of the Circle. Theoretical Computer Science 411, no. 1 (2010): 259-265....
For more information on the published version, visit Mathematical Association of Amercia's (MAA) Website., Richeson, David. The Japanese Theorem for Nonconvex Polygons. Convergence (December 2013)....
Let ℘ be the Weierstrass ℘-function. Then ℘(2z)=R(℘(z)) for some rational function R· It was shown by Lattès (1919) that the Julia set of this rational function R is the whole sphere. A similar example using Jacobian elliptic...
Digital Edition., Richeson, David. Letters of Recommendation. XRDS (Crossroads: The ACM Magazine for Students) 17, no. 3 (Spring 2011): 6. https://xrds.acm.org/article.cfm?aid=1925052, HTML, For more information on the...
Binary quadratic and higher-order polynomial programs are widely studied in the optimization literature by both theoreticians and practitioners alike. Despite boasting many diverse applications in a variety of settings, these...
Bryant, Sarah, Amy Buchmann, Michelle Craddock Guinn, Susan D'Agostino, and Leona Harris. The Long-Lasting Impact of EDGE: Testimonials from the EDGE Community. In A Celebration of the EDGE Program's Impact on the Mathematics...
Published as:Koss, Lorelei. Manipulatives for 3-Dimensional Coordinate Systems. PRIMUS 21, no. 4 (2011): 364-76. For more information on the published version, visit Taylor and Francis's Website. and We describe a set of...
For more information on the published version, visit MAA's (Mathematical Association of America) Website., I discuss my experience at Dickinson College teaching a first-year seminar investigating the portrayals of...
Every first-year student at Dickinson College is required to take a first-year seminar. The summer before the students arrive they each select six seminars among all the seminar choices. Each student is then assigned to a...
For more information on the published version, visit MAA's (Mathematical Association of America) Website., The purpose of this volume is to share with undergraduate mathematics faculty ideas for teaching a...
The programs supporting diversity in mathematics are as important as ever. So why are they losing funding? And what hope do they have of thriving in the current political climate? In this collaborative interview, two past...
The study of braids started in the early 20th century with the motivation of revealing properties of knots and links. The Artin braid group gives an algebraic tool to analyze the braid actions and the equivalence of braids....
Operations research practitioners frequently need to enforce logical conditions, such as if-then implications, within a mixed-integer linear program (MILP). Unfortunately, it is not always clear how to represent such conditions...
We describe some connections between differential equations, music, and dance. Some of these connections involve using differential equations to understand and explain the physical world around us, such as modeling sound...
We study the structure of p-parts of Weyl group multiple Dirichlet series. In particular, we extend results of Chinta, Friedberg, and Gunnells and show, in the stable case, that the p-parts of Chinta and Gunnells agree with...
We investigate the symmetric spaces associated to the family of semidihedral groups of order 2n. We begin this study by analyzing the structure of the automorphism group and by determining which automorphims are involutions. We...
This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Hindawi Publishing Corporation's Website., We prove that there are...
Friedlander, Holley, William Grodzicki, Wayne Johnson, Gail Radcliff, Anna Romanov, Benjamin Strasser, and Brent Wessel. An Orbit Model for the Spectra of Nilpotent Gelfand Pairs. Transformation Groups 25 (2020): 859-886....
Koss, Lorelei. Ordinary Differential Equations and Easter Island: A Survey of Recent Research Developments on the Relationship Between Humans, Trees, and Rats. European Journal of Mathematics (Article published online April...
Published as:Hawkins, Jane and Lorelei Koss. Parametrized Dynamics of the Weierstrass Elliptic Function. Conformal Geometry and Dynamics 8, no. 1 (2004): 1-35. For more information on the published version, visit American...
On November 14, 1750 Leonhard Euler sent a letter from Berlin to his friend Christian Goldbach in St. Petersburg announcing his discovery of a simple relationship between the features on a polyhedron. This observation, now...
For more information on the published version, visit Science Direct’s Website., We introduce the notions of weakly and strongly positively expansive (wPE and sPE, respectively) discrete dynamical systems. Both are topological...
Richeson, David, and Jim Wiseman. Positively Expansive Homeomorphisms of Compact Spaces. International Journal of Mathematics and Mathematical Sciences Volume 2004, Article ID 821324, 4 pp....
Using the Japanese theorem on cyclic polygons, we visually show that the sum of inradii in a triangulation of a regular polygon approaches the diameter of the circumcircle as the number of sides tends to infinity., Richeson,...
We analyze the dynamics of a sequence of families of non-polynomial rational maps, {f a,d }, for a ∈ C* = C \ {0}, d ≥ 2. For each d, {f a,d } is a family of rational maps of degree d of the Riemann sphere parametrized by a ∈...
For more information on the published version, visit American Mathematical Society's (AMS) Website. See also: Furno, Joanna, and Lorelei Koss. Relating Singularly Perturbed Rational Maps to Families of Entire Maps. In...
Published as: Franks, John, and David Richeson. Shift Equivalence and the Conley Index. Transactions of the American Mathematical Society 352, no. 7 (2000): 3305-3322....
We analyze the existence and types of unbounded Fatou components for elliptic functions and other meromorphic functions with doubly periodic Julia sets. We show that apart from Herman rings and Siegel disks, all types of...
Das, Tarun, Keonhee Lee, David Richeson, and Jim Wiseman. Spectral Decomposition for Topologically Anosov Homeomorphisms on Noncompact and Non-Metrizable Spaces. Topology and its Applications 160, no. 1 (2013): 149-158....
Bryant, Lance, Sarah Bryant, and Diana White. Striking the Right Chord: Math Circles Promote (Joyous) Professional Growth. In The Celebration of the EDGE Program's Impact on the Mathematics Community and Beyond, edited by...
The mathematical study of frieze symmetry in art is well established; to date, scholarship has focused primarily on historical artefacts or traditional crafts. Here, we apply established tools to an emerging craft of a global...
Richeson, David S. Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity. Princeton, NJ: Princeton University Press, 2019., For more information on the published version, visit Princeton...
Forrester, Richard J. Tightening Concise Linear Reformulations of 0-1 Cubic Programs. Optimization 65, no. 4 (2016): 877-903., For more information on the published version, visit Taylor and Francis's Website., and A common...
Grading is a way for faculty to both assess student work and provide feedback to students on their level of understanding of a course’s material. Whether your grading system is traditional or nontraditional, the feedback-giving...
For more information on the published version, visit World Scientific’s Website., We introduce topological helicity, an invariant for oriented framed links. Topological helicity provides an elementary means of computing...
Besson, Marc, and Barry Tesman. Tr - Span of Directed Wheel Graphs. Discussiones Mathematicae Graph Theory 38 (2018): 871-888., In this paper, we consider T-colorings of directed graphs. In particular, we consider as a T-set...
This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit The WAC Clearinghouse's Website., Bryant, Sarah, Noreen Lape, and Jennifer...
In 1928, Henry Scudder described how to use a carpenter's square to trisect an angle. We use the ideas behind Scudder's technique to define a trisectrix—a curve that can be used to trisect an angle. We also describe a compass...
Though posters have been used as a pedagogical tool in a variety of fields, the literature suggests that the use of posters as an educational assessment tool by the mathematics community has been limited. This is unfortunate...