The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy,
2016
CUNY Graduate Center
The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer
Dissertations, Theses, and Capstone Projects
Nationwide, there is a crisis in math learning and math achievement at all levels of education. Upwards of 80% of students who enter the City University of New York’s community colleges from New York City’s Department of Education high schools fail to meet college level math proficiencies and as a result, are funneled into the system’s remedial math system. Once placed into pre-college remedial arithmetic, pre-algebra, and elementary algebra courses, students fail at alarming rates and research indicates that students’ failure in remedial math has negative ripple effects on their persistence and degree completion. CUNY is not alone in facing …
Method Of Lines Transpose: High Order L-Stable {O}(N) Schemes For Parabolic Equations Using Successive Convolution,
2016
Kettering University
Method Of Lines Transpose: High Order L-Stable {O}(N) Schemes For Parabolic Equations Using Successive Convolution, Matthew F. Causley, Hana Cho, Andrew J. Christlieb, David C. Seal
Mathematics Publications
We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a one-dimensional heat equation solver that uses fast $\mathcal O(N)$ convolution. This fundamental solver has arbitrary order of accuracy in space and is based on the use of the Green's function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct …
The Collatz Conjecture And Integers Of The Form 2KB−M And 3KB−1,
2016
Kutztown University
The Collatz Conjecture And Integers Of The Form 2KB−M And 3KB−1, Patrick Wiltrout, Eric Landquist
Furman University Electronic Journal of Undergraduate Mathematics
One of the more well-known unsolved problems in number theory is the Collatz (3n + 1) Conjecture. The conjecture states that iterating the map that takes even n ∈ N to n/2 and odd n to (3n+1)/2 will eventually yield 1. This paper is an exploration of this conjecture on positive integers of the form 2kb−m and 3kb−1, and stems from the work of the first author's Senior Seminar research. We take an elementary approach to prove interesting relationships and patterns in the number of iterations, called …
The Search For One As A Prime Number: From Ancient Greece To Modern Times,
2016
University of Tennessee at Martin
The Search For One As A Prime Number: From Ancient Greece To Modern Times, Angela Reddick, Yeng Xiong
Furman University Electronic Journal of Undergraduate Mathematics
It has often been asked if one is a prime number, or if there was a time when most mathematicians thought one was prime. Whether or not the number one is prime is simply a matter of definition, but definitions are often decided by the use of mathematics. In this paper we will survey the history of the definition of prime as applied to the number one, from the ancient Greeks to the modern times. For the Greeks the numbers (αριθμος) were multiples of the unit, and for this reason one did not fall into the category of …
On The Dead End Depth Of Thompson's Group F,
2016
University of Wisconsin–Stout
On The Dead End Depth Of Thompson's Group F, Justin Halverson
Furman University Electronic Journal of Undergraduate Mathematics
Thompson’s group F was introduced by Richard Thompson in the 1960’s and has since found applications in many areas of mathematics including algebra, logic and topology. We focus on the dead end depth of F, which is the minimal integer N such that for any group element, g, there is guaranteed to exist a path of length at most N in the Cayley graph of F leading from g to a point farther from the identity than g is. By viewing F as a diagram group, we improve the greatest known lower bound for the dead end depth …
Relative Goldbach Partitions And Goldbach's Conjecture,
2016
Abilene Christian University
Relative Goldbach Partitions And Goldbach's Conjecture, Houston Hutchinson
Furman University Electronic Journal of Undergraduate Mathematics
In this note, we utilize techniques from discrete mathematics to develop first an inequality, and then second a counting formula that is connected to Goldbach's conjecture. In order to do this, we introduce the notion of a Relative Goldbach Partition.
Integers Of The Form A2±B2,
2016
University of North Carolina at Charlotte
Integers Of The Form A2±B2, Robert Zeman
Furman University Electronic Journal of Undergraduate Mathematics
This paper explores which integers can be expressed in the form a2±2b2 by using rings of the form Z[√d], particularly when d = 2 and d = −2.
Paths And Circuits In G-Graphs Of Certain Non-Abelian Groups,
2016
Lamar University
Paths And Circuits In G-Graphs Of Certain Non-Abelian Groups, A. Dewitt, A. Rodriguez, Jennifer Daniel
Furman University Electronic Journal of Undergraduate Mathematics
In [BJRTD08], necessary and suffcient conditions were given for the existence of Eulerian and Hamiltonian paths and circuits in the G-graph of the dihedral group Dn. In this paper, we consider the G-graphs of the quasihedral, modular, and generalized quaternion group. These groups are of rank 2 and we consider only the graphs Γ(G, S) where |S|= 2.
The Relationships Between Cg, Bfgs, And Two Limited-Memory Algorithms,
2016
University of British Columbia
The Relationships Between Cg, Bfgs, And Two Limited-Memory Algorithms, Zhiwei (Tony) Qin
Furman University Electronic Journal of Undergraduate Mathematics
For the solution of linear systems, the conjugate gradient (CG) and BFGS are among the most popular and successful algorithms with their respective advantages. The limited-memory methods have been developed to combine the best of the two. We describe and examine CG, BFGS, and two limited-memory methods (L-BFGS and VSCG) in the context of linear systems. We focus on the relationships between each of the four algorithms, and we present numerical results to illustrate those relationships.
Finding Prime Numbers: Miller Rabin And Beyond,
2016
Spelman College
Finding Prime Numbers: Miller Rabin And Beyond, Christina Mcintosh
Furman University Electronic Journal of Undergraduate Mathematics
This expository paper motivates and explains the Miller Rabin test and gives some generalizations of it. The Miller Rabin test is a standard probabilistic test used to find large prime numbers quickly.
Carolinas Mathematics Undergraduate Research Conference Abstracts,
2016
Furman University
Carolinas Mathematics Undergraduate Research Conference Abstracts, John Harris
Furman University Electronic Journal of Undergraduate Mathematics
On Friday, March 24, 2006, Furman University hosted the Carolinas Mathematics Undergraduate Research Conference. The conference was supported by the Mathematical Association of America (NSF Grant DMS-0241090). These are the abstracts for the eight undergraduate talks given on that day.
Notes On Gabriel's Horn,
2016
University of North Carolina at Greensboro
Notes On Gabriel's Horn, Joseph Krenicky, Jan Rychtář
Furman University Electronic Journal of Undergraduate Mathematics
A smooth bounded solid of finite volume and infinite surface is constructed. It is a variant of the classical Gabriel’s horn that is often taught in Calculus classes.
Derham Cohomology Of The Rectangular Torus,
2016
Williams College
Derham Cohomology Of The Rectangular Torus, Eric M. Katerman
Furman University Electronic Journal of Undergraduate Mathematics
For the special case of a rectangular at torus, we present and prove DeRham's Theorem, which says that cohomology is given by closed differential forms modulo exact forms.
The University Of North Carolina At Greensboro Regional Undergraduate Mathematics Conference Abstracts,
2016
University of North Carolina at Greensboro
The University Of North Carolina At Greensboro Regional Undergraduate Mathematics Conference Abstracts, Jan Rychtář
Furman University Electronic Journal of Undergraduate Mathematics
It was a very chaotic day, says Kathryn Sikes. Indeed, mutants spread everywhere, according to Brian Stadler. Bacterial wars raged all over the place, adds Dan MacMartin. Everybody was stealing, reported Christian Sykes. There were no limits to it, witnessed by Samuel Grundman. Only the fittest survived and got out of the prison, noted by Joseph Krenicky. The group was set free by Steven Piantadosi. We almost got lost in cyclic paths, said Heather Allmond. At least, our weight was a perfect number, smiles Michael Shiver, because we were not oversized thanks to Martha Shott. Finally, a picture was taken …
On The Nonexistence Of Singular Equilibria In The Four-Vortex Problem,
2016
University of Minnesota Duluth
On The Nonexistence Of Singular Equilibria In The Four-Vortex Problem, Marshall Hampton, Andrea Peterson, Heather Stoller, Albert Wang
Furman University Electronic Journal of Undergraduate Mathematics
In this paper we provide a partial answer to a question recently posed by Hassan Aref et. al. in their article Vortex Crystals, namely whether there are certain singular equilibria of point vortices. We prove that there are no such equilibria in the four-vortex case.
Properties Of The Iterates Of The Weierstrass-℘ Function,
2016
Cornell University
Properties Of The Iterates Of The Weierstrass-℘ Function, Walter H. Chen, Michael S. Willis
Furman University Electronic Journal of Undergraduate Mathematics
This paper discusses several properties of the Weierstrass-℘ function, as defined on the fundamental parallelogram C/Γ, where C is the complex plane and Γ is the lattice generated by ω1 and ω2. Using the addition formula for ℘(z1 + z2), we develop a reccurence relation for ℘(nz) in terms of ℘(z). We then examine the degree of this expression, some coefficients, and patterns concerning the poles of this function. We also consider the geometric interpretation of taking an arbitrary z0 and adding it to itself, both in the fundamental parallelogram C/Γ and …
A Dynamical Programming Solution For Shortest Path Itineraries In Robotics,
2016
Ryerson University
A Dynamical Programming Solution For Shortest Path Itineraries In Robotics, Martin Talbot
Furman University Electronic Journal of Undergraduate Mathematics
In robotics, more precisely Autonomous Mobile Robotics (AMR), robots, much like human beings, are confronted regularly with the problem of finding the best path to take from a source location to a destination location. This is an optimization concern, since the robot wants to minimize its cost in time or in energy while achieving its goal. Different algorithms exist for shortest path computation; the famous Dijkstra’s Shortest Path Algorithm will solve single-source shortest path problems in near linear time (O(mn log n)). However, for certain complex optimization path-planning problems, this algorithm alone is insufficient. We will …
Vertex Magic,
2016
Elon University
Vertex Magic, Daisy Cunningham
Furman University Electronic Journal of Undergraduate Mathematics
This paper addresses labeling graphs in such a way that the sum of the vertex labels and incident edge labels are the same for every vertex. Bounds on this so-called magic number are found for cycle graphs. If a graph has an odd number of vertices, algorithms can be found to produce different magic-vertex graphs with the maximum and minimum magic number. Also, every cycle graph with an odd number of vertices can be made into a vertexmagic graph if the odd numbers or even numbers are placed on the vertices. Some interesting problems arise when one begins to look …
Some Geometry Of H(RN),
2016
Grand Valley State University
Some Geometry Of H(RN), Christopher Frayer
Furman University Electronic Journal of Undergraduate Mathematics
If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X), h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(Rn). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B, ∈ H(Rn), there exist infinitely many points on the line joining A and B. We characterize some points on the lines formed using closed …
Tiling By (K, N)-Crosses,
2016
Carleton University
Tiling By (K, N)-Crosses, Joanne Charlebois
Furman University Electronic Journal of Undergraduate Mathematics
We investigate lattice tilings of n-space by (k, n)-crosses, establishing necessary and sufficient conditions for tilings with certain small values of k. We give a necessary condition for tilings corresponding to nonsingular splittings with general values of k. We also prove one case of a conjecture made by Stein and Szabó in [4].
