Physical Sciences and Mathematics Commons^™

Developing Preservice Teachers’ Mathematical And Pedagogical Knowledge Using An Integrated Approach, Marta Magiera, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper describes how an integrated mathematics content and early field-experience course provides opportunities for preservice elementary teachers to develop understanding of mathematics and mathematics teaching. Engaging preservice teachers in solving and discussing mathematical tasks and providing opportunities to implement these tasks with elementary students creates an authentic context for the future teachers to reflect on their own understanding of mathematics, mathematics teaching, and students’ mathematical thinking. Essential elements of the cycle of events in the integrated model of instruction are discussed: preservice students’ acquisition of mathematical concepts in the context of selected tasks in the content course; subsequent posing …

Gliomapredict: A Clinically Useful Tool For Assigning Glioma Patients To Specific Molecular Subtypes, Aiguo Li, Serdar Bozdag, Yuri Kotliarov, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Advances in generating genome-wide gene expression data have accelerated the development of molecular-based tumor classification systems. Tools that allow the translation of such molecular classification schemas from research into clinical applications are still missing in the emerging era of personalized medicine.

Results: We developed GliomaPredict as a computational tool that allows the fast and reliable classification of glioma patients into one of six previously published stratified subtypes based on sets of extensively validated classifiers derived from hundreds of glioma transcriptomic profiles. Our tool utilizes a principle component analysis (PCA)-based approach to generate a visual representation of the analyses, quantifies …

Distance Functions And Attribute Weighting In A K-Nearest Neighbors Classifier, Alyssa C. Frazee, Matthew A. Hathcock, Samantha C. Bates Prins

Undergraduate Mathematics Day: Past Content

To assess environmental health of a stream, field, or other ecological object, characteristics of that object should be compared to a set of reference objects known to be healthy. Using streams as objects, we propose a k-nearest neighbors algorithm (Bates Prins and Smith, 2006) to find the appropriate set of reference streams to use as a comparison set for any given test stream. Previously, investigations of the k-nearest neighbors algorithm have utilized a variety of distance functions, the best of which has been the Interpolated Value Difference Metric (IVDM), proposed by Wilson and Martinez (1997). We propose two alternatives to …

2010 Vol. 4 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

On The Construction Of Order Six Multilevel Hadamard Matrices, Keli Parker

Undergraduate Mathematics Day: Past Content

The existence of multilevel Hadamard matrices (MHMs) of all orders as well as a construction for full-rate circulant MHMs of all orders n 6= 4 is known. We use computer search methods to look for previously unknown full-rate circulant MHMs of orders 5, 6, and 7 and find solutions that potentially do not follow from the known construction. We then give an alternate construction to explain some order six MHMs.

Just Sit Back And Let The Girth Model Make Money For You, Ellham Negahdary

Undergraduate Mathematics Day: Past Content

The Girth Model will use the 10-period exponential moving average (EMA) and the 20-period EMA as their proxy for market trend. The Girth Model is a trend following model incorporating volatility, momentum and velocity. We will use girth as an early close indication to both long and short positions. Typically, early exit due to decreasing girth results in a more favorable profit position than that taken if the trader simply waited for an exit on the EMA cross to the downside.

The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, Bonita A. Lawrence, Richard P. Merritt, Devon A. Tivener

Undergraduate Mathematics Day: Past Content

Mechanical integration is an idea dating back to the late 1800's discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter's …

Uniqueness Of Solutions Implies Existence And Uniqueness Of Solutions Of Boundary Value Problems For Third Order Differential Equations, Veronica Respress

Undergraduate Mathematics Day: Past Content

In this paper we are concerned with uniqueness implies uniqueness and uniqueness implies existence questions for solutions of a class of boundary value problems for the third order ordinary differential equation (ODE). First we show uniqueness of solutions of a class of two-point problems implies the uniqueness of solutions of an associated class of three-point problems. Then we establish uniqueness of solutions of the class of two-point problems implies the existence of solutions of the class of two point problems and the associated class of three-point problems.

The Maximal Pure Spectrum Of An Abelian Group, Brendan Goldsmith, Ruediger Goebel

Articles

This paper introduces the notion of the maximal pure spectrum of an Abelian group - this is the set of isomorphism classes of maximal proper pure subgroups - and focuses on the situation in which this spectrum is small. The converse situation is also examined i.e. given a collection of isomorphism classes of groups, can one find an Abelian group having precisely this collection as its maximal pure spectrum. Finally, it is shown that in some familiar situations, the answers to these questions may be undecidable.

Schrödinger Operators With Δ'Interactions And The Krein–Stieltjes String, Aleksey Kostenko, M. M. Malamud

Articles

We investigate one dimensional symmetric Schrödinger operator HX, β with δ' interactions of strength β = ⊂ on a discrete set X = ⊂ [0, b), b ≤ +∞ (xn ↑ b). We consider HX, β as an extension of the minimal operator Hmin := –d2/dx2 (\X) and study its spectral properties in the frame work of the extension theory by using the technique of boundary triplets and the corresponding Weyl functions. The construction of a boundary triplet for is given in the case d∗ := infn ∈ |xn – xn – 1| = 0. We show that spectral properties …

Heat Transfer Through The Boundary Layer On A Moving Cylindrical Fibre, Brendan Redmond, David Mcdonnell

Articles

This paper applies boundary layer theory to the process of manufacturing polymer fibres known as the melt spinning process. The rate of heat loss of the fibre during this process, characterised by the local Nusselt number, is evaluated by means of a Pohlhausen integral method.

Local Out-Tournaments With Upset Tournament Strong Components I: Full And Equal {0,1}-Matrix Ranks, Kim A. S. Factor, Rebecca M. Kohler, Jason M. Derby

Mathematics, Statistics and Computer Science Faculty Research and Publications

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided.

Digraphs With Isomorphic Underlying And Domination Graphs: Pairs Of Paths, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UG^c (D) is the union of two disjoint paths.

Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Locomotion Of A Running Quadruped Robotic System, Bradley Savon

Undergraduate Journal of Mathematical Modeling: One + Two

Very little is known about the locomotion of quadruped robotic systems. In Latin, the term quadruped means 'having four feet'. The robotic system analyzed in this project was a software simulation program modeled after a horse. Simulation data was recorded to resolve the relationship between foot position and impulses required to accelerate or to decelerate the system while trotting. These sets of data were then analyzed in MATLAB to produce graphical representations which allowed for a better understanding of the robot's motion in the simulation environment. A function was fit to the graph of discrete data values measured in the …

Finding The Area Of An Irregularly Shaped Room, Justin Walls

Undergraduate Journal of Mathematical Modeling: One + Two

This experiment utilized integration in a practical sense by determining the floor area of an irregularly shaped room. By taking the integral summation of three sections formed from semi-circles, the desired areas as well as positive results were found. The final data determined that the floor area of the irregularly shaped room was around 580 square feet.

Automated Determination Of A Package's Center Of Mass, Ayaz Hemani

Undergraduate Journal of Mathematical Modeling: One + Two

In order to address the issue of increased efficiency and better planning for parcel shipments, an automated computer program was developed in Microsoft Excel that calculates center of mass and moments of mass with greater speed and reliability than currently implemented systems. This simple program requires only a variable density function and limits of integration for a given object as input within the spreadsheet system. Once the required input has been provided, a series of chain calculations, with the help of a Visual Basic for Applications (VBA) script, is able to process the input, which is done through integration and …

Pollination Of A Canary Tree Flower, Abbie O'Hern Weeks

Undergraduate Journal of Mathematical Modeling: One + Two

Pollination is an essential part of the life cycle of flowering plants. We perform an experiment to determine how long a canary tree flower is accessible to pollinating insects so that fertilization can take place. We conducted an observational study where we measured the size of the same flower and charted its growth each day. With the observational data we constructed a scatter plot and from the graph we fit a cubic function to the data. We conclude that in the lifespan of a canary tree flower, pollination begins at 5 1/2 days and ends approximately 9 days later.

Nerve Cell Deterioration Associated With Alzheimer's Disease, Yaping Tu

Undergraduate Journal of Mathematical Modeling: One + Two

Alzheimer's disease is an extremely serious condition that is challenging to diagnose. We have used experimental data to compare the rate of decay of entorhinal cortex (EC) neurons in various stages of Alzheimer's. We observed that the rate of EC neuron decay in the patients without Alzheimer's is close to zero, linear in mild cases, and quadratic in severe cases. We believe that described estimates may help to diagnose the disease as well as its stage.

Mathematical Reasoning In Service Courses: Why Students Need Mathematical Modeling Problems, Kris H. Green, Allen Emerson

The Mathematics Enthusiast

In this paper we argue that conventional mathematics word problems are not aligned with the typical learning goals and expectations partner disciplines, especially business, have in requiring that their students take mathematics courses. Using the taxonomy of educational objectives presented by Anderson and Krathwohl (2001) we show how mathematical modeling problems can be used to promote the needed alignment and contrast two examples to illustrate the differences. We then demonstrate how the more conventional word problem can be rewritten as a modeling problem. Sample assessment materials and instructional activities are included to support teachers in making the transition to the …

From Permutahedron To Associahedron, Colum Watt, Thomas Brady

Articles

For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type-$W$ non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for $W$.

Calculating The Time Constant Of An Rc Circuit, Sean Dunford

Undergraduate Journal of Mathematical Modeling: One + Two

In this experiment, a capacitor was charged to its full capacitance then discharged through a resistor. By timing how long it took the capacitor to fully discharge through the resistor, we can determine the RC time constant using calculus.

A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero

Theses, Dissertations and Culminating Projects

This research applies time series methods to determine relationships among a set of weather variables which are continually monitored in the Hackensack Meadowlands region of northern New Jersey. Weather data includes chemical and atmospheric factors. Chemical factors are Nitrogen Oxide, atmospheric Ozone, Carbon Monoxide, and Carbon Dioxide. Weather factors are wind speed, barometric pressure, air temperature, humidity, and solar radiation. Additionally, traffic density and time of week are brought in as categorical factors. This research attempts to (a) introduce the reader to various time series methodologies, (b) find a significant and efficient model for forecasting Nitrogen Oxide levels, and (c) …

Book Review: Visual Motion Of Curves And Surfaces, Andrei Ludu

Publications

This is Dr. Ludu's review of the book Visual Motion of Curves and Surfaces by Roberto Cipolla and Peter Giblin. Published by Cambridge University Press in 2009. ISBN: 978-0-521-63251-5.

Review: Nontangential Limits In Pt(Μ)-Spaces And The Index Of Invariant Subgroups, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: The Spectrum Of Some Compressions Of Unilateral Shifts, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Unitary Equivalence To A Complex Symmetric Matrix: Geometric Criteria, Levon Balayan '09, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix. Equivalently, we characterize those matrices having distinct eigenvalues which lie in the unitary orbit of the complex symmetric matrices.

Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.

Review: Common Cyclic Vectors For Unitary Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: Classification Of Quasi-Trigonometric Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.