Mathematics Commons^™

2005 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

Shuffle Up And Deal; Should We Have Jokers Wild? (Abstract), Kristen Lampe

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

From the Interactive Media Lab at the University of Florida to the Poker News blog to the Christian Science Monitor, everyone is talking about the rise in poker’s popularity.

2005 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

2004 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2004 Fall Colloquium

Conversations Among Women In Mathematics (Workshop Information), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

Fifth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Curvature And The Shape Of The Universe, Chikako Mese

Undergraduate Mathematics Day: Past Content

We may have an intuitive idea of what it means for surfaces to be curved, but what does it mean for higher dimensional spaces to be curved? In this talk, we will try to quantify curvature on a surface and try to extend this notion to three dimensional spaces. We will show that with an understanding of curvature, we can make sense of a universe which is finite but without boundary.

Newton-Raphson Versus Fisher Scoring Algorithms In Calculating Maximum Likelihood Estimates, Andrew Schworer, Peter Hovey

Undergraduate Mathematics Day: Past Content

In this work we explore the difficulties and the means by which maximum likelihood estimates can be calculated iteratively when direct solutions do not exist. The Newton-Raphson algorithm can be used to do these calculations. However, this algorithm has certain limitations that will be discussed. An alternative algorithm, Fisher scoring, which is less dependent on specific data values, is a good replacement. The Fisher scoring method converged for data sets available to the authors, that would not converge when using the Newton-Raphson algorithm. An analysis and discussion of both algorithms will be presented. Their real world application on analysis of …

Pebbling On Directed Graphs, Gayatri Gunda, Aparna Higgins

Undergraduate Mathematics Day: Past Content

Consider a finite connected graph G whose vertices are labeled with non-negative integers representing the number of pebbles on each vertex. A pebbling move on a graph G is defined as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number f(G) of a connected graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified but arbitrary vertex. We consider pebbling on directed graphs and study what configurations of directed graphs allow for pebbling …

Newton’S Unfinished Business: Uncovering The Hidden Powers Of Eleven In Pascal’S Triangle, Robert Arnold, Tom Attenweiler, Christopher Brockman, Bethany Lesko, Christine Martinek, Colleen Mccormick, Jessica Mcquiston, Jessica Parker, Amy Rohmiller

Undergraduate Mathematics Day: Past Content

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle.

2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

Some Interesting Multiples Of Nine: Use Your Digits To Get The Digits!, Kevin Hurley

Undergraduate Mathematics Day: Past Content

We have unraveled two neat and powerful algorithms for calculating certain multiples of nine. These discussions might make for an interesting introduction to a number theory course, or a supplemental project in calculus or advanced algebra. The mathematics involved is within a student’s grasp, and the results are quite startling.

Ramanujan Graphs In The Construction Of Ldpc Codes, Walter H. Chen

Undergraduate Mathematics Day: Past Content

Low-density parity-check (LDPC) codes have recently become a popular interdisciplinary area of research. Widely unknown after their invention by Gallager in 1965, the existence of efficient encoding and decoding algorithms coupled with performance that operates near theoretical limits has led to the rediscovery of LDPC codes. This paper will address the reasoning and construction of LDPC codes with Ramanujan graphs.

How Not To Get Lost While On A Random Walk, Robert Lewand

Undergraduate Mathematics Day: Past Content

What happens if you go on a random walk? Will you ever return home? Well, sometimes yes (probably) and sometimes no (probably). During this talk we will derive some elementary identities in favor you're not getting lost while on a random walk.

2004 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

2004 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2004 Winter Colloquium

Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

Curvature (Abstract), Chikako Mese

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

We may have an intuitive idea of what it means for surfaces to be curved, but what does it mean for higher dimensional spaces to be curved?

A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng

Mathematics Faculty Publications

In this paper we continue to explore cross-symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales. Dynamic equations under delta and nabla differentiations are considered. It is proven that, by introducing a proper companion problem, the solution of a dynamic equation is cross-symmetric to the solution of the companion problem. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.

Fourth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

2003 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Poster of Undergraduate Mathematics Day events held Saturday, November 1, 2003.

2003 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Program and abstracts of papers presented at the 2003 Undergraduate Mathematics Day at the University of Dayton

Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao

Mathematics Faculty Publications

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe

Mathematics Faculty Publications

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova

Mathematics Faculty Publications

The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.

Third Kenneth C. Schraut Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

How To Keep Up With Mathematics (Abstract), Paul Campbell

Kenneth C. Schraut Memorial Lectures

You are a mathematics major perhaps because you are good at it and it’s useful, but more likely mainly because you enjoy it.

Most undergraduate mathematics is decades or even centuries old, in part because of the hierarchical nature of the subject. Meanwhile, your fellow students in biology and other sciences use textbooks that feature crucial work of the last five or ten years.

Recall, though, what you were told in orientation to college and often since: Much learning in college has to take place outside the classroom, at your own initiative. After your formal education ends, all mathematics learning …

Nonlinear Eigenvalue Problems For Higher Order Lidstone Boundary Value Problems, Paul W. Eloe

Mathematics Faculty Publications

In this paper, we consider the Lidstone boundary value problem y(t) = λa(t)f(y(t), . . . , y(t), . . . y(t)), 0 < t < 1, y(0) = 0 = y(1), i = 0, . . . , m − 1, where (−1)f > 0 and a is nonnegative. Growth conditions are imposed on f and inequalities involving an associated Green’s function are employed which enable us to apply a well-known cone theoretic fixed point theorem. This in turn yields a λ interval on which there exists a nontrivial solution in a cone for each λ in that interval. The methods of the paper are known. The emphasis here is that f depends upon higher order derivatives. Applications are made to …

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.