Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 8 of 8
Full-Text Articles in Entire DC Network
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
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.
Ramanujan Graphs In The Construction Of Ldpc Codes, Walter H. Chen
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.
Some Interesting Multiples Of Nine: Use Your Digits To Get The Digits!, Kevin Hurley
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.
How Not To Get Lost While On A Random Walk, Robert Lewand
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.
Pebbling On Directed Graphs, Gayatri Gunda, Aparna Higgins
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-Raphson Versus Fisher Scoring Algorithms In Calculating Maximum Likelihood Estimates, Andrew Schworer, Peter Hovey
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 …
Curvature And The Shape Of The Universe, Chikako Mese
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.
2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics
2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Past Content
No abstract provided.