• An invariant of metric spaces under bornologous equivalences 

  Miller, Brittany; Stibich, Laura; Moore, Julie (2010)

  We define bornologous equivalence between metric spaces, which is a morerestrictive equivalence than coarse equivalence. It requires spaces to have thesame cardinality. We define an invariant of metric spaces under ...
• Turning Tables, Slicing Pizza, and the Brouwer Fixed-Point Theorem 

  Cai, Jei (2010)

  Mathematics is everywhere in life. Even within the short dinner time, it helps me solve two big problems. Scene 1: I have confidence in saying that the four legs of my kitchen table have the same length, since it cost me ...
• Application of Cox Proportional Hazard Model to the Stock Exchange Market 

  Ni, Jiayi (2009)

  Survival analysis is widely used in mechanical research, engineering and many other fields. This paper introduces the properties and modeling methods for survival data, then fits a Cox Proportional Hazards Model for stock ...
• A Word from the Editor 

  Mohammed, Ahmed (2009)

  As part of an ongoing effort to make the Mathematics Exchange a forum of mathematical ideas among an ever expanding undergraduate student readership we have enlarged the editorial board to include faculty from other colleges ...
• The Oberwolfach Problem in Graph Theory 

  Zentz, Andrea (2008)

  During the summer of 2007, I participated in a Research Experience for Undergraduates(REU)atIllinoisStateUniversity. Iwasoneofeightundergraduates, all of whom were mathematics education majors. During my eight week experience, ...
• The Banach-Tarski Paradox 

  Coleman, Neal (2008)

  A paradox is, generally speaking, a disproof of our intuitive sense of what “should” be true. Through the ages, then, there have been many instructive and interesting paradoxes that have informed and reshaped mathematical ...
• Mathematical Modeling 

  Livshits, Irene; Coleman, Neal (2008)

  Mathematical modeling is a scientific attempt to describe real life phenomena using mathematical tools. Each model consists of a set of variable parameters and rules of evolution for these parameters. By applying these rules ...
• Elaboration on the Hexagonal Grid and Spiral Method for Data Collection Via Pole Figures 

  Rizzie, Anthony C. (2008)

  There exist various techniques to “scan” an object using x-rays, the most common of which uses a polar sampling grid, all relying on the diffraction equation known as Bragg’s Law [1, 6]. During my internship at Oak Ridge ...
• Crime Deterrents 

  Long, Eileen (2008)

  Crime has always been an important topic in every culture. No one wants to live in fear of being stripped of their valuable belongings. In the United States, in particular, crime has consistently risen in the 1970s and ...
• Biocomputational Immersive Learning 

  Blakey, Ann; Bagga, Jay; Begum, Munni (2008)

  Biocomputational methods can broadly be viewed as information management systems at the interface of mathematics, statistics, computer science, and molecular biology/genetics. The main objective is to use the tools and ...
• Analyzing and Addressing Common Mathematics Errors in Secondary Education 

  Elbrink, Megan (2008)

  After much research and discussion with mathematics educators, it is apparent that secondary education students make many common errors in mathematics. As a result, it is important to analyze what causes and how to address ...
• A Word from the Chair 

  Emert, John (2008)

  In 1899, Charles H. Duell as Commissioner of the U.S. Patent and Trademark Office penned the memorable quote, “everything that can be invented has been.” Of course, this was not the case! In mathematics, a new result often ...
• The Mathematics Education Colloquium 

  Stump, Sheryl (2006)

  As described by Dr. Ralph Bremigan in a previous Mathematics Exchange article, MATHS 497: The Student-Faculty Colloquium is “one of the most unique and exciting courses offered in the Department of Mathematical ...
• Some Proofs of the Existence of Irrational Numbers 

  Coleman, Neal (2006)

  Over the course of this article, we will discuss irrational numbersand severaldifferent ways to prove their existence. As is commonly known, the real num-bers can be partitioned into rational numbers and irrational numbers. ...
• Calculating Retained Austenite in Steel Post Magnetic Processing Using X-Ray Diffraction 

  Pappas, Nathan (2006)

  During the summer of 2006, I had the opportunity to participate in an intern-ship through the U.S. Department of Energy (DOE) at Oak Ridge NationalLaboratory (ORNL). ORNL is the nations largest national laboratory that ...
• Urban Semester 

  Mouchaham, Pamela G.; Barnhart, Amanda R (2006)

  Pamela G. Mouchaham and Amanda R. Barnhart are two of the 30 elementarypreservice teachers who chose to participate in the Urban Semesterprogramduring Fall 2006. The Urban Semester is an immersive experience wherepreser-vice ...
• Economic Dynamic Modeling: An Overview of Stability 

  Berggoetz, Nathan (2006)

  Economics often focuses on the end result of changes in the economy. Forexample, it is important to know now, if increases in government spendingthis year will affect real income and interest rates in the long run. ...
• The Distribution of Primes 

  Lorch, John (2005)

  To understand the natural numbers, wemust first understand the primes. Yet the be-havior of the primes remains for the most parta mystery. For example, despite the efforts of many great mathematicians over hundreds of ...
• Elliptic Curves and Elliptic Curve Cryptography 

  O’Maley, Amiee (2005)

  Quadratic equationsare studied extensively within mathematics throughout astudent’s high school and college careers. The standard form for these equations(in the variablex) is given by
• Negatively Curved Groups 

  Malone, William (2005)

  The notion of a negatively curved group is at first highly non-intuitive because it links two areas of mathematics that are not usually associated with one another. Curvature is generally a property that we associate with ...

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