• Seeing Better: Optimizing Surgically Induced Astigmatism Correction Factors for Cataract Surgery 

  Milne, Erin; Winkler, Nelson (2011)

  Cataract surgery is one of the most common operations performed in the United States each year [1]. Cataract surgery is seen as a 'routine' procedure; however, it is not without complications. The surgery changes the natural ...
• Characterization of a Family of Cubic Dynamical Systems 

  Kothari, Shan (2011)

  Motivated by the fact that cubic maps have found potential appli- cations to modeling of biological and physical processes, we examine a family of discrete, non-linear dynamical systems comprising one-parameter real variable ...
• Graphical Modeling 

  Afriyie, Prince; Begum, Munni (2011)

  Graphical models have been an area of active research since the beginning of the twentieth century. Graphical models have wide scope of ap- plicability in various scienti􏰀c 􏰀elds. This paper presents applications of ...
• A Coarse Invariant for all Metric Spaces 

  DeLyser, M.; LaBuz, B.; Wetsell, B. (2011)

  In [2] an invariant of metric spaces under bornologous equivalences is defined. In [3] this invariant is extended to coarse equivalences. In both papers the invariant is defined for a class of metric spaces called sigma ...
• A Word from the Editor 

  Mohammed, Ahmed (2011)

  The editorial team of the Mathematics Exchange is pleased to present this latest issue which contains five articles on diverse areas of Mathematics Sciences.
• NCTM Conference Experience 

  Augustyn, Mark; Dobson, Lisa; Hosking, Michael; Keenan, Nicole; Van Duzer, Zachary (2010)

  What does it mean to be a professional in your chosen field? Professionals continually seek out knowledge and experiences with the goal of improving what they do and how they do it. Professionalism can take on many forms ...
• Hermite polynomials in Quantum Harmonic Oscillator 

  Aravanis, Christos T. (2010)

  In quantum mechanics and in other branches of physics, it is common to approach physical problems using algebraic and analytic methods. Examples include the use of differential equations for many interesting models, the ...
• A Derivation of the Navier-Stokes Equations 

  Coleman, Neal (2010)

  The Navier-Stokes equations are a set of second-order partial differential equa-tions relating first and second derivatives of fluid velocity, which is representedas a smooth vector field. While simple in principle, they ...
• 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 ...

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