• Random Number Generators 

  Dibble, Chris; Turner, Hannah (2014)

  From simple gambling thousands of years ago, to modern statistical sampling, humans have created random number generators. Methods ranging from a simple coin flip to complex deterministic equations have ...
• Two Aspects of Proof: Examining the Amount of Logic in Student-Constructed Proofs and Mathematicians’ Actions in Recovering From Proving Impasses 

  Savic, Milos (2014)

  To obtain a Master’s or PhD in mathematics, or even to succeed in proof-based courses in an undergraduate mathematics major, one must often be able to construct original proofs, a common difficulty for students ...
• The Efficacy of a Frequency-Interval Model Applied to Byzantine Music 

  Hindeleh, Firas; Sears, Jessica; Copenhaver, Lee (2014)

  The songs found in Byzantine music possess great cultural significance, a beautiful sound, and wonderful mathematics. The purpose of this paper is to show that Byzantine music satisfies a similar exponential relation ...
• Mathematical Modeling on Open Limestone Channel 

  Bandstra, Joel; Li, Ying; Wu, Naiyu (2014)

  Acid mine drainage (AMD) is the outflow of acidic water from metal mines or coal mines. When exposed to air and water, metal sulfides from the deposits of the mines are oxidized and produce acid, metal ions and sulfate, ...
• A Word from the Editor 

  Mohammed, Ahmed (2014)

  The Mathematics Exchange continues to reach more readers as it publishes quality articles that focus on topics of interest to undergraduate mathematics students across the globe. The editorial team has no other priority ...
• 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 ...

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