• 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 ...
• Mathematics Exchange Volume 14 

  Unknown author (2020-10)

  Complete issue of Volume 14, published in Fall 2020
• A Word from the Editor 

  Stankewitz, Rich (2020-10)
• Exploring Bounds for the Frobenius Number 

  El Turkey, Houssein; Shackett, Alec; Svitlik, Andrew (2020-10)

  Let G be a set of three natural numbers, G = {a, b, c}, such that gcd(a, b, c) = 1. The Frobenius number of G is the largest integer that cannot be written as a non-negative linear combination of elements of G. In this ...
• AM-GM Any Baby’s BMs 

  Trujillo, Timothy; del Valle, Vanessa; Robles, Jacob; Daniels, Elisha; Jimenez, Jacqueline; Rodriguez, Diana; Clark, Alex (2020-10)

  Reusable diapers are growing in popularity due to new and improved designs. The total cost associated with reusable diapers is the sum of the upfront cost of purchasing the diapers and the reoccurring cost of cleaning ...
• Another view of the coarse invariant σ 

  Imamura, Takuma (2020-10)

  Miller, Stibich and Moore developed a set-valued coarse invariant σ (X, ξ) of pointed metric spaces. DeLyser, LaBuz and Tobash provided a different way to construct σ (X, ξ) (as the set of all sequential ends). This paper ...
• A Proof of the Equivalence Between the Polytabloid Bases and Specht Polynomials for Irreducible Representations of the Symmetric Group 

  Howe, R. Michael; Liu, Hengzhou; Vaughan, Michael (2020)

  We show an equivalence between the standard basis vectors in the space of polytabloids and the basis vectors of Specht polynomials for irreducible representations of the symmetric group. The authors have been unable to ...
• 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 ...

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