# Mathematics Exchange

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Random Number Generators
(2014) Dibble, Chris; Turner, Hannah
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 been employed for amusement, statistics, and science. However, the use of random number generators, even today, is still not completely understood. Our foray into random number generation barely scrapes the surface of the subject. Thus, much of this work is a compilation of previous research. Our aim has been to condense the wealth of information on random number generation into a simple overview and further, execute several established generators. Through original computer applets, we attempted to test the degree of randomness of the generators, using several traditional statistical tests.
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Two Aspects of Proof: Examining the Amount of Logic in Student-Constructed Proofs and Mathematicians’ Actions in Recovering From Proving Impasses
(2014) Savic, Milos
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 [18, 30]. This process of proof construction is usually explicitly taught, if at all, to U.S. undergraduates as a small part of a course, such as linear algebra, whose stated goal is something else, or in a transition-to-proof or “bridge” course. Students might also get discouraged when attempting a proof, perhaps due to the differences between proving and prior exercises [15] asked of them. Students may often complain about “getting stuck.” In this article, I attempt to address two questions in proving: what extent does logic appear on the surface of student-constructed proofs, and what do mathematicians do when they “get stuck.”
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The Efficacy of a Frequency-Interval Model Applied to Byzantine Music
(2014) Hindeleh, Firas; Sears, Jessica; Copenhaver, Lee
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 F=c(I+1)D that some classical music pieces studied by K. Hs ̈u and A. Hs ̈u in[2] satisfy. Here F denotes the frequency of a note interval I between successive notes, D is the dimension of the model, and cis a proportionality constant.
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Mathematical Modeling on Open Limestone Channel
(2014) Bandstra, Joel; Li, Ying; Wu, Naiyu
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, which lower the pH value of the water. An open limestone channel (OLC) is a passive and low cost way to neutralize AMD. The dissolution of calcium into the water increases the pH value of the solution. A differential equation model is numerically solved to predict the variation of concentration of each species in the OLC solution. The diffusion of calcium due to iron precipitates is modeled by a linear equation. The results give the variation of pH value and the concentration of calcium.
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A Word from the Editor
(2014) Mohammed, Ahmed
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 than making sure that the readers of the Mathematics Exchange get articles that motivate and inspire them to love mathematics and pursue this as the core part of their future career path.