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Volume XII
Don’t Drink The Water! A Mathematical Model of
Pollution Absorption in River Substrate Abstract: When a pollutant is introduced into a stream, it affects many aspects of the stream’s ecosystem. A mathematical model using differential equations was created to approximate the amount of pollution contained within the stream’s substrate at any given time. The validity of this model was then tested. Press My
Buttons Abstract: “Circle Mania” is a small puzzle with 3-10 different colored buttons arranged in a ring. The goal of “Circle Mania” is to change the buttons until they are all one color in the least number of moves possible. In order to change the colors of the buttons, one button is selected. The selected button along with the buttons on both sides change colors through a designated rotation. In this paper, we analyze the game of "Circle Mania" using a number of mathematical tools.
The Battle of the Medieval City Abstract: Within the tiling game Cathedral, I studied the different combinations of game pieces besides the ones given, that would completely tile the game board and increase the level of difficulty I also focused on the strategy of gaining territory and determined which pieces would be best to use.
Pick a Card, Any Card! Abstract: We deciphered the meaning of a card trick by looking at the properties of each card and analyzing the steps of the trick. We then took the analysis we found and expanded the trick and created a new trick.
Proofs by Induction Abstract: Given the proposition p divides qn – r, we find the necessary and sufficient conditions for the truth of the proposition. Simpson2 Abstract: For the differential equation y'=f(x,y), we use quadratic, cubic, and quartic functions to approximate a solution y. We derive a formula for the coefficients of an n-point quadrature method. |
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