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Volume VII
Monopoly: Strategy
or Luck
By Eric Gerend
Abstract: We
calculate the probability of landing on any square in the game of Monopoly and
show how this helps us to develop a winning strategy.
Betsy Takes a
Lunar Path
By Paul Kolmodin and Amos Sookraj
Abstract:
Given the set of differential equations governing the motion of three
bodies in space, we find a set of initial conditions that successfully send a
cow over the moon and back to Earth.
Word Search
Puzzles
By Brock O’Leary
Abstract:
Have you ever worked on a crossword puzzle that left you with only
one clue you simply could not solve?
Have you ever wondered how many words in the dictionary end in some
particular letter or combination of letters?
We will be using the mathematics of recursion and the language of regular
expression to develop a general pattern-matching algorithm for solving such
problems.
Mars Expedition
By Matthew Domeier and Matija Maretic
Abstract:
Using the Runge-Kutta approximation method, we will approximate a
trajectory for a rocket flying from Earth to Mars.
Just What Can We
Construct?
By Emilie Darling
Abstract:
We reduce the Double Bubble problem to its two-dimensional analog.
We show that the most efficient double circle for enclosing a pair of
equal regions having fixed total area is the two-dimensional cross-section of
the Double Bubble.
We then prove that it is impossible to construct the radius of fixed area
double circles using only compass and straight-edge construction.
The Chicken Pox
Epidemic
By Karissa Paulsen
Abstract:
We derive a model to predict how a population may become infected,
recover, and become re-infected with a disease using given rates of birth and
death, contact, contagion, recovery, and contagion for a second infection.
The Good, the Bad,
and the Ugly: The Wolves, the Rabbits, and the Hunters
By Jerry Madden
Abstract:
We will determine the implications of factoring a hunting season into
predator-prey analysis.
We will see the results when hunters are reducing the wolf population
during the winter and summer seasons.
AaaChoo!
The Spread of Disease
By Lisa Siorek and Shawn Zook
Abstract:
Starting with a SEIR differential equation disease model and initial
coefficients, we map the spread of a disease through a population over time and
discuss the role of various coefficients in the model.
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