Student Awards and Pi Mu Epsilon Ceremony

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Student Awards and Pi Mu Epsilon Ceremony

• April 2010

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President Ronald Regan said

• Despite the increasing importance of mathematics
  to the progress of our economy and society,
  enrollment in mathematics programs has been
  declining at all levels of the American
  educational system. Yet the application of
  mathematics is indispensable in such diverse
  fields as medicine, computer sciences, space
  exploration, the skilled trades, business,
  defense, and government. To help encourage the
  study and utilization of mathematics, it is
  appropriate that all Americans be reminded of the
  importance of this basic branch of science to our
  daily lives.

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Mathematical Explanation of Ecosystem
Homogenization by Adrian Coles

• In recent years, ecologists have begun to refine
  the mathematical study of complex networks of
  interactions between species within an
  ecosystem.   In particular, Network Environs
  Analysis (NEA) has made use of linear algebra to
  formalize analysis of the relative importance of
  direct and indirect connections between species. 
  One of the many indicators used to quantify such
  description is homogenization, which is a measure
  of the propensity of a network to distribute
  material throughout all species along all
  connections.  We examine a matrix-theoretic
  formulation of the homogenization indicator and
  describe how linear algebraic tools can be
  refined to determine which species and paths may
  exert strongest influence on the behavior of an
  ecosystem.

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Environ centrality reveals the relative
functional roles of species in ecosystem
networks.By Sarah Fann

• Ecologists and conservation biologists often need
  to know what roles species perform in ecosystems
  in order to make informed management decisions
  and allocate limited resources most effectively.
  However, quantifying the functional roles of
  species has proved difficult because species are
  embedded in complex networks of interactions and
  a species importance cannot be understood in
  isolation. Here we introduce environ centrality
  (EC), a metric that quantifies the relative roles
  of species in generating ecosystem activity and
  demonstrate its functionality over four
  empirically-based ecosystem network models. Our
  results highlight the relative evenness of
  species roles in ecosystems and demonstrates how
  indirect relationships promote this evenness.

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Numerical Simulation of Air Pollution Dynamics
Due to Point Source Emissions from an Industrial
Stack.By Erik Minges

• Mathematical modeling of the spreading of air
  pollutants in a windy atmosphere has become a
  crucial field of study over the past several
  decades. With the advances in computer
  technology and development of sophisticated
  programming languages, scientists have become
  able to evaluate evolutionary partial
  differential equations using numerical methods
  with a high degree of accuracy. Computer
  simulations of air pollution dynamics will help
  to reveal crucial properties about the forces
  interacting in gaseous systems, and will also
  help scientists to create accurate models that
  predict global weather patterns, climate change,
  global warming, air pollution spread through
  cities, and many other critical studies. Two
  very common numerical methods for solving
  evolutionary partial differential equations will
  be presented in this research finite difference
  methods and finite volume methods. A thorough
  investigation into the accuracies and faults
  between each of these two drastically different
  methods will be discussed. A detailed discussion
  on the hydrodynamical equations used to model the
  spread of air pollution will be approached in an
  elementary, but intense physical sense. The
  parameters involved, as well as the source terms
  that provide the forcing for the emission of
  pollutants, will be introduced and thoroughly
  dissected. An analysis of the mass density
  profiles of the transport of pollutants in the
  atmosphere of the Earth obtained from this study
  will be presented at the end. A discussion about
  the accuracy of the theoretical simulations and
  its relationship between actual experimental data
  will ultimately be considered.