Sharyn A. Campbell - Statistical Tests for Markov-Dependence
A statistical test for Markov-dependence will be developed by first considering
one-step Markov-dependence and extending these results to r-step Markov-dependence.
The likelihood ratio of the Neyman-Pearson Lemma will be used to obtain
the "best test", where then null hypothesis is independent trials and the
alternative hypothesis is trials are stationary Markov-dependent of the
order r.
Vladimir Dimitrijevic - Elaboration on Usefulness of Constructively Limited
and Irresolvable Demonstrations
The purpose of this project is to introduce computational methods, espicially
algebraic analysis, applied in solving constructive problems, and the reverse
impact of this method which provides geometric solutions to lower degree
polynomial and other equations. The major emphasis is given to the discussion
of optimial approaches and possibilities of solving constructive problems
given data with various properties and relationships, as well as the theory
behind "straight edge and compass" geometric solutions to selected types
of equations.
Shelly L. Martin - Patchwork Mathematics
Quilting, a historically favorite form of artistic expression and symbolism,
was brought to America by Dutch and English settlers. The beautiful designs
and motifs have been handed down for generations. From a different view
however, one can see the deep mathematical world of symmetry, translations,
and patterns in each quilt.
Traca E. Tithof - Probabilities Associated with Plinko
Utilizing the Markov theory of random walks and theories of probability
to analyze the Plinko game from the T.V. game show The Price is Right.
Christina T. Tsiaparas - A Tool for Solving 2-Dimensional Systems of Equations
The intermediate value theorm is generalized, via the winding number of
a closed curve about a point, to a two dimensional case involving two functions
of two unknowns. Also an extension of the secant method to two functions
in two unknowns is discussed. Finally a computer program utilizing both
of these concepts id described, and applications are given.
