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Presents original research results on the leading edge of mathematics research.Advances in Mathematics Research presents original research results on the leading edge of mathematics research. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Some topics included in this compilation are: problem-solving techniques; exact evaluation of bias in Rasch model residuals; learning algorithms for discounted MDP's with constraints; spectrum results in Galois geometries; and novel solutions of a non-linear differential equation.