This volume presents research and expository papers presented at the third and fifth meetings of the Council for African American Researchers in the Mathematical Sciences (CAARMS). The CAARMS is a group dedicated to organizing an annual conference that showcases the current research primarily, but not exclusively, of African Americans in the mathematical sciences, including mathematics, operations research, statistics, and computer science. Held annually since 1995, significant numbers of researchers have presented their current work in hour-long technical presentations, and graduate students have presented their work in organized poster sessions. The events create an ideal forum for mentoring and networking where attendees can meet researchers and graduate students interested in the same fields. For volumes based on previous CAARMS proceedings, see African Americans in Mathematics II (Volume 252 in the AMS series, Contemporary Mathematics), and African Americans in Mathematics (Volume 34 in the AMS series, DIMACS).

Readership

Graduate students and research mathematicians.

Table of Contents

• E. R. Barnes -- A lower bound for the chromatic number of a graph
• M. R. Currie and E. H. Goins -- The fractional parts of \(\frac NK\)
• D. E. Davenport -- Ultrafilters and Ramsey theory
• E. H. Goins -- Artins' conjecture and elliptic curves
• C. Graham -- Chaoticity results for "join the shortest queue"
• J. S. Ivy and S. M. Pollock -- Maintenance of deteriorating machines with probabilistic monitoring and silent failures
• B. V. Saunders -- The application of numerical grid generation to problems in computational fluid dynamics
• D. Stephens and G. Howell -- The elementary residual method
• M. Y. Stephens and Z. Liu -- The response of the upper ocean to surface buoyancy forcing: A characteristic solution to wave propagation
• S. A. F. Stephens and V. Lakshmikantham -- An overview of integro-differential equations and variational Lyapunov method

• J. P. King -- The art of mathematics
• W. A. Massey -- Mathematics is four dimensional

• S. W. Williams -- Compact! A tutorial