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The Second Conference for African-American Researchers in the Mathematical Sciences was held for three days at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in Piscataway, New Jersey, June 26-28, 1996. It was organized by Nathaniel Dean and William A. Massey, both of Bell Laboratories, the research division of Lucent Technologies. The main goal of the conference was to highlight current research by African-American researchers and graduate students in mathematics, to strengthen the mathematical sciences by encouraging the increased participation of African-American and underrepresented groups, to facilitate working relationships between them, and to help cultivate their careers.
We had over 100 researchers and graduate students in attendance who were exposed to a variety of technical and cultural events. Participants were introduced to some of the major research centers in New Jersey: DIMACS at Rutgers University in Piscataway, the Institute for Advanced Study (IAS) in Princeton, as well as Bell Laboratories and AT&T Labs who were both located in Murray Hill. Visiting all these research institutions was a first for most of the participants. There were twelve one-hour invited technical talks given by researchers spanning a variety of mathematical and scientific disciplines. At IAS we held group discussions, led by Fern Hunt (NIST) and Camille McKayle (Lafayette College) that focused on issues surrounding minority participation in mathematics, such as: The Career Life Cycle of an African-American Mathematician; Jobs of the Present, Jobs of the Future; The Public Image of Mathematics and Mathematicians in the African-American Community; and Affirmative Action. At Murray Hill, a select group of 17 graduate students presented their current research during the poster session where they interacted in smaller groups with conference attendees as well as researchers both from Bell Labs and AT&T Labs. This volume includes papers by the invited speakers and poster presenters as well as papers on issues related to African-American involvement in the mathematical sciences.
We wish to thank the staff at DIMACS for helping to organize and host this event. We thank DIMACS, the Sloan Foundation, and AT&T Labs for providing funds, and we thank DIMACS, Bell Labs, and IAS for the use of their facilities. We would also like to thank the participants of the conference, the authors, the anonymous referees, and Christine M. Thivierge of AMS for helping with this event and the preparation of this volume.
Nathaniel Dean and William A. Massey
Foreword ix Preface xi Part I: Invited Research Talks Chain decompositon theorems for ordered sets and other musings Jonathan David Farley 3 Unimodality and the independent set numbers of matroids Carolyn R. Mahoney 15 On achieving channels in a bipolar game Curtis Clark 23 Discrete approximation of invariant measures for multidimensional maps Walter M. Miller 29 Some numerical methods for a maximum entropy problem Nathaniel Whitaker 47 Hydrodynamic stability, differential operators and spectral theory Isom H. Herron 57 The role of Selberg's trace formula in the computation of Casimir energy for certain Clifford-Klein space-times Floyd L. Williams 69 Some dynamics on the irrationals Scott W. Williams 83 Part II: Poster Presentations Finding elliptic curves defined over Q of high rank Garikai Campbell 107 Symplectic matrix structure in numerical integration Michael Keeve 111 A numerical algorithm for the computation of invariant circles Kossi Edoh 117 Classification of nilpotent orbits in symmetric spaces Alfred G. Noel 123 Evaluating texture measures for low-level features in color images of human skin Kori E. Needham 129 Lattice paths and RNA secondary structures Asamoah Nkwanta 137 Nuprl as a concurrent interactive theorem prover Roderick Moten 149 Part III: Historical Articles Yesterday, today and tomorrow Lee Lorch 157 The challenge of diversity Etta Z. Falconer 169 What next? A meta-history of black mathematicians Patricia Clark Kenschaft 183 A personal history of the origins of the National Association of Mathematicians' "Presentations by Recipients of Recent Ph.D.'s" Donald M. Hill 187 Dr. J. Ernest Wilkins, Jr.: The man and his works Nkechi Agwu and Asamoah Nkwanta 195