Near the beginning of this decade William Massey of Bell Laboratories (then AT&T, now Lucent Technologies) had an idea for an organization devoted mainly to addressing critical issues involving African-American researchers and graduate students in the mathematical sciences. It was envisioned that this organization would

- highlight current research by African-American researchers and graduate students in mathematics,
- strengthen the mathematical sciences by encouraging increased participation of African-Americans and members of other underrepresented groups,
- facilitate working relations among them, and provide assistance to them in cultivating their careers.

This organization became known as the Conference for African-American Researchers in the Mathematical Sciences (CAARMS).

It was Massey's industry, determination and energy, coupled with that of Raymond Johnson, James Turner and others, that led to the first meeting of the organization (CAARMS1) which was held at the Mathematical Sciences Research Institute in Berkeley, California, June 1995. CAARMS2 was held at DIMACS at Rutgers University in Piscataway, the Institute for Advanced Study in Princeton, and the Bell Laboratories and the AT&T Laboratories in Murray Hill, New Jersey, June 26-28, 1996; CAARMS3 was held at Morgan State University in Baltimore, Maryland, and the National Security Agency in Fort Meade, Maryland, June 1997; and the CAARMS4 will be held at Rice University in Houston, Texas, June 1998.

The book under review here contains some of the invited papers and poster presentations given at CAARMS2, and other papers pertaining to objectives and purposes of CAARMS. It is divided into three sections: (I) Invited Research Talks, (II) Poster Presentations and (III) Historical Articles. The first section of this book contains eight of the invited research talks:

*Chain decomposition theorems for ordered sets and other musings* by Jonathan David Farley of MSRI and Vanderbilt University.
*Unimodality and the independent set numbers of matroids* by Carolyn R. Mahoney.
*On achieving channels in a bipolar game* by Curtis Clark of Morehouse College.
*Discrete approximation of invariant measures for multidimensional maps* by Walter M. Miller of Howard University.
*Some numerical methods for a maximum entropy problem* by Nathaniel Whittaker of the University of Massachusetts.
*Hydrodynamic stability, differential operators and spectral theory* by Isom Herron of Rennselear Polytechnic Institute.
*The role of Selberg's trace formula in the computation of Casmir energy for certain Clifford-Klein space-times* by Floyd L. Williams of the University of Massachusetts.
*Some dynamics on the irrationals* by Scott W. Williams of the State University of New York, Buffalo.

Invited speakers were encouraged to include sufficient background material to enable the non-specialist to gain an understanding of the interest and importance of the research question under investigation. For the most part, the authors of the papers in this section accomplished this task admirably before discussing their own results. It is anticipated that these papers will be reviewed individually elsewhere.

In the second section are contained seven papers by students that were included in the Poster Presentation session of CAARMS2:

*Finding elliptic curves defined over Q of high rank* by Garikai Campbell.
*Symplectic matrix structure in numerical integration* by Michael Keeve of Georgia Institute of Technology.
*A numerical algorithm for the computation of invariant circles* by Kossi Edoh of Simon Fraser University.
*Classification of nilpotent orbits in symmetric spaces* by Alfred G. Noel of Northeastern University.
*Evaluating texture measures for low-level features in color images of human skin* by Kori E. Needham of the University of North Carolina, Chapel Hill.
*Lattice paths and RNA secondary structures* by Asamoah Nkwanta of Howard University.
*Nuprl as a concurrent interactive theorem prover* by Roderick Moten of Cornell University.

The material in the third section, of interest to a more general audience, contains

*Yesterday, today and tomorrow* by Lee Lorch of York University,
*The Challenge of Diversity* by Etta Z. Falconer of Spelman College,
*What next? A meta-history of black mathematicians* by Patricia Clark Kenschaft of Montclair State University,
*A personal history of the origins of the National Association of Mathematicians' ``Presentations by Recipients of Recent Ph. D.'s''* by Donald M. Hill of Florida A & M University, and
*Dr. J. Ernest Wilkins, Jr.: The Man and his works* by Nkechi Agwu of Borough of Manhattan Community College of the City University of New York and Asamoah Nkwanta of Howard University.

The papers by Lorch, Hill, and Agwu and Nkwanta illuminate some aspects of the history of participation in mathematics by African-Americans. Kenschaft's paper provides sources of published information about black mathematicians prior to 1986 and suggests other areas where historical work might be important. Finally, Falconer's paper treats the broader subject of participation of African-American, Hispanic Americans and Native Americans in mathematics. Very useful data are given and analyzed in this paper, and a list of changes are proposed for mathematics departments to enable them to them to increase the production of mathematicians from these groups.

There are a few (proof-reading) errors which the reviewer found: the last sentence on page 20 is incomplete, the last two lines on page 30 are repeated as the first two lines of page 31, ``Joseph Alphonso'' should be replaced by ``Joseph Alphonso Pierce'' in the thirteenth line from the bottom of page 184, ``Ruben'' should be replaced by ``Reuben'' and ``Certain'' should be replaced by ``Certaine'' on page 186.

Overall, the editor has succeeded in organizing the content of the volume to reflect faithfully the objectives of CAARMS. There is something for nearly everyone, especially those persons interested in making mathematics participation more inclusive. I am pleased to recommend this book to you for your consideration.

James A. Donaldson ( jad@scs.howard.edu) is a professor at Howard University, Washington, DC. His main professional interests are analysis and differential equations. He is also interested in increasing the number of mathematicians from groups traditionally underrepresented in mathematics, and in the history of mathematics.