The Society for the Foundations of Computational Mathematics supports fundamental research in a wide spectrum of computational mathematics and its application areas. As part of its endeavor to promote research in computational mathematics, it regularly organises conferences and workshops which bring together leading researchers in the diverse fields impinging on all aspects of computation. Major conferences have been held in Park City (1995), Rio de Janeiro (1997), and Oxford (1999).

The next major FoCM conference will take place at the Institute for Mathematics and its Application (IMA) in Minneapolis in the summer of 2002. More information about FoCM can be obtained from its website at www.focm.net.

The conference in Oxford, England, on July 18-28,1999, was attended by over 300 scientists. Workshops were held on fourteen subjects dealing with diverse research topics from computational mathematics. In addition, eighteen plenary lectures, concerned with various computational issues, were given by some of the world's foremost researchers. This volume presents thirteen papers from these plenary speakers. Some of these papers are a survey of state of the art in an important area of computational mathematics, others present new material. The range of the topics: from complexity theory to the computation of partial differential equations, from optimization to computational geometry to stochastic systems, is an illustration of the wide sweep of contemporary computational mathematics and the intricate web of its interaction with pure mathematics and application areas.