During recent years a great deal of interest has been devoted to large scale computing applications. This has occurred in great part because of the introduction of advanced high performance computer architectures. The book contains survey articles as well as chapters on specific research applications, development and analysis of numerical algorithms, and performance evaluation of algorithms on advanced architectures. The effect of specialized architectural features on the performance of large scale computation is also considered by several authors. Several areas of applications are represented, including the numerical solution of partial differential equations, iterative techniques for large structured problems, the numerical solution of boundary value problems for ordinary differential equations, numerical optimization, and numerical quadrature. Mathematical issues in computer architecture are also presented, including the description of grey codes for generalized hypercubes. The results presented in this volume give, in our opinion, a representative picture of today’s state of the art in several aspects of large scale computing.

As requested by the National Science Foundation (NSF) and the Interagency Committee for Extramural Mathematics Programs (ICEMAP), this report updates the 1984 Report known as the "David Report." Specifically, the charge directed the committee to (1) update that report, describing the infrastructure and support for U.S. mathematical sciences research; (2) assess trends and progress over the intervening five years against the recommendations of the 1984 Report; (3) briefly assess the field scientifically and identify significant opportunities for research, including cross-disciplinary collaboration; and (4) make appropriate recommendations designed to ensure that U.S. mathematical sciences research will meet national needs in coming years. Of the several components of the mathematical sciences community requiring action, its wellspring--university research departments--is the primary focus of this report. The progress and promise of research--described in the 1984 Report relative to theoretical development, new applications, and the refining and deepening of old applications--have if anything increased since 1984, making mathematics research ever more valuable to other sciences and technology. Although some progress has been made since 1984 in the support for mathematical sciences research, the goals set in the 1984 Report have not been achieved. Practically all of the increase in funding has gone into building the infractructure, which had deteriorated badly by 1984. While graduate and postdoctoral research, computer facilities, and new institutes have benefited from increased resources, some of these areas are still undersupported by the standards of other sciences. And in the area of research support for individual investigators, almost no progress has been made. A critical storage of qualified mathematical sciences researchers still looms, held at bay for the moment by a large influx of foreign researchers, an uncertain solution in the longer term. While government has responded substantially to the 1984 Report's recommendations, particularly in the support of infrastructure, the universities generally have not, so that the academic foundations of the mathematical sciences research enterprise are as shaky now as in 1984. The greatet progress has been made in the mathematics sciences community, whose members have shown a growing awareness of the problems confronting their discipline and increased interest in dealing with the problems, particularly in regard to communication with the public and government agencies and involvement in education. (AA)

This book is an intellectually stimulating excursion into mathematical machines and structures capable for a universal computation. World top experts in computer science and mathematics overview exciting and intriguing topics of logical theory of monoids, geometry of Gauss word, philosophy of mathematics in computer science, asynchronous and parallel P-systems, decidability in cellular automata, splicing systems, reversible Turing machines, information flows in two-way finite automata, prime generators in automaton arrays, Grossone and Turing machines, automaton models of atomic lattices. The book is full of visually attractive examples of mathematical machines, open problems and challenges for future research. Those interested in the advancement of a theory of computation, philosophy of mathematics, future and emergent computing paradigms, architectures and implementations will find the book vital for their research and development.

This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.

Papers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.

Elements of Combinatorial Computing focuses on the processes, principles, methodologies, and approaches involved in combinatorial computing. The publication first takes a look at a language for combinatorial computing, language implementation and program efficiency, and computer representation of mathematical objects. Discussions focus on geometric configurations, elementary combinatorial configurations, sets and vectors, natural numbers, program optimization, data representation, set manipulation, notation for iteration and recursion, and nested iteration and recursive programming. The text then takes a look at backtrack programming, generation of elementary configurations, and additional basic techniques and manipulations. Topics include isomorph rejection, transformations, finite set covering, sorting techniques, permutations with repeated objects, compositions, partitions, subsets and combinations, and basic backtracking and impasse detection. The book examines additional basic techniques and manipulations and applications of advanced algorithms. The publication is highly recommended for computer science experts and researchers interested in the elements in combinatorial computing.

In the summer of 1988 in Providence, the AMS celebrated its centennial with a wide range of mathematical activities. Among those was a symposium, Mathematics into the Twenty-first Century, which brought together a number of the top research mathematicians who will likely have a significant impact on the mathematics of this century. This book contains the lectures presented by 16 of the 18 individuals who spoke during the symposium. Written by some of the major international figures in mathematical research, this group of articles covers a panorama of the vital areas of mathematics at the turn of the 21st century and gives the general mathematical reader a broad perspective on some of the major trends in research.