Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific dis ciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathe matics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A successful concurrent numerical simulation requires physics and math ematics to develop and analyze the model, numerical analysis to develop solution methods, and computer science to develop a concurrent implemen tation. No single course can or should cover all these disciplines. Instead, this course on concurrent scientific computing focuses on a topic that is not covered or is insufficiently covered by other disciplines: the algorith mic structure of numerical methods.

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This text covers the fundamental issues of developing programs for scientific computation on concurrent computers. Its purpose is to construct a conceptual framework that is a basis for understanding the real issues of concurrency. The core problems are often buried by mountains of technical detail. The conceptual framework allows us to cut through non-issues. It is, therefore, a basis for developing new numerical methods and new software tools that solve the real problems. Anyone who wishes to use concurrent computers should benefit from this text. Because the book covers numerical algorithms, an elementary background of linear algebra and advanced calculus is required. A previous contact with structured programming techniques will be helpful. The level of the text is aimed at advanced undergraduate and graduate students and researchers. The few sections that contain more advanced mathematical material can be omitted upon a first reading of the book. All algorithms are developed in detail, in a unified notation, and according to a coherent methodology. This is not an encyclopedia of recipes. Rather, the book stresses the methodology behind developing one's own concurrent programs for scientific computing. The approach is new because the text introduces formal program development to scientific computing. Readers can expect to cut down the time needed to develop concurrent programs. By following the same methodology, the user's programs will be easier to integrate into libraries, easier to use, and portable to a wide variety of concurrent computers.