Readership: Undergraduates, graduate students, and research scientists in computational physics, engineering, physical science, applied physics, and fractals.

Thomas Brody had one of the most powerful and wide-ranging intellects of his generation. Although primarily a physicist who worked on statistical prob lems in nuclear physics, on probability theory and on computational physics he had an extensive knowledge of the philosophy of science and of philosophy, and was fluent in many languages. He is well-known among physicists for the Brody-Moshinsky transformation but his extensive work on probability and on the philosophy of science remained almost unknown. This was because the originality of his ideas entailed many lengthy battles with uncomprehending referees, and he frequently published in Mexican journals of limited circula tion. In addition, his strongly critical spirit inhibited his willingness to publish his ideas. He was always most concerned by the very unsatisfactory situation in the philosophy of physics, that is largely due to the generally poor knowledge that physicists and philosophers have of each other's disciplines. Philosophers of science write at length about physics without any detailed first-hand knowl edge of how research is actually carried out. Physicists, for their part, often implicitly assume naive or erroneous philosophical ideas, and this often hinders their scientific work, besides spreading further confusion if they try to give an account of what they are doing.

No basic or applied physics research can be done nowadays without the support of computing systems, ranging from cheap personal computers to large multi-user mainframes. Some research fields like high energy physics would not exist if computers had not been invented. Departing from the more conventional numerical applications, this series of workshops has been initiated to focus on Artificial Intelligence (AI) related developments, such as symbolic manipulation for lengthy and involved algebraic computations, software engineering to assist groups of developers in the design, coding and maintenance of large packages, expert systems to mimic human reasoning and strategy in the diagnosis of equipment or neural networks to implement a model of the brain to solve pattern recognition problems. These techniques, developed some time ago by AI researchers, are confronted by down-to-earth problems arising in high-energy and nuclear physics. All this and more are covered in these proceedings.

A vivid example of the growing need for frontier physics experiments to make use of frontier technology is in the field of Artificial Intelligence (AI) and related themes.By AI we are referring here to the use of computers to deal with complex objects in an environment based on specific rules (Symbolic Manipulation), to assist groups of developers in the design, coding and maintenance of large packages (Software Engineering), to mimic human reasoning and strategy with knowledge bases to make a diagnosis of equipment (Expert Systems) or to implement a model of the brain to solve pattern recognition problems (Neural Networks). These techniques, developed some time ago by AI researchers, are confronted by down-to-earth problems arising in high-energy and nuclear physics. However, similar situations exist in other 'big sciences' such as space research or plasma physics, and common solutions can be applied.The magnitude and complexity of the experiments on the horizon for the end of the century clearly call for the application of AI techniques. Solutions are sought through international collaboration between research and industry.

Elements of Mathematical Methods for Physics provides students with an approachable and innovative introduction to key concepts of mathematical physics, accompanied by clear and concise explanations, relevant real-world examples and problems that help them to master the fundamentals of mathematical physics. The topics are presented at a basic level, for students lacking a prior mathematical background. This book is designed to be covered in two semesters, presenting 18 chapters on topics varying from differential equations, matrix algebra and tensor analysis to Fourier transform, including special functions and dynamical systems. Upper-level undergraduate and graduate students of physics and engineering as well as professionals will gain a better grip of the basics and a deeper insight into and appreciation for mathematical methods for physics. Key Features: • Reviews and presents the basic math skills needed at the undergraduate level. • Chapters accompanied by examples and end-of-chapter problems to enhance understanding. • Introduces dynamical systems and includes a chapter on Hilbert Space

This volume contains the contributions to the INTERNATIONAL SUMMER INSTITUTE ON THEORETICAL PHYSICS 1980 held from September 1st to September 12th in Bad Honnef, Germany. This Institute was organized by Wuppertal University. It was the eleventh in a series of Summer Schools on particle physics carried out by German Universities. The Institute was aimed to review the present status of gauge theories in elementary particle physics, with emphasis both on the phenomenological and formal aspects. The first part of the volume covers the recent progress in the development of perturbative methods both in quantum chromodynamics (QCD) and flavor dynamics (QFD). Applications to available data from electron positron storage rings and deep inelastic scattering are discussed. The second part presents new results on classical solutions and non-perturbative methods in gauge theories and related field theories like non linear a-models. A very topical account is given on the application of Monte Carlo methods within lattice gauge theories. At present these methods appear to be the most promising technique to establish the quark confinement hypothesis within the framework of non-Abelian gauge theories. The volume is closed with a progress report on the present understanding of sup~rgravity and its relation to grand unification schemes. The lectures on Grand Unified Theories given by Dr. D. V. Nanopoulos at the Bad Honnef meeting can be found in the proceedings of the 1980 Rencontre de Moriond (Ed. J. Tran Thanh Van).

Discrete Numerical Methods in Physics and Engineering