This proceedings is based on research work on formula manipulation and computer algebra, culminating in the design and construction of a formula manipulation machine at RIKEN known as the FLATS project.

Annotation This volume consists of papers presented to the Second International Conference on the Theory of Groups held in Canberra in August 1973 together with areport by the chairman of the Organizing Committee and a collection of problems. The manuscripts were typed by Mrs Geary, the bulk of the bibliographie work was done by Mrs Pinkerton, and a number of colleagues helped with proof-reading; Professor Neumann, Drs Cossey, Kovacs, MeDougall, Praeger, Pride, Rangaswamy and Stewart. I here reeord my thanks to all these people for their lightening of the editorial burden. M.F. Newrnan CONTENTS 1 Introduction . . 8 yan, Periodic groups of odd exponent Reinhold Baer, Einbettungseigenschaften von Normalteilern: der Schluss vom 13 Endlichen aufs Unendliche D.W. Barnes, Characterisation of the groups with the Gaschutz cohomology property 63 Gi Ibert Baumslag, Finitely presented metabe1ian groups 65 Gi Ibert Baumslag, Some problems on one-relator groups 75 A.J. Ba, J. Kautsky and J.W. Wamsley, Computation in nilpotent groups (application) 82 Wi I I iam W. Boone, Between logic and group theory 90 Richard Brauer, On the structure of blocks of characters of finite groups 103 A.M. Brunner, Transitivity-systems of certain one-relator groups 131 Egg8r M. Bryant, Characteristic subgroups of free groups 141 y, Metabe1ian varieties of groups 150 R.A. Bryce and John Cossey, Subdirect product c10sed Fitting c1asses 158 R.G."

This book gives an overview of the works performed by the Computer and Automation Institute of the Hungarian Academy of Sciences. Since the late 1970s, there was a need for the recognition of the fundamental role of adequate abstractions and higher level conceptual models in all fields of computer applications. The approach presented explores various conceptual descriptive methods of specification processing.

Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.

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.

The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems

These proceedings are devoted to communicating significant developments in all areas pertinent to Parallel Symbolic Computation.The scope includes algorithms, languages, software systems and application in any area of parallel symbolic computation, where parallelism is interpreted broadly to include concurrent, distributive, cooperative schemes, and so forth.

"This comprehensive reference work provides immediate, fingertip access to state-of-the-art technology in nearly 700 self-contained articles written by over 900 international authorities. Each article in the Encyclopedia features current developments and trends in computers, software, vendors, and applications...extensive bibliographies of leading figures in the field, such as Samuel Alexander, John von Neumann, and Norbert Wiener...and in-depth analysis of future directions."

This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001. The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.