The focus of algorithmic group theory shifted from the decidability/undecidability type of result to the complexity of algorithms. This title contains papers that reflect that paradigm shift. It presents articles that are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science.
The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
"The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results." "This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles." "Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal."--BOOK JACKET.
Electrocatalysis applications are employed in a large number of industries worldwide, ranging from old technologies such as galvanoplasty to the most up-to-date deployments involving ultracapacitators. Recognizing electrocatalysis as a useful interfacial approach to a dynamic interdisciplinary science, Electrocatalysis: Computational, Experimental,
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Computational Social Psychology showcases a new approach to social psychology that enables theorists and researchers to specify social psychological processes in terms of formal rules that can be implemented and tested using the power of high speed computing technology and sophisticated software. This approach allows for previously infeasible investigations of the multi-dimensional nature of human experience as it unfolds in accordance with different temporal patterns on different timescales. In effect, the computational approach represents a rediscovery of the themes and ambitions that launched the field over a century ago. The book brings together social psychologists with varying topical interests who are taking the lead in this redirection of the field. Many present formal models that are implemented in computer simulations to test basic assumptions and investigate the emergence of higher-order properties; others develop models to fit the real-time evolution of people’s inner states, overt behavior, and social interactions. Collectively, the contributions illustrate how the methods and tools of the computational approach can investigate, and transform, the diverse landscape of social psychology.
This book is based on a nuclear physics course the author has taught to graduate students at the Physics Department, College of Science, University of Baghdad, Iraq, for the period 19782007. Also, it is based on the authors experiences in the field of nuclear physics, teaching, researching, and administration of certain scientific institutions and organizations. It consists of nine chapters and an appendix of some solved problems to illustrate the subject to the students. As a textbook in nuclear physics, it actually deals with the physics of the nucleus of the atom, from the time of discovering the nucleus by the alpha particle (a) scattering by gold film experiment by Rutherford (1911). Therefore, it describes and demonstrates the following important subjects: Nuclear radius and shapes, properties The nuclear force, properties, and features Proposed nuclear models Nuclear potential, different suggested types Nuclear constituents, the protons (p) and the neutrons (N) The nucleon as identity to p and N according to the charge and energy state The angular momentum of the nucleus and its quadruple moment The nuclear interactions The rotation properties of the nucleus The electromagnetic properties of the nucleus Transitions, properties, and Fermi golden rules Beta decay and the nonconservation of parity and the CPT conservation, the helicity Nuclear particles physics Solved problems
Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.
One of the pathways by which the scientific community confirms the validity of a new scientific discovery is by repeating the research that produced it. When a scientific effort fails to independently confirm the computations or results of a previous study, some fear that it may be a symptom of a lack of rigor in science, while others argue that such an observed inconsistency can be an important precursor to new discovery. Concerns about reproducibility and replicability have been expressed in both scientific and popular media. As these concerns came to light, Congress requested that the National Academies of Sciences, Engineering, and Medicine conduct a study to assess the extent of issues related to reproducibility and replicability and to offer recommendations for improving rigor and transparency in scientific research. Reproducibility and Replicability in Science defines reproducibility and replicability and examines the factors that may lead to non-reproducibility and non-replicability in research. Unlike the typical expectation of reproducibility between two computations, expectations about replicability are more nuanced, and in some cases a lack of replicability can aid the process of scientific discovery. This report provides recommendations to researchers, academic institutions, journals, and funders on steps they can take to improve reproducibility and replicability in science.
