Download or read book Irreducibility and Computational Equivalence written by Hector Zenil and published by Springer Science & Business Media. This book was released on 2012-12-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge--from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today's widespread Wolfram's Behavioural Classification to his principles of Irreducibility and Computational Equivalence. This volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram's seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram's NKS book. Featuring 39 authors, its 23 contributions are organized into seven parts: Mechanisms in Programs & Nature Systems Based on Numbers & Simple Programs Social and Biological Systems & Technology Fundamental Physics The Behavior of Systems & the Notion of Computation Irreducibility & Computational Equivalence Reflections and Philosophical Implications.
Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
Download or read book Symmetry and Complexity written by Klaus Mainzer and published by World Scientific. This book was released on 2005-06-10 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity. Contents:Symmetry and Complexity in Early Culture and PhilosophySymmetry and Complexity in MathematicsSymmetry and Complexity in Physical SciencesSymmetry and Complexity in Chemical SciencesSymmetry and Complexity in Life SciencesSymmetry and Complexity in Economic and Social SciencesSymmetry and Complexity in Computer ScienceSymmetry and Complexity in Philosophy and Arts Readership: Upper-level undergraduates, graduate students, researchers, academics, and professionals in interdisciplinary sciences. Keywords:Symmetry;Symmetry Breaking;Complexity;Nonlinear Science;Dynamical System;Chaos;Bifurcation;Fractal;Computational System;Information Dynamics;Philosophy of Science;ArtsKey Features:Valuable insights from natural, social and computer sciencesAttractive pictures and illustrations enhancing the spirit and beauty of nonlinear scienceReviews:“This outstanding book is a general overview of the notion of symmetry and its many connections to the ideas of complexity … The book will be especially useful to the intelligent general reader as well as advanced undergraduate students looking for challenging technical problems to solve, reconfigure, or redefine.”Zentralblatt MATH '
Download or read book A Project to Find the Fundamental Theory of Physics written by Stephen Wolfram and published by Wolfram Media. This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. A Project to Find the Fundamental Theory of Physics includes an accessible introduction to the project as well as core technical exposition and rich, never-before-seen visualizations.
Download or read book The Cellular Automaton Interpretation of Quantum Mechanics written by Gerard 't Hooft and published by Springer. This book was released on 2016-09-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.
Download or read book Adventures of a Computational Explorer written by Stephen Wolfram and published by Wolfram Media. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of essays the author has written over the past dozen years for various occasions.
Download or read book Modular Forms a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Download or read book Distributed Computing and Artificial Intelligence 11th International Conference written by Sigeru Omatu and published by Springer. This book was released on 2014-05-30 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 11th International Symposium on Distributed Computing and Artificial Intelligence 2014 (DCAI 2014) is a forum to present applications of innovative techniques for studying and solving complex problems. The exchange of ideas between scientists and technicians from both the academic and industrial sector is essential to facilitate the development of systems that can meet the ever-increasing demands of today’s society. The present edition brings together past experience, current work and promising future trends associated with distributed computing, artificial intelligence and their application in order to provide efficient solutions to real problems. This year’s technical program presents both high quality and diversity, with contributions in well-established and evolving areas of research (Algeria, Brazil, China, Croatia, Czech Republic, Denmark, France, Germany, Ireland, Italy, Japan, Malaysia, Mexico, Poland, Portugal, Republic of Korea, Spain, Taiwan, Tunisia, Ukraine, United Kingdom), representing a truly “wide area network” of research activity. DCAI'14 Special Sessions have been a very useful tool in order to complement the regular program with new or emerging topics of particular interest to the participating community. Special Sessions that emphasize on multi-disciplinary and transversal aspects, such as AI-driven methods for Multimodal Networks and Processes Modeling and Multi-Agents Macroeconomics have been especially encouraged and welcome. This symposium is organized by the Bioinformatics, Intelligent System and Educational Technology Research Group (http://bisite.usal.es/) of the University of Salamanca. The present edition was held in Salamanca, Spain, from 4th to 6th June 2014.
Download or read book Integral Closure of Ideals Rings and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Download or read book Turing Computability written by Robert I. Soare and published by Springer. This book was released on 2016-06-20 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author has honed the content over decades according to feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Download or read book Being You written by Anil Seth and published by Penguin. This book was released on 2021-10-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTERNATIONAL BESTSELLER A Best Book of 2021—Bloomberg Businessweek; A Best Science Book of 2021—The Guardian; A Best Science Book of 2021—Financial Times; A Best Philosophy Book of 2021—Five Books; A Best Book of 2021—The Economist Anil Seth's quest to understand the biological basis of conscious experience is one of the most exciting contributions to twenty-first-century science. What does it mean to “be you”—that is, to have a specific, conscious experience of the world around you and yourself within it? There may be no more elusive or fascinating question. Historically, humanity has considered the nature of consciousness to be a primarily spiritual or philosophical inquiry, but scientific research is now mapping out compelling biological theories and explanations for consciousness and selfhood. Now, internationally renowned neuroscience professor, researcher, and author Anil Seth is offers a window into our consciousness in BEING YOU: A New Science of Consciousness. Anil Seth is both a leading expert on the neuroscience of consciousness and one of most prominent spokespeople for this relatively new field of science. His radical argument is that we do not perceive the world as it objectively is, but rather that we are prediction machines, constantly inventing our world and correcting our mistakes by the microsecond, and that we can now observe the biological mechanisms in the brain that accomplish this process of consciousness. Seth has been interviewed for documentaries aired on the BBC, Netflix, and Amazon and podcasts by Sam Harris, Russell Brand, and Chris Anderson, and his 2017 TED Talk on the topic has been viewed over 11 million times, a testament to his uncanny ability to make unimaginably complex science accessible and entertaining.
Download or read book Algorithmic Algebra written by Bhubaneswar Mishra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.
Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Download or read book Galois Theory Through Exercises written by Juliusz Brzeziński and published by Springer. This book was released on 2018-03-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Download or read book The End of Theory written by Richard Bookstaber and published by Princeton University Press. This book was released on 2019-04-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth look at how to account for the human complexities at the heart of today’s financial system Our economy may have recovered from the Great Recession—but not our economics. The End of Theory discusses why the human condition and the radical uncertainty of our world renders the standard economic model—and the theory behind it—useless for dealing with financial crises. What model should replace it? None. At least not any version we’ve been using for the past two hundred years. Richard Bookstaber argues for a new approach called agent-based economics, one that takes as a starting point the fact that we are humans, not the optimizing automatons that standard economics assumes we are. Sweeping aside the historic failure of twentieth-century economics, The End of Theory offers a novel perspective and more realistic framework to help prevent today's financial system from blowing up again.
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
