Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Introduction to the Theory of Computation written by Michael Sipser and published by Cengage Learning. This book was released on 2012-06-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now you can clearly present even the most complex computational theory topics to your students with Sipser’s distinct, market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today’s computational theory course, this highly anticipated revision retains the unmatched clarity and thorough coverage that make it a leading text for upper-level undergraduate and introductory graduate students. This edition continues author Michael Sipser’s well-known, approachable style with timely revisions, additional exercises, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. This edition’s refined presentation ensures a trusted accuracy and clarity that make the challenging study of computational theory accessible and intuitive to students while maintaining the subject’s rigor and formalism. Readers gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E’s comprehensive coverage makes this an ideal ongoing reference tool for those studying theoretical computing. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Download or read book Understanding Computation written by Tom Stuart and published by "O'Reilly Media, Inc.". This book was released on 2013-05-15 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finally, you can learn computation theory and programming language design in an engaging, practical way. Understanding Computation explains theoretical computer science in a context you’ll recognize, helping you appreciate why these ideas matter and how they can inform your day-to-day programming. Rather than use mathematical notation or an unfamiliar academic programming language like Haskell or Lisp, this book uses Ruby in a reductionist manner to present formal semantics, automata theory, and functional programming with the lambda calculus. It’s ideal for programmers versed in modern languages, with little or no formal training in computer science. Understand fundamental computing concepts, such as Turing completeness in languages Discover how programs use dynamic semantics to communicate ideas to machines Explore what a computer can do when reduced to its bare essentials Learn how universal Turing machines led to today’s general-purpose computers Perform complex calculations, using simple languages and cellular automata Determine which programming language features are essential for computation Examine how halting and self-referencing make some computing problems unsolvable Analyze programs by using abstract interpretation and type systems

Download or read book An Introduction to High performance Scientific Computing written by Lloyd Dudley Fosdick and published by MIT Press. This book was released on 1996 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduates, An Introduction to High-Performance Scientific Computing assumes a basic knowledge of numerical computation and proficiency in Fortran or C programming and can be used in any science, computer science, applied mathematics, or engineering department or by practicing scientists and engineers, especially those associated with one of the national laboratories or supercomputer centers. This text evolved from a new curriculum in scientific computing that was developed to teach undergraduate science and engineering majors how to use high-performance computing systems (supercomputers) in scientific and engineering applications. Designed for undergraduates, An Introduction to High-Performance Scientific Computing assumes a basic knowledge of numerical computation and proficiency in Fortran or C programming and can be used in any science, computer science, applied mathematics, or engineering department or by practicing scientists and engineers, especially those associated with one of the national laboratories or supercomputer centers. The authors begin with a survey of scientific computing and then provide a review of background (numerical analysis, IEEE arithmetic, Unix, Fortran) and tools (elements of MATLAB, IDL, AVS). Next, full coverage is given to scientific visualization and to the architectures (scientific workstations and vector and parallel supercomputers) and performance evaluation needed to solve large-scale problems. The concluding section on applications includes three problems (molecular dynamics, advection, and computerized tomography) that illustrate the challenge of solving problems on a variety of computer architectures as well as the suitability of a particular architecture to solving a particular problem. Finally, since this can only be a hands-on course with extensive programming and experimentation with a variety of architectures and programming paradigms, the authors have provided a laboratory manual and supporting software via anonymous ftp. Scientific and Engineering Computation series

Download or read book Introduction to Computation and Programming Using Python second edition written by John V. Guttag and published by MIT Press. This book was released on 2016-08-12 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of an introductory text that teaches students the art of computational problem solving, covering topics ranging from simple algorithms to information visualization. This book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of data science for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT's OpenCourseWare) and was developed for use not only in a conventional classroom but in in a massive open online course (MOOC). This new edition has been updated for Python 3, reorganized to make it easier to use for courses that cover only a subset of the material, and offers additional material including five new chapters. Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming. This edition offers expanded material on statistics and machine learning and new chapters on Frequentist and Bayesian statistics.

Download or read book An Introduction to Natural Computation written by Dana H. Ballard and published by MIT Press. This book was released on 1999-01-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It is now clear that the brain is unlikely to be understood without recourse to computational theories. The theme of An Introduction to Natural Computation is that ideas from diverse areas such as neuroscience, information theory, and optimization theory have recently been extended in ways that make them useful for describing the brains programs. This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It stresses the broad spectrum of learning models—ranging from neural network learning through reinforcement learning to genetic learning—and situates the various models in their appropriate neural context. To write about models of the brain before the brain is fully understood is a delicate matter. Very detailed models of the neural circuitry risk losing track of the task the brain is trying to solve. At the other extreme, models that represent cognitive constructs can be so abstract that they lose all relationship to neurobiology. An Introduction to Natural Computation takes the middle ground and stresses the computational task while staying near the neurobiology.

Download or read book Physical Computation written by Gualtiero Piccinini and published by Oxford University Press, USA. This book was released on 2015 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computation permeates our world, but a satisfactory philosophical theory of what it is has been lacking. Gualtiero Piccinini presents a mechanistic account of what makes a physical system a computing system. He argues that computation does not entail representation or information-processing, although information-processing entails computation.

Download or read book Theory of Computation written by James L. Hein and published by Jones & Bartlett Pub. This book was released on 1996-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Information Physics and Computation written by Marc Mézard and published by Oxford University Press. This book was released on 2009-01-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

Download or read book Biological Computation written by Ehud Lamm and published by CRC Press. This book was released on 2011-05-25 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of biologically inspired computing, or biological computation, involves the development of new, biologically based techniques for solving difficult computational problems. A unified overview of computer science ideas inspired by biology, Biological Computation presents the most fundamental and significant concepts in this area. In the book

Download or read book Natural Computation written by Whitman Richards and published by MIT Press (MA). This book was released on 1988 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for the MIT course, "Natural Computation, this extensive book of readings combines mathematics, artificial intelligence, computer science, experimental psychology, and neurophysiology in studying perception. Mathematics is emphasized for making perceptual inferences and the spectrum of mathematical techniques used is very broad. While the more than thirty readings focus primarily on vision, they also encompass the study of sound perception and the interpretation and application of forces including movement.Each article is a self contained example of how a perceptual problem may be tackled and solved. For example, what makes wood look like wood not like stone, sand, or grass? How can we represent three dimensional shapes when the same shape is rarely seen in exactly the same way? Each of the five sections is preceded by an introduction and the book concludes with problem sets.Whitman A. Richards is Professor in the Brain and Cognitive Science Department at MIT. A Bradford Book.

Download or read book Mathematical Theory of Computation written by Zohar Manna and published by Courier Dover Publications. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students. Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and algol-like programs); flowchart schemas (basic notions, decision problems, formalization in predicate calculus, and translation programs); and the fixpoint theory of programs (functions and functionals, recursive programs, and verification programs). The treamtent is self-contained, and each chapter concludes with bibliographic remarks, references, and problems.

Download or read book An Introduction to Online Computation written by Dennis Komm and published by Springer. This book was released on 2016-10-31 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains online computation in different settings, with particular emphasis on randomization and advice complexity. These settings are analyzed for various online problems such as the paging problem, the k-server problem, job shop scheduling, the knapsack problem, the bit guessing problem, and problems on graphs. This book is appropriate for undergraduate and graduate students of computer science, assuming a basic knowledge in algorithmics and discrete mathematics. Also researchers will find this a valuable reference for the recent field of advice complexity.

Download or read book A Pragmatic Introduction to Secure Multi Party Computation written by David Evans and published by Foundations and Trends (R) in Privacy and Security. This book was released on 2018-12-19 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practitioners and researchers seeking a concise, accessible introduction to secure multi-party computation which quickly enables them to build practical systems or conduct further research will find this essential reading.

Download or read book Complexity and Real Computation written by Lenore Blum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.

Download or read book Models of Computation written by Roberto Bruni and published by Springer. This book was released on 2017-04-03 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in their basic form the most important models of computation, their basic programming paradigms, and their mathematical descriptions, both concrete and abstract. Each model is accompanied by relevant formal techniques for reasoning on it and for proving some properties. After preliminary chapters that introduce the notions of structure and meaning, semantic methods, inference rules, and logic programming, the authors arrange their chapters into parts on IMP, a simple imperative language; HOFL, a higher-order functional language; concurrent, nondeterministic and interactive models; and probabilistic/stochastic models. The authors have class-tested the book content over many years, and it will be valuable for graduate and advanced undergraduate students of theoretical computer science and distributed systems, and for researchers in this domain. Each chapter of the book concludes with a list of exercises addressing the key techniques introduced, solutions to selected exercises are offered at the end of the book.

Download or read book The Nature of Computation written by Cristopher Moore and published by OUP Oxford. This book was released on 2011-08-11 with total page 1498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.