Products related to Theory:
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Information and Coding Theory
As this Preface is being written, the twentieth century is coming to an end.Historians may perhaps come to refer to it as the century of information, just as its predecessor is associated with the process of industrialisation.Successive technological developments such as the telephone, radio, television, computers and the Internet have had profound effects on the way we live.We can see pic tures of the surface of Mars or the early shape of the Universe.The contents of a whole shelf-load of library books can be compressed onto an almost weight less piece of plastic.Billions of people can watch the same football match, or can keep in instant touch with friends around the world without leaving home.In short, massive amounts of information can now be stored, transmitted and processed, with surprising speed, accuracy and economy.Of course, these developments do not happen without some theoretical ba sis, and as is so often the case, much of this is provided by mathematics.Many of the first mathematical advances in this area were made in the mid-twentieth century by engineers, often relying on intuition and experience rather than a deep theoretical knowledge to lead them to their discoveries.Soon the math ematicians, delighted to see new applications for their subject, joined in and developed the engineers' practical examples into wide-ranging theories, com plete with definitions, theorems and proofs.
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Concise Encyclopedia of Coding Theory
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon.Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance boundsPart II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphsPart III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
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Introduction To Algebraic Coding Theory
We live in the age of technology where messages are transmitted in sequences of 0's and 1's through space.It is possible to make an error with noisy channels, so self-correcting codes become vital to eradicate all errors (as the number of errors is small).These self-correcting codes are widely used in the industry for a variety of applications including e-mail, telephone, remote sensing (e.g., photographs of Mars), amongst others.We will present some essentials of the theory in this book.Using linear algebra, we have the salient Hamming codes.The next level of coding theory is through the usage of ring theory, especially polynomials, rational functions and power series, to produce BCH codes, Reed-Solomon codes and the classical Goppa codes.Then we progress to the geometric Goppa code using Algebraic Geometry.
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Algebraic Coding Theory (Revised Edition)
This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm.Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems.Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two.Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
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Is learning programming and software development very challenging?
Learning programming and software development can be challenging for some people, as it requires logical thinking, problem-solving skills, and attention to detail. However, with dedication, practice, and the right resources, it is definitely achievable. Breaking down complex concepts into smaller, more manageable parts and seeking help from online tutorials, courses, and communities can make the learning process easier and more enjoyable. Ultimately, the level of challenge will vary depending on the individual's background, experience, and learning style.
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Which programming languages are used in software development?
There are many programming languages used in software development, including popular languages such as Java, Python, C++, JavaScript, and Ruby. Each language has its own strengths and is used for different purposes in software development. For example, Java is commonly used for building enterprise-level applications, while Python is known for its simplicity and versatility. C++ is often used for system software and game development, while JavaScript is essential for web development. Overall, the choice of programming language depends on the specific requirements of the software being developed.
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What is the difference between software development and programming?
Software development is a broader term that encompasses the entire process of creating software, including planning, designing, testing, and maintaining software applications. Programming, on the other hand, refers specifically to the act of writing code to instruct a computer to perform certain tasks. While programming is a key component of software development, software development involves a more comprehensive approach that includes various stages beyond just writing code.
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Which programming language is suitable for software development for the PC?
There are several programming languages that are suitable for software development for the PC, but some of the most popular and widely used ones include C++, Java, and C#. C++ is a powerful and versatile language that is commonly used for developing system software and applications that require high performance. Java is a popular choice for developing cross-platform applications, as it can run on any operating system that has a Java Virtual Machine. C# is commonly used for developing Windows applications and is well-integrated with the .NET framework. Ultimately, the choice of programming language depends on the specific requirements of the software being developed and the preferences of the development team.
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Development of Social Theory
Originally published in 1924, Development of Social Theory was written to expand on an outline of the subject in order to turn it into a year’s course of graduate study.From Plato to the writers and teachers of the time, it presents the theorists themselves, giving a historic background, followed by their theory and its subsequent development.It was highly regarded, and widely used as a text for many years.Today it can be read in its historical context.
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Information Theory : From Coding to Learning
This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning, equipping students with a uniquely well-rounded and rigorous foundation for further study.Introduces core topics such as data compression, channel coding, and rate-distortion theory using a unique finite block-length approach.With over 210 end-of-part exercises and numerous examples, students are introduced to contemporary applications in statistics, machine learning and modern communication theory.This textbook presents information-theoretic methods with applications in statistical learning and computer science, such as f-divergences, PAC Bayes and variational principle, Kolmogorov's metric entropy, strong data processing inequalities, and entropic upper bounds for statistical estimation.Accompanied by a solutions manual for instructors, and additional standalone chapters on more specialized topics in information theory, this is the ideal introductory textbook for senior undergraduate and graduate students in electrical engineering, statistics, and computer science.
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Educational Theory in the 21st Century : Science, Technology, Society and Education
This open access book reviews the effects of the twenty-first century scientific-technological and social developments on the educational theory.The first part handles the subject, focusing on technology and educational philosophy.In the second part, the implications of new human and social conceptions towards the education paradigms are examined.In the chapters of the last part of the book, more practical dimensions of education are discussed.Transforming school designs, school management, learning-teaching approaches and teacher competencies are discussed in the context of broader social, cultural and technological changes.
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Stochastic Control Theory : Dynamic Programming Principle
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons.Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory.When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise.This problem is treated in the same frameworks, via the nonlinear semigroup.Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise).Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation.The existence and uniqueness of solutions and regularities as well as Itô's formula are stated.A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space.The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with.Here, for finite time-horizon control problems, DPP was formulated as aone-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method.The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes.Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.
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Which education is suitable for IT security or software development?
For a career in IT security or software development, a formal education in computer science, information technology, or a related field is typically recommended. A bachelor's degree in computer science can provide a strong foundation in programming, algorithms, and computer systems, which are essential skills for both IT security and software development roles. Additionally, pursuing certifications in cybersecurity or software development can also help enhance your skills and credibility in the field. Ultimately, the most suitable education will depend on your specific career goals and interests within the IT industry.
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What are identity theory and competition theory?
Identity theory is a sociological perspective that focuses on how individuals develop and maintain a sense of self and identity through their interactions with others and their social environment. It emphasizes the importance of social roles, relationships, and cultural influences in shaping one's identity. Competition theory, on the other hand, is a perspective that examines how competition for resources, power, and status shapes social relationships and structures. It emphasizes the role of competition in driving social change, inequality, and conflict within societies. Both theories offer valuable insights into the ways in which individuals and societies are shaped by their social interactions and the broader social context.
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Who is better in programming and software development: mechatronics engineers or IT specialists?
It is difficult to determine who is better in programming and software development between mechatronics engineers and IT specialists as both have their own strengths and expertise. Mechatronics engineers have a strong foundation in mechanical, electrical, and computer engineering, allowing them to develop software for embedded systems and control systems. On the other hand, IT specialists have a deep understanding of software development and programming languages, with a focus on creating applications and managing information systems. Ultimately, the better choice depends on the specific requirements of the project and the expertise of the individual professionals involved.
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Is the Big Bang Theory just a theory?
The Big Bang Theory is more than just a theory; it is a well-supported scientific model that explains the origin and evolution of the universe. It is supported by a wide range of observational evidence, such as the cosmic microwave background radiation and the redshift of galaxies. The theory has also made successful predictions about the abundance of light elements in the universe. While it is called a "theory," in scientific terms, a theory is a well-substantiated explanation of some aspect of the natural world that is based on a body of evidence. Therefore, the Big Bang Theory is a robust and widely accepted scientific explanation for the origin of the universe.
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