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Books in Theory and mathematics general

  • Complexity in Mathematical Biology for Sustainable Development

    Modeling Climate, Disease, and Ecosystems through Difference, Differential, and Fractional Theory
    • 1st Edition
    • Fatma Bozkurt
    • English
    Complexity in Mathematical Biology for Sustainable Development: Modeling Climate, Disease, and Ecosystems through Difference, Differential, and Fractional Theory introduces new mathematical methods to derive complex modeling solutions for a wide range of engineering and scientific research applications. The book strikes a balance between high-level mathematical theory and technical derivations, offering step-by-step explanations, real-world case studies, and clear introductions to advanced mathematical models. Solutions include modeling and quantifying complexity, with emphasis placed on the growing need for interdisciplinary collaboration, the integration of real-time data into models, and the development of adaptive frameworks challenges such as pandemics, biodiversity loss, and climate uncertainty.The book is designed to meet the needs of a diverse primary audience, from graduate students to professionals in fields such as computer science, public health, environmental policy, applied mathematics, and biotechnology. By providing both theoretical foundations and practical applications, the book equips readers with the skills and knowledge to tackle pressing global challenges through mathematical models, making it a valuable resource for both academic and professional development.
  • Fundamentals of Statistics for Researchers and Data Analysts

    • 1st Edition
    • Shashi A. Chiplonkar + 1 more
    • English
    Fundamentals of Statistics for Researchers and Data Analysts explains statistical methods, and the assumptions and prerequisites for applying various analytical tools from an statistical point of view. Statistical analysis has become indispensable in almost all fields of science, business, industry and medicine, for evidence-based decision making and forecasting. However, due to lack of fundamental understanding of statistics, results of data analysis often remain inconclusive or erroneous. In addition, data analysts or even statistical advisers may not be familiar with the subject area of the data, leading to inaccurate application of statistical tools and interpretation of results. To address these issues, this book breaks down the concepts of statistics into accessible, practical explanations with real-world examples. The book is organized by first explaining what statistical thinking is and how one should proceed with formulating their question in terms of a statistical hypothesis. Then step by step, topics are explained in detail, including data generation by choice of proper study design, data collection methods, identifying outliers, methods of data analysis, and finally interpretation of results to help make the required decision. Essential statistical methods such as classification techniques, correlation analysis, regression models, probability distributions, model building and statistical tests of significance are explained with live datasets using Excel and SPSS. Fundamentals of Statistics for Researchers and Data Analysts instructs readers on the precise methodology of analyzing data and interpretation of statistical results to arrive at a valid conclusion. Readers can use the same methodology from the case studies given in the book for their own applications and research by replacing the variables in the examples with the variables from their own datasets. The book ensures that readers are well-prepared for data-driven roles in various sectors.
  • Fractional Modeling of Fluid Flow and Transport Phenomena

    • 1st Edition
    • Mohamed F. El-Amin
    • English
    Fractional Modeling of Fluid Flow and Transport Phenomena focuses on mathematical and numerical aspects of fractional-order modeling in fluid flow and transport phenomena. The book covers fundamental concepts, advancements, and practical applications, including modeling developments, numerical solutions, and convergence analysis for both time and space fractional order models. Various types of flows are explored, such as single- and multi-phase flows in porous media, involving different fluid types like Newtonian, non-Newtonian, nanofluids, and ferrofluids. This book serves as a comprehensive reference on fractional-order modeling of fluid flow and transport phenomena, offering a single resource that is currently unavailable.Fraction... modeling has gained traction in engineering and science, particularly in fluid dynamics and transport phenomena. However, its mathematical and numerical advancements have progressed relatively slowly compared to other aspects. Therefore, this book emphasizes the fractional-order modeling of fluid flow and transport phenomena to bridge this gap. Each chapter in the book delves into a specific topic closely related to the others, ensuring a cohesive and self-contained structure.
  • Fractional Calculus

    Bridging Theory with Computational and Contemporary Advances
    • 1st Edition
    • Behzad Ghanbari
    • English
    Fractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calculus, offering a unique blend of theoretical foundations, numerical algorithms, practical applications, and innovative perspectives. This book explores the mathematical framework of fractional calculus and its relevance across various disciplines, providing readers with a deep understanding of this rapidly growing field. The author presents a rigorous yet accessible approach to fractional calculus, making it suitable for mathematicians, researchers, academics, graduate students, and professionals in engineering and applied sciences. The book covers a wide range of topics, including numerical methods for fractional calculus equations, fractional differential equations, fractal dynamics, and fractional control systems. It also explores applications in areas such as physics, engineering, signal processing, and data analysis. Fractional Calculus: Bridging Theory with Computational and Contemporary Advances equips readers with the necessary tools to tackle challenging problems involving fractional calculus, empowering them to apply these techniques in their research, professional work, or academic pursuits. The book provides a comprehensive introduction to the fundamentals of fractional calculus, explaining the theoretical concepts and key definitions in a clear and accessible manner. This helps readers build a strong foundation in the subject. The book then covers a range of numerical algorithms specifically designed for fractional calculus problems, explaining the underlying principles, step-by-step implementation, and computational aspects of these algorithms. This enables readers to apply numerical techniques to solve fractional calculus problems effectively. The book also provides examples that illustrate how fractional calculus is applied to solve real-world problems, providing readers with insights into the wide-ranging applications of the subject.
  • Smart Sensors Networks

    Communication Technologies and Intelligent Applications
    • 1st Edition
    • Fatos Xhafa + 2 more
    • English
    Smart Sensors Networks: Communication Technologies and Intelligent Applications explores the latest sensor and sensor networks techniques and applications, showing how networked wireless sensors are used to monitor and gather intelligence from our surrounding environment. It provides a systematic look at the unique characteristics of wireless sensor networks through their usage in a broad range of areas, including healthcare for the elderly, energy consumption, industrial automation, intelligent transportation systems, smart homes and cities, and more. The book shows how sensor-networks work and how they are applied to monitor our surrounding environment. It explores the most important aspects of modern sensors technologies, providing insights on the newest technologies and the systems needed to operate them. Readers will find the book to be an entry point for understanding the fundamental differences between the various sensor technologies and their use in for different scenarios. Indexing: The books of this series are submitted to EI-Compendex and SCOPUS
  • Physically Based Rendering

    From Theory to Implementation
    • 3rd Edition
    • Matt Pharr + 2 more
    • English
    Physically Based Rendering: From Theory to Implementation, Third Edition, describes both the mathematical theory behind a modern photorealistic rendering system and its practical implementation. Through a method known as 'literate programming', the authors combine human-readable documentation and source code into a single reference that is specifically designed to aid comprehension. The result is a stunning achievement in graphics education. Through the ideas and software in this book, users will learn to design and employ a fully-featured rendering system for creating stunning imagery. This completely updated and revised edition includes new coverage on ray-tracing hair and curves primitives, numerical precision issues with ray tracing, LBVHs, realistic camera models, the measurement equation, and much more. It is a must-have, full color resource on physically-based rendering.
  • Computational Network Science

    An Algorithmic Approach
    • 1st Edition
    • Henry Hexmoor
    • English
    The emerging field of network science represents a new style of research that can unify such traditionally-divers... fields as sociology, economics, physics, biology, and computer science. It is a powerful tool in analyzing both natural and man-made systems, using the relationships between players within these networks and between the networks themselves to gain insight into the nature of each field. Until now, studies in network science have been focused on particular relationships that require varied and sometimes-incompatib... datasets, which has kept it from being a truly universal discipline. Computational Network Science seeks to unify the methods used to analyze these diverse fields. This book provides an introduction to the field of Network Science and provides the groundwork for a computational, algorithm-based approach to network and system analysis in a new and important way. This new approach would remove the need for tedious human-based analysis of different datasets and help researchers spend more time on the qualitative aspects of network science research.
  • Scientific Computing

    An Introduction with Parallel Computing
    • 1st Edition
    • Gene H. Golub + 1 more
    • English
    This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.
  • Generating Functionology

    • 2nd Edition
    • Herbert S. Wilf
    • English
    This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter.
  • The Lambda Calculus

    Its Syntax and Semantics
    • 2nd Edition
    • Volume 103
    • H.P. Barendregt
    • English
    The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
  • The Single Server Queue

    • 2nd Edition
    • Volume 8
    • J.W. Cohen
    • English
    This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.
  • Dynamic Programming

    Sequential Scientific Management
    • 1st Edition
    • Volume 37
    • A. Kaufmann + 1 more
    • English
    This work discusses the value of dynamic programming as a method of optimization for the sequential phenomena encountered in economic studies or in advanced technological programs such as those associated with space flights. The dynamic programs which are considered are defined for a deterministic universe, or one with probabilities; both categories are of equal importance in the practice of operations research or of scientific management.
  • Problems in the Philosophy of Mathematics

    • 1st Edition
    • Volume 47
    • Brouwer
    • English
  • Probabilities and Potential, B

    Theory of Martingales
    • 1st Edition
    • Volume 72
    • C. Dellacherie + 1 more
    • English
  • Theories of Computational Complexity

    • 1st Edition
    • Volume 35
    • C. Calude
    • English
    This volume presents four machine-independent theories of computational complexity, which have been chosen for their intrinsic importance and practical relevance. The book includes a wealth of results - classical, recent, and others which have not been published before.In developing the mathematics underlying the size, dynamic and structural complexity measures, various connections with mathematical logic, constructive topology, probability and programming theories are established. The facts are presented in detail. Extensive examples are provided, to help clarify notions and constructions. The lists of exercises and problems include routine exercises, interesting results, as well as some open problems.
  • Probabilities and Potential, C

    Potential Theory for Discrete and Continuous Semigroups
    • 1st Edition
    • Volume 151
    • C. Dellacherie + 1 more
    • English
    This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents.The fourth and last part of the English edition will be devoted to the theory of Markov processes.
  • Enveloping Algebras

    • 1st Edition
    • Volume 14
    • Diximier
    • English
  • Multiparametric Statistics

    • 1st Edition
    • Vadim Ivanovich Serdobolskii
    • English
    This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematica... theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science.
  • Computational Complexity: A Quantitative Perspective

    • 1st Edition
    • Volume 196
    • Marius Zimand
    • English
    There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations (e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest extensively.The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the number of hard inputs at each length.One chapter is dedicated to abstract complexity theory, an older field which, however, deserves attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors, derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems, and others.The book should appeal to graduate computer science students, and to researchers who have an interest in computer science theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.
  • Mastering Mathematica

    Programming Methods and Applications
    • 2nd Edition
    • John W. Gray
    • English
    This new edition of Mastering Mathematica focuses on using Mathematica as a programming language, because programming in Mathematica is the best way to use the software to its fullest capacity. The book covers functional programming, imperative programming, rewrite programming, and object-oriented programming. It also addresses the use of Mathematica as a symbolic manipulator and a general tool for knowledge representation.
  • Automata Reasoning ***Replacement*** Disk

    • 1st Edition
    • Replacement
    • English
  • Relational Database Systems

    • 1st Edition
    • Dan A. Simovici + 1 more
    • English
    Relational Database Systems provides a timely introduction to the type of systems that are the current mainstay of the database management field. This book serves as a text for advanced undergraduate and graduate students, as well as an informative reference for researchers and professionals in all database aspects of computer science. It presents important querying systems including SQL and QUEL, and covers their respective theoretical foundations in relational algebra, tuple calculus, and domain calculus.The presentation of SQL adheres to the ANSI standard; however, the book discusses the most popular SQL dialects; a separate chapter covers imbedded SQL. The text also contains references to many significant relational database products, including INGRES, ORACLE, DB2, PARADOX, and SYBASE.Relational Database Systems concentrates on those issues that are most relevant to database design and application development. Exercises that constitute important extensions of the material are provided at the end of each chapter. The book assumes a knowledge of programming languages and datastructures, and some mathematical induction.
  • The Vector-Valued Maximin

    • 1st Edition
    • Volume 193
    • Slukvadze
    • English
  • Matrix Logic and Mind

    A Probe into a Unified Theory of Mind and Matter
    • 1st Edition
    • A. Stern
    • English
    In this revolutionary work, the author sets the stage for the science ofthe 21st Century, pursuing an unprecedented synthesis of fields previouslyconsidered unrelated. Beginning with simple classical concepts, he endswith a complex multidisciplinary theory requiring a high level ofabstraction. The work progresses across the sciences in severalmultidiscipli... directions: Mathematical logic, fundamental physics,computer science and the theory of intelligence. Extraordinarily enough,the author breaks new ground in all these fields.In the field offundamental physics the author reaches the revolutionary conclusion thatphysics can be viewed and studied as logic in a fundamental sense, ascompared with Einstein's view of physics as space-time geometry. This opensnew, exciting prospects for the study of fundamental interactions. Aformulation of logic in terms of matrix operators and logic vector spacesallows the author to tackle for the first time the intractable problem ofcognition in a scientific manner. In the same way as the findings ofHeisenberg and Dirac in the 1930s provided a conceptual and mathematicalfoundati... for quantum physics, matrix operator logic supports an importantbreakthroug... in the study of the physics of the mind, which is interpretedas a fractal of quantum mechanics. Introducing a concept of logic quantumnumbers, the author concludes that the problem of logic and theintelligence code in general can be effectively formulated as eigenvalueproblems similar to those of theoretical physics. With this important leapforward in the study of the mechanism of mind, the author concludes thatthe latter cannot be fully understood either within classical or quantumnotions. A higher-order covariant theory is required to accommodate thefundamental effect of high-level intelligence. The landmark resultsobtained by the author will have implications and repercussions for thevery foundations of science as a whole. Moreover, Stern's Matrix Logic issuitable for a broad spectrum of practical applications in contemporarytechnolo...
  • Classical Recursion Theory

    The Theory of Functions and Sets of Natural Numbers
    • 1st Edition
    • Volume 125
    • P. Odifreddi
    • English
    1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles.Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
  • Nonlinear Equations in the Applied Sciences

    • 1st Edition
    • Volume 185
    • W. F. Ames
    • English
  • Decentralized Control of Complex Systems

    • 1st Edition
    • Volume 184
    • S?iljak
    • English
  • Formal Models and Semantics

    • 1st Edition
    • Volume B
    • Bozzano G Luisa
    • English
    The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing.
  • Matrix Perturbation Theory

    • 1st Edition
    • G. W. Stewart + 1 more
    • English
    This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.
  • Model Theory

    • 3rd Edition
    • Volume 73
    • C.C. Chang + 1 more
    • English
    Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
  • Nonlinear Boundary Value Problems in Science and Engineering

    • 1st Edition
    • Volume 183
    • C. Rogers + 1 more
    • English
    Overall, our object has been to provide an applications-oriente... text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.
  • Computability, Complexity, Logic

    • 1st Edition
    • Volume 128
    • E. Börger
    • English
    The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems.The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory.It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.
  • Linear Dynamical Systems

    • 1st Edition
    • Volume 135
    • Casti
    • English
  • Nonlinear System Theory

    • 1st Edition
    • Volume 175
    • Casti
    • English
  • Topics in the Theory of Computation

    • 1st Edition
    • Volume 24
    • M. Karpinski + 1 more
    • English
    This volume contains nine selected papers presented at the Borgholm conference. They were chosen on the basis of their immediate relevance to the most fundamental aspects of the theory of computation and the newest developments in this area.These papers, which have been extended and refereed, fall into eight categories: 1. Constructive Mathematics in Models of Computation and Programming; 2. Abstract Calculi and Denotational Semantics; 3. Theory of Machines, Computations and Languages; 4. Nondeterminism, Concurrency and Distributed Computing; 5. Abstract Algebras, Logics and Combinatorics in Computation Theory; 6. General Computability and Decidability; 7. Computational and Arithmetic Complexity; 8. Analysis of Algorithms and Feasible Computing.
  • Decision and Control in Uncertain Resource Systems

    • 1st Edition
    • Volume 172
    • Mangel
    • English
  • Bilinear Transformation Method

    • 1st Edition
    • Volume 174
    • Matsuno
    • English
  • Computational Methods for Optimizing Distributed Systems

    • 1st Edition
    • Volume 173
    • Charles Teo
    • English
    Optimal control theory of distributed parameter systems has been a very active field in recent years; however, very few books have been devoted to the studiy of computational algorithms for solving optimal control problems. For this rason the authors decided to write this book. Because the area is so broad, they confined themselves to optimal control problems involving first and second boundary-value problems of a linear second-order parabolic partial differential equation. However the techniques used are by no means restricted to these problems. They can be and in some cases already have been applied to problems involving other types of distributed parameter system. The authors aim is to devise computational algorithms for solving optimal control problems with particular emphasis on the mathematical theory underlying the algorithms. These algorithms are obtained by using a first-order strong variational method or gradient-type methods.
  • Generalized Functions: Theory and Technique

    • 1st Edition
    • Volume 171
    • Kanwal
    • English
  • Volterra Integral and Differential Equations

    • 1st Edition
    • Volume 167
    • Burton
    • English
  • Stochastic Systems

    • 1st Edition
    • Volume 169
    • Adomian
    • English
  • The Stability of Input-Output Dynamical Systems

    • 1st Edition
    • Volume 168
    • Harris
    • English