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Discrete Mathematics, Probability Theory and Stochastic Processes: For Applications in Engineering and Computer Science (Modeling and Optimization in Science and Technologies #20)
by Samir Brahim Belhaouari Halima Bensmail Farshid MehrdoustThis book provides a comprehensive overview of discrete mathematics, probability theory, and stochastic processes, covering a wide range of topics in each area. It is designed to be a self-contained resource for students and professionals wishing to improve their understanding of these important mathematical concepts. The book takes a practical approach to the subject matter, providing real-world examples and applications to help readers understand how these mathematical concepts are used in various fields, such as computer science, engineering, and finance.
Discrete Mathematics: A Concise Introduction (Synthesis Lectures on Mathematics & Statistics)
by George TourlakisThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics.
Discrete Mathematics: An Open Introduction (Discrete Mathematics and Its Applications)
by Oscar LevinDiscrete Mathematics: An Open Introduction, Fourth Edition aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors, especially those who intend to teach middle and high school mathematics. The book began as a set of notes for the Discrete Mathematics course at the University of Northern Colorado. This course serves both as a survey of the topics in discrete math and as the “bridge” course for math majors. Features Uses problem-oriented and inquiry-based methods to teach the concepts. Suitable for undergraduates in mathematics and computer science. New to the 4th edition Large scale restructuring. Contains more than 750 exercises and examples. New sections on probability, relations, and discrete structures and their proofs.
Discrete Mathematics: Graph Algorithms, Algebraic Structures, Coding Theory, and Cryptography
by R. Balakrishnan Sriraman SridharanConveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also toindividuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm (AKS Algorithm) for testing if a givenpositive integer is prime or not in polynomial time is presented- the first time in a textbook. Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given.
Discrete Mathematics: Proofs, Structures and Applications, Third Edition
by John Taylor Rowan GarnierTaking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow prog
Discrete Mechanics, Geometric Integration and Lie–Butcher Series: Dmgilbs, Madrid, May 2015 (Springer Proceedings in Mathematics & Statistics #267)
by Kurusch Ebrahimi-Fard María Barbero LiñánThis volume resulted from presentations given at the international “Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie–Butcher Series”, that took place at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. It combines overview and research articles on recent and ongoing developments, as well as new research directions. Why geometric numerical integration? In their article of the same title Arieh Iserles and Reinout Quispel, two renowned experts in numerical analysis of differential equations, provide a compelling answer to this question. After this introductory chapter a collection of high-quality research articles aim at exploring recent and ongoing developments, as well as new research directions in the areas of geometric integration methods for differential equations, nonlinear systems interconnections, and discrete mechanics. One of the highlights is the unfolding of modern algebraic and combinatorial structures common to those topics, which give rise to fruitful interactions between theoretical as well as applied and computational perspectives. The volume is aimed at researchers and graduate students interested in theoretical and computational problems in geometric integration theory, nonlinear control theory, and discrete mechanics.
Discrete Mechanics: Concepts and Applications (Iste Ser.)
by Jean-Paul CaltagironeThe discrete vision of mechanics is based on the founding ideas of Galileo and the principles of relativity and equivalence, which postulate the equality between gravitational mass and inertial mass. To these principles are added the Hodge–Helmholtz decomposition, the principle of accumulation of constraints and the hypothesis of the duality of physical actions. These principles make it possible to establish the equation of motion based on the conservation of acceleration considered as an absolute quantity in a local frame of reference, in the form of a sum of the gradient of the scalar potential and the curl of the vector potential. These potentials, which represent the constraints of compression and rotation, are updated from the discrete operators. Discrete Mechanics: Concepts and Applications shows that this equation of discrete motion is representative of the compressible or incompressible flows of viscous or perfect fluids, the state of stress in an elastic solid or complex fluid and the propagation of nonlinear waves.
Discrete Optimization and Operations Research
by Panos Pardalos Yury Kochetov Michael Khachay Vladimir Beresnev Evgeni NurminskiThis book constitutes the proceedings of the 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, held in Vladivostok, Russia, in September 2016. The 39 full papers presented in this volume were carefully reviewed and selected from 181 submissions. They were organized in topical sections named: discrete optimization; scheduling problems; facility location; mathematical programming; mathematical economics and games; applications of operational research; and short communications.
Discrete Optimization in Architecture
by Machi ZawidzkiThis book is comprised of two parts, both of which exploremodular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents severalmethods of creating PZ and TZ structures subjected to discrete optimization. The algorithms presented employ graph-theoretic and heuristic methods. Theunderlying idea of both systems is to create free-form structures using theminimal number of types of modular elements. PZ is more conceptual, as it formssingle-branch mathematical knots with a single type of module. Conversely, TZis a skeletal system for creating free-form pedestrian ramps and ramp networksamong any number of terminals in space. In physical space, TZ uses two types ofmodules that are mirror reflections of each other. The optimization criteriadiscussed include: the minimal number of units, maximal adherence to the givenguide paths, etc.
Discrete Optimization in Architecture
by Machi ZawidzkiThis book is comprised of two parts, both of which exploremodular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents severalmethods of creating PZ and TZ structures subjected to discrete optimization. The algorithms presented employ graph-theoretic and heuristic methods. Theunderlying idea of both systems is to create free-form structures using theminimal number of types of modular elements. PZ is more conceptual, as it formssingle-branch mathematical knots with a single type of module. Conversely, TZis a skeletal system for creating free-form pedestrian ramps and ramp networksamong any number of terminals in space. In physical space, TZ uses two types ofmodules that are mirror reflections of each other. The optimization criteriadiscussed include: the minimal number of units, maximal adherence to the givenguide paths, etc.
Discrete Problems in Nature Inspired Algorithms
by Ritu Tiwari Anupam ShuklaThis book includes introduction of several algorithms which are exclusively for graph based problems, namely combinatorial optimization problems, path formation problems, etc. Each chapter includes the introduction of the basic traditional nature inspired algorithm and discussion of the modified version for discrete algorithms including problems pertaining to discussed algorithms.
Discrete Simulation and Animation for Mining Engineers
by John SturgulGeneral Purpose Simulation System (GPSS) is a special computer programming language primarily used to simulate what can be classified as discrete systems. A discrete system is one where, at any given instant in time, a countable number of things can take place. The basic operation of a mine itself can be considered such a system. Discrete Simulatio
Discrete Stochastic Models and Applications for Reliability Engineering and Statistical Quality Control
by Serkan EryilmazDiscrete stochastic models are tools that allow us to understand, control, and optimize engineering systems and processes. This book provides real-life examples and illustrations of models in reliability engineering and statistical quality control and establishes a connection between the theoretical framework and their engineering applications. The book describes discrete stochastic models along with real-life examples and explores not only well-known models, but also comparatively lesser known ones. It includes definitions, concepts, and methods with a clear understanding of their use in reliability engineering and statistical quality control fields. Also covered are the recent advances and established connections between the theoretical framework of discrete stochastic models and their engineering applications. An ideal reference for researchers in academia and graduate students working in the fields of operations research, reliability engineering, quality control, and probability and statistics.
Discrete Stochastic Processes and Applications
by Jean-François ColletThis unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
Discrete Stochastic Processes: Tools for Machine Learning and Data Science (Springer Undergraduate Mathematics Series)
by Nicolas PrivaultThis text presents selected applications of discrete-time stochastic processes that involve random interactions and algorithms, and revolve around the Markov property. It covers recurrence properties of (excited) random walks, convergence and mixing of Markov chains, distribution modeling using phase-type distributions, applications to search engines and probabilistic automata, and an introduction to the Ising model used in statistical physics. Applications to data science are also considered via hidden Markov models and Markov decision processes. A total of 32 exercises and 17 longer problems are provided with detailed solutions and cover various topics of interest, including statistical learning.
Discrete Structures (Undergraduate Texts in Mathematics)
by Andreas Klappenecker Hyunyoung LeeThe aim of this text is to introduce discrete mathematics to beginning students of mathematics or computer science. It does this by bringing some coherency into the seemingly incongruent subjects that compose discrete math, such as logic, set theory, algebra, and combinatorics. It emphasizes their theoretical foundations and illustrates proofs along the way. The book prepares readers for the analysis of algorithms by discussing asymptotic analysis and a discrete calculus for sums. The book also deduces combinatorial methods from the foundations that are laid out. Unlike other texts on this subject, there is a greater emphasis on foundational material that leads to a better understanding. To further assist the reader in grasping and practicing concepts, roughly 690 exercises are provided at various levels of difficulty. Readers are encouraged to study the examples in the text and solve as many of the exercises as possible. The text is intended for freshman or sophomore undergraduate students in mathematics, computer science, or similar majors. The assumed background is precalculus. The chapter dependency chart included is designed to help students, independent readers, and instructors follow a systematic path for learning and teaching the material, with the option to explore material in later chapters.
Discrete Structures and Their Interactions
by Jason I. BrownDiscover the Connections between Different Structures and FieldsDiscrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics,
Discrete Systems And Integrability
by J. Hietarinta N. Joshi F. W. NijhoffThis first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.
Discrete Taylor Transform and Inverse Transform
by Alireza Baghai-WadjiRevolutionize the calculation of mixed derivatives with this groundbreaking text Transform and inverse transform techniques, such as the Fourier transform and the Laplace transform, enable scientists and engineers to conduct research and design in transformed domains where the work is simpler, after which the results can be converted back into the real domain where they can be applied or actualized. This latter stage in the process, the inverse transform, ordinarily poses significant challenges. New transform/inverse transform techniques carry extraordinary potential to produce revolutionary new science and engineering solutions. Discrete Taylor Transform and Inverse Transform presents the groundbreaking discovery of a new transform technique. Placing a novel emphasis on the “position variable” and “derivative operator” as main actors, the Discrete Taylor Transform and Inverse Transform (D-TTIT) will facilitate the calculation of mixed derivatives of multivariate functions to any desired order. The result promises to create new applications not only in its allied fields of quantum physics and quantum engineering, but potentially much more widely. Readers will also find: Discussion of possible applications in electrical engineering, acoustics, photonics, and many more Analysis of functions depending on one, two, or three independent variables Tools for theoreticians and practitioners to design their own algorithms for solving specific boundary-value problems Discrete Taylor Transform and Inverse Transform is ideal for any scientific or engineering professional looking to understand a cutting-edge research and design tool.
Discrete Time Branching Processes in Random Environment
by Götz Kersting Vladimir VatutinBranching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Discrete Variational Derivative Method: A Structure-Preserving Numerical Method for Partial Differential Equations (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series)
by Daisuke Furihata Takayasu MatsuoNonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving num
Discrete Wavelet Transformations: An Elementary Approach with Applications
by Patrick J. Van FleetUpdated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet’s highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field. Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: Two new chapters covering wavelet packets and the lifting method A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques A new comprehensive chapter that explains filter derivation using Fourier techniques Over 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges.
Discrete and Algebraic Structures: A Concise Introduction (Mathematics Study Resources #18)
by Ulrich Knauer Kolja KnauerThis textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation. Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly. Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists. Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids. This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation.
Discrete and Computational Geometry
by Joseph O'Rourke Satyan L. DevadossAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems.The essential introduction to discrete and computational geometryCovers traditional topics as well as new and advanced materialFeatures numerous full-color illustrations, exercises, and unsolved problemsSuitable for sophomores in mathematics, computer science, engineering, or physicsRigorous but accessibleAn online solutions manual is available (for teachers only).
Discrete and Computational Geometry and Graphs
by Jin Akiyama Hiro Ito Toshinori SakaiThis book constitutes the thoroughly refereed post-conference proceedings of the 16th Japanese Conference on Discrete and computational Geometry and Graphs, JDCDGG 2013, held in Tokyo, Japan, in September 2013. The total of 16 papers included in this volume was carefully reviewed and selected from 58 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.