Discrete

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Discrete Mathematics

Oscar Levin
Discrete Mathematics Book PDF

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 48,6 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Discrete Systems and Digital Signal Processing with MATLAB

Taan S. ElAli,Taan ElAli
Discrete Systems and Digital Signal Processing with MATLAB Book PDF

Author : Taan S. ElAli,Taan ElAli
Publisher : CRC Press
Page : 688 pages
File Size : 42,7 Mb
Release : 2003-09-29
Category : Technology & Engineering
ISBN : 9780203487112

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Discrete Systems and Digital Signal Processing with MATLAB by Taan S. ElAli,Taan ElAli Pdf

Books on linear systems typically cover both discrete and continuous systems together in one book. However, with coverage of this magnitude, not enough information is presented on either of the two subjects. Discrete linear systems warrant a book of their own, and Discrete Systems and Digital Signal Processing with MATLAB provides just that. It offers comprehensive coverage of both discrete linear systems and signal processing in one volume. This detailed book is firmly rooted in basic mathematical principles, and it includes many problems solved first by using analytical tools, then by using MATLAB. Examples that illustrate the theoretical concepts are provided at the end of each chapter.

Integral and Discrete Transforms with Applications and Error Analysis

Abdul Jerri
Integral and Discrete Transforms with Applications and Error Analysis Book PDF

Author : Abdul Jerri
Publisher : CRC Press
Page : 852 pages
File Size : 45,7 Mb
Release : 1992-06-11
Category : Mathematics
ISBN : 0824782526

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Integral and Discrete Transforms with Applications and Error Analysis by Abdul Jerri Pdf

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Resources for Teaching Discrete Mathematics

Brian Hopkins
Resources for Teaching Discrete Mathematics Book PDF

Author : Brian Hopkins
Publisher : MAA
Page : 342 pages
File Size : 53,7 Mb
Release : 2009
Category : Computers
ISBN : 0883851849

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Resources for Teaching Discrete Mathematics by Brian Hopkins Pdf

Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.

Applied Discrete Structures

K. D. Joshi
Applied Discrete Structures Book PDF

Author : K. D. Joshi
Publisher : New Age International
Page : 966 pages
File Size : 52,5 Mb
Release : 1997
Category : Computer science
ISBN : 8122408265

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Applied Discrete Structures by K. D. Joshi Pdf

Although This Book Is Intended As A Sequel To Foundations Of Discrete Mathematics By The Same Author, It Can Be Read Independently Of The Latter, As The Relevant Background Needed Has Been Reviewed In Chapter 1. The Subsequent Chapters Deal With Graph Theory (With Applications), Analysis Of Algorithms (With A Detailed Study Of A Few Sorting Algorithms And A Discussion Of Tractability), Linear Programming (With Applications, Variations, Karmarkars Polynomial Time Algorithm, Integer And Quadratic Programming), Applications Of Algebra (To Polyas Theory Of Counting, Galois Theory, Coding Theory Of Designs). A Chapter On Matroids Familiarises The Reader With This Relatively New Branch Of Discrete Mathematics.Even Though Some Of The Topics Are Relatively Advanced, An Attempt Has Been Made To Keep The Style Elementary, So That A Sincere Student Can Read The Book On His Own. A Large Number Of Comments, Exercises, And References Is Included To Broaden The Readers Scope Of Vision. A Detailed Index Is Provided For Easy Reference.

Singular Integral Equations and Discrete Vortices

Ivan K. Lifanov
Singular Integral Equations and Discrete Vortices Book PDF

Author : Ivan K. Lifanov
Publisher : VSP
Page : 494 pages
File Size : 51,6 Mb
Release : 1996
Category : Mathematics
ISBN : 906764207X

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Singular Integral Equations and Discrete Vortices by Ivan K. Lifanov Pdf

This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Continuous Symmetries and Integrability of Discrete Equations

Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Continuous Symmetries and Integrability of Discrete Equations Book PDF

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 41,9 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Discrete Transforms

J.M. Firth
Discrete Transforms Book PDF

Author : J.M. Firth
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401123587

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Discrete Transforms by J.M. Firth Pdf

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree course in which transform techniques will have a significant application. In other disciplines the readership will be past the second year undergraduate stage. In either case, the text is also intended for earlier graduates whose degree courses did not include this type of material and who now find themselves, in a professional capacity, requiring a knowledge of discrete transform methods.

Discrete Analogues in Harmonic Analysis

Ben Krause
Discrete Analogues in Harmonic Analysis Book PDF

Author : Ben Krause
Publisher : American Mathematical Society
Page : 592 pages
File Size : 43,8 Mb
Release : 2023-01-19
Category : Mathematics
ISBN : 9781470468576

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Discrete Analogues in Harmonic Analysis by Ben Krause Pdf

This timely book explores certain modern topics and connections at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics. The main ideas were pioneered by Bourgain and Stein, motivated by questions involving averages over polynomial sequences, but the subject has grown significantly over the last 30 years, through the work of many researchers, and has steadily become one of the most dynamic areas of modern harmonic analysis. The author has succeeded admirably in choosing and presenting a large number of ideas in a mostly self-contained and exciting monograph that reflects his interesting personal perspective and expertise into these topics. —Alexandru Ionescu, Princeton University Discrete harmonic analysis is a rapidly developing field of mathematics that fuses together classical Fourier analysis, probability theory, ergodic theory, analytic number theory, and additive combinatorics in new and interesting ways. While one can find good treatments of each of these individual ingredients from other sources, to my knowledge this is the first text that treats the subject of discrete harmonic analysis holistically. The presentation is highly accessible and suitable for students with an introductory graduate knowledge of analysis, with many of the basic techniques explained first in simple contexts and with informal intuitions before being applied to more complicated problems; it will be a useful resource for practitioners in this field of all levels. —Terence Tao, University of California, Los Angeles

Discrete Geometry for Computer Imagery

Christophe Reutenauer
Discrete Geometry for Computer Imagery Book PDF

Author : Christophe Reutenauer
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 50,8 Mb
Release : 2009-09-11
Category : Computers
ISBN : 9783642043963

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Discrete Geometry for Computer Imagery by Christophe Reutenauer Pdf

This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.

Discrete-Time Sliding Mode Control for Networked Control System

Dipesh H. Shah,Axaykumar Mehta
Discrete Time Sliding Mode Control for Networked Control System Book PDF

Author : Dipesh H. Shah,Axaykumar Mehta
Publisher : Springer
Page : 157 pages
File Size : 51,9 Mb
Release : 2018-03-16
Category : Technology & Engineering
ISBN : 9789811075360

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Discrete-Time Sliding Mode Control for Networked Control System by Dipesh H. Shah,Axaykumar Mehta Pdf

This book presents novel algorithms for designing Discrete-Time Sliding Mode Controllers (DSMCs) for Networked Control Systems (NCSs) with both types of fractional delays namely deterministic delay and random delay along with different packet loss conditions such as single packet loss and multiple packet loss that occur within the sampling period. Firstly, the switching type and non-switching type algorithms developed for the deterministic type fractional delay where the delay is compensated using Thiran’s approximation technique. A modified discrete-time sliding surface is proposed to derive the discrete-time sliding mode control algorithms. The algorithm is further extended for the random fractional delay with single packet loss and multiple packet loss situations. The random fractional delay is modelled using Poisson’s distribution function and packet loss is modelled by means of Bernoulli’s function. The condition for closed loop stability in all above situations are derived using the Lyapunov function. Lastly, the efficacy of the proposed DSMC algorithms are demonstrated by extensive simulations and also experimentally validated on a servo system.

Modern Discrete Mathematics and Analysis

Nicholas J. Daras,Themistocles M. Rassias
Modern Discrete Mathematics and Analysis Book PDF

Author : Nicholas J. Daras,Themistocles M. Rassias
Publisher : Springer
Page : 521 pages
File Size : 51,9 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319743257

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Modern Discrete Mathematics and Analysis by Nicholas J. Daras,Themistocles M. Rassias Pdf

A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.

Quantitative Analysis and Optimal Control of Energy Efficiency in Discrete Manufacturing System

Yan Wang,Cheng-Lin Liu,Zhi-Cheng Ji
Quantitative Analysis and Optimal Control of Energy Efficiency in Discrete Manufacturing System Book PDF

Author : Yan Wang,Cheng-Lin Liu,Zhi-Cheng Ji
Publisher : Springer Nature
Page : 291 pages
File Size : 52,8 Mb
Release : 2020-06-01
Category : Science
ISBN : 9789811544620

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Quantitative Analysis and Optimal Control of Energy Efficiency in Discrete Manufacturing System by Yan Wang,Cheng-Lin Liu,Zhi-Cheng Ji Pdf

This book provides energy efficiency quantitative analysis and optimal methods for discrete manufacturing systems from the perspective of global optimization. In order to analyze and optimize energy efficiency for discrete manufacturing systems, it uses real-time access to energy consumption information and models of the energy consumption, and constructs an energy efficiency quantitative index system. Based on the rough set and analytic hierarchy process, it also proposes a principal component quantitative analysis and a combined energy efficiency quantitative analysis. In turn, the book addresses the design and development of quantitative analysis systems. To save energy consumption on the basis of energy efficiency analysis, it presents several optimal control strategies, including one for single-machine equipment, an integrated approach based on RWA-MOPSO, and one for production energy efficiency based on a teaching and learning optimal algorithm. Given its scope, the book offers a valuable guide for students, teachers, engineers and researchers in the field of discrete manufacturing systems.

Discrete Event Systems: Modeling and Control

S. Balemi,P. Kozák,R. Smedinga
Discrete Event Systems Modeling and Control Book PDF

Author : S. Balemi,P. Kozák,R. Smedinga
Publisher : Birkhäuser
Page : 224 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891202

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Discrete Event Systems: Modeling and Control by S. Balemi,P. Kozák,R. Smedinga Pdf

Research of discrete event systems is strongly motivated by applications in flex ible manufacturing, in traffic control and in concurrent and real-time software verification and design, just to mention a few important areas. Discrete event system theory is a promising and dynamically developing area of both control theory and computer science. Discrete event systems are systems with non-numerically-valued states, inputs, and outputs. The approaches to the modelling and control of these systems can be roughly divided into two groups. The first group is concerned with the automatic design of controllers from formal specifications of logical requirements. This re search owes much to the pioneering work of P.J. Ramadge and W.M. Wonham at the beginning of the eighties. The second group deals with the analysis and op timization of system throughput, waiting time, and other performance measures for discrete event systems. The present book contains selected papers presented at the Joint Workshop on Discrete Event Systems (WODES'92) held in Prague, Czechoslovakia, on Au gust 26-28, 1992 and organized by the Institute of Information Theory and Au tomation of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia, by the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH) , Zurich, Switzerland, and by the Department of Computing Science of the University of Groningen, Groningen, the Netherlands.

Approximate and Noisy Realization of Discrete-Time Dynamical Systems

Yasumichi Hasegawa
Approximate and Noisy Realization of Discrete Time Dynamical Systems Book PDF

Author : Yasumichi Hasegawa
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 47,6 Mb
Release : 2008-06-02
Category : Technology & Engineering
ISBN : 9783540794332

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Approximate and Noisy Realization of Discrete-Time Dynamical Systems by Yasumichi Hasegawa Pdf

This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in ?ltering theory and system theory. From noisy or noiseless data, reductionwillbemade.Anewmethodwhichreducesnoiseormodelsinformation will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the e?cacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the e?ectiveness of our method, many actual examples of noise and model information reduction will also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of technology after 1966 for emphasizing e?ciency in the ?elds of control, economy, numerical analysis, and others. Noise reduction problems in the analysis of noisy dynamical systems may havebecomeamajorthemeoftechnologyafter1974foremphasizinge?ciencyin control.However,thesubjectsoftheseresearcheshavebeenmainlyconcentrated in linear systems. In common model reduction of linear systems in use today, a singular value decompositionofaHankelmatrixisusedto?ndareducedordermodel.However, the existence of the conditions of the reduced order model are derived without evaluationoftheresultantmodel.Inthecommontypicalnoisereductionoflinear systems in use today, the order and parameters of the systems are determined by minimizing information criterion. Approximate and noisy realization problems for input/output relations can be roughly stated as follows: A. The approximate realization problem. For any input/output map, ?nd one mathematical model such that it is similar totheinput/outputmapandhasalowerdimensionthanthegivenminimalstate spaceofadynamicalsystemwhichhasthesamebehaviortotheinput/outputmap. B. The noisy realization problem.