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Books > Computing & IT > General theory of computing > Mathematical theory of computation
R for College Mathematics and Statistics encourages the use of R in mathematics and statistics courses. Instructors are no longer limited to ``nice'' functions in calculus classes. They can require reports and homework with graphs. They can do simulations and experiments. R can be useful for student projects, for creating graphics for teaching, as well as for scholarly work. This book presents ways R, which is freely available, can enhance the teaching of mathematics and statistics. R has the potential to help students learn mathematics due to the need for precision, understanding of symbols and functions, and the logical nature of code. Moreover, the text provides students the opportunity for experimenting with concepts in any mathematics course. Features: Does not require previous experience with R Promotes the use of R in typical mathematics and statistics course work Organized by mathematics topics Utilizes an example-based approach Chapters are largely independent of each other
Taking an interdisciplinary approach, this new book provides a modern introduction to scientific computing, exploring numerical methods, computer technology, and their interconnections, which are treated with the goal of facilitating scientific research across all disciplines. Each chapter provides an insightful lesson and viewpoints from several subject areas are often compounded within a single chapter. Written with an eye on usefulness, longevity, and breadth, Lessons in Scientific Computing will serve as a "one stop shop" for students taking a unified course in scientific computing, or seeking a single cohesive text spanning multiple courses. Features: Provides a unique combination of numerical analysis, computer programming, and computer hardware in a single text Includes essential topics such as numerical methods, approximation theory, parallel computing, algorithms, and examples of computational discoveries in science Not wedded to a specific programming language
Do big math on small machines Write fast and accurate library functions Master analytical and numerical calculus Perform numerical integration to any order Implement z-transform formulas Need to learn the ins and outs of the fundamental math functions in
Although there are hundreds of books about MATLAB, there are no books that fully explore its value in the field of business economics. Few books describe how geographic information can be explicitly incorporated in business decisions, or explain how sophisticated MATLAB applications can be provided to users via the Internet using a remote-hosted, thin client environment.
More than ever before, complicated mathematical procedures are integral to the success and advancement of technology, engineering, and even industrial production. Knowledge of and experience with these procedures is therefore vital to present and future scientists, engineers and technologists.
Among the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science.
This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future.
Rapid developments in the field of genetic algorithms along with the popularity of the first edition precipitated this completely revised, thoroughly updated second edition of The Practical Handbook of Genetic Algorithms. Like its predecessor, this edition helps practitioners stay up to date on recent developments in the field and provides material they can use productively in their own endeavors.
Transfer function form, zpk, state space, modal, and state space modal forms. For someone learning dynamics for the first time or for engineers who use the tools infrequently, the options available for constructing and representing dynamic mechanical models can be daunting. It is important to find a way to put them all in perspective and have them available for quick reference.
In this book, the development of the English dictionary is examined, along with the kinds of dictionary available, the range of information they contain, factors affecting their usage, and public attitudes towards them. As well as an descriptive analysis of word meaning, the author considers whether a thematic, thesaurus-like presentation might be more suited than the traditional alphabetical format to the description of words and their meaning.
Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.
This text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendices that provide more background on some of the more abstract concepts.
This book introduces an important group of logics that have come to
be known under the umbrella term 'susbstructural'. Substructural
logics have independently led to significant developments in
philosophy, computing and linguistics. An Introduction to
Substrucural Logics is the first book to systematically survey the
new results and the significant impact that this class of logics
has had on a wide range of fields.The following topics are covered:
Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.
Although the computing facilities available to scientists are becoming more powerful, the problems they are addressing are increasingly complex. The mathematical methods for simplifying the computing procedures are therefore as important as ever. Microcomputer Algorithms: Action from Algebra stresses the mathematical basis behind the use of many algorithms of computational mathematics, providing detailed descriptions on how to generate algorithms for a large number of different uses. Covering a wide range of mathematical and physical applications, the book contains the theory of 25 algorithms. The mathematical theory for each algorithm is described in detail prior to discussing the algorithm in full, with complete program listings. The book presents the algorithms in modular form, allowing for easy interpretation, for the adaptation to readers' specific requirements without difficulty, and for use with various microcomputers. Blending mathematics and programming in one volume, this book will be of broad interest to all scientists and engineers, particularly those physicists using microcomputers for scientific problem handling. Students handling numerical data for research projects will also find the book useful.
This book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.This book presents the latest developments in the highly active and rapidly growing field of diffusion MRI. While offering new perspectives on the most recent research challenges in the field, the selected articles also provide a valuable starting point for anyone interested in learning computational techniques for diffusion MRI. The book includes rigorous mathematical derivations, a large number of rich, full-colour visualizations, and clinically relevant results. As such, it is of interest to researchers and practitioners in the fields of computer science, MRI physics, and applied mathematics. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice.
Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences.
Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises. The authors present the core principles of modern cryptography, with emphasis on formal definitions, rigorous proofs of security.
This unique reference presents in-depth coverage of the latest methods and applications of digital image processing describing various computer architectures ideal for satisfying specific image processing demands.
Computational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each including a complete analysis of a computer code written in transportable Fortran 77. Each example also includes a discussion of the problem equations, the coding of the equations, and the computed numerical solution. The benefits of using quality general-purpose library routines to solve ODE/DAE/PDE problems are illustrated as well.
Taking a highly pragmatic approach to presenting the principles and applications of chemical engineering, this companion text for students and working professionals offers an easily accessible guide to solving problems using computers. The primer covers the core concepts of chemical engineering, from conservation laws all the way up to chemical kinetics, without heavy stress on theory and is designed to accompany traditional larger core texts. The book presents the basic principles and techniques of chemical engineering processes and helps readers identify typical problems and how to solve them. Focus is on the use of systematic algorithms that employ numerical methods to solve different chemical engineering problems by describing and transforming the information. Problems are assigned for each chapter, ranging from simple to difficult, allowing readers to gradually build their skills and tackle a broad range of problems. MATLAB and Excel (R) are used to solve many examples and the more than 70 real examples throughout the book include computer or hand solutions, or in many cases both. The book also includes a variety of case studies to illustrate the concepts and a downloadable file containing fully worked solutions to the book's problems on the publisher's website. Introduces the reader to chemical engineering computation without the distractions caused by the contents found in many texts. Provides the principles underlying all of the major processes a chemical engineer may encounter as well as offers insight into their analysis, which is essential for design calculations. Shows how to solve chemical engineering problems using computers that require numerical methods using standard algorithms, such as MATLAB (R) and Excel (R). Contains selective solved examples of many problems within the chemical process industry to demonstrate how to solve them using the techniques presented in the text. Includes a variety of case studies to illustrate the concepts and a downloadable file containing fully worked solutions to problems on the publisher's website. Offers non-chemical engineers who are expected to work with chemical engineers on projects, scale-ups and process evaluations a solid understanding of basic concepts of chemical engineering analysis, design, and calculations.
Fast Solvers for Mesh-Based Computations presents an alternative way of constructing multi-frontal direct solver algorithms for mesh-based computations. It also describes how to design and implement those algorithms. The book's structure follows those of the matrices, starting from tri-diagonal matrices resulting from one-dimensional mesh-based methods, through multi-diagonal or block-diagonal matrices, and ending with general sparse matrices. Each chapter explains how to design and implement a parallel sparse direct solver specific for a particular structure of the matrix. All the solvers presented are either designed from scratch or based on previously designed and implemented solvers. Each chapter also derives the complete JAVA or Fortran code of the parallel sparse direct solver. The exemplary JAVA codes can be used as reference for designing parallel direct solvers in more efficient languages for specific architectures of parallel machines. The author also derives exemplary element frontal matrices for different one-, two-, or three-dimensional mesh-based computations. These matrices can be used as references for testing the developed parallel direct solvers. Based on more than 10 years of the author's experience in the area, this book is a valuable resource for researchers and graduate students who would like to learn how to design and implement parallel direct solvers for mesh-based computations.
The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called "FuzzySTs" which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods. |
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