Coding The Matrix Linear Algebra Through Applications To Computer Science

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Author : Philip N. Klein
ISBN : 061585673X
Genre : Algebras, Linear
File Size : 61.82 MB
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An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Author : Philip N. Klein
ISBN : 0615880991
Genre : Mathematics
File Size : 79.70 MB
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An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program

Author : Thomas W. Miller
ISBN : 9780133892147
Genre : Computers
File Size : 59.98 MB
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Master predictive analytics, from start to finish Start with strategy and management Master methods and build models Transform your models into highly-effective code—in both Python and R This one-of-a-kind book will help you use predictive analytics, Python, and R to solve real business problems and drive real competitive advantage. You’ll master predictive analytics through realistic case studies, intuitive data visualizations, and up-to-date code for both Python and R—not complex math. Step by step, you’ll walk through defining problems, identifying data, crafting and optimizing models, writing effective Python and R code, interpreting results, and more. Each chapter focuses on one of today’s key applications for predictive analytics, delivering skills and knowledge to put models to work—and maximize their value. Thomas W. Miller, leader of Northwestern University’s pioneering program in predictive analytics, addresses everything you need to succeed: strategy and management, methods and models, and technology and code. If you’re new to predictive analytics, you’ll gain a strong foundation for achieving accurate, actionable results. If you’re already working in the field, you’ll master powerful new skills. If you’re familiar with either Python or R, you’ll discover how these languages complement each other, enabling you to do even more. All data sets, extensive Python and R code, and additional examples available for download at http://www.ftpress.com/miller/ Python and R offer immense power in predictive analytics, data science, and big data. This book will help you leverage that power to solve real business problems, and drive real competitive advantage. Thomas W. Miller’s unique balanced approach combines business context and quantitative tools, illuminating each technique with carefully explained code for the latest versions of Python and R. If you’re new to predictive analytics, Miller gives you a strong foundation for achieving accurate, actionable results. If you’re already a modeler, programmer, or manager, you’ll learn crucial skills you don’t already have. Using Python and R, Miller addresses multiple business challenges, including segmentation, brand positioning, product choice modeling, pricing research, finance, sports, text analytics, sentiment analysis, and social network analysis. He illuminates the use of cross-sectional data, time series, spatial, and spatio-temporal data. You’ll learn why each problem matters, what data are relevant, and how to explore the data you’ve identified. Miller guides you through conceptually modeling each data set with words and figures; and then modeling it again with realistic code that delivers actionable insights. You’ll walk through model construction, explanatory variable subset selection, and validation, mastering best practices for improving out-of-sample predictive performance. Miller employs data visualization and statistical graphics to help you explore data, present models, and evaluate performance. Appendices include five complete case studies, and a detailed primer on modern data science methods. Use Python and R to gain powerful, actionable, profitable insights about: Advertising and promotion Consumer preference and choice Market baskets and related purchases Economic forecasting Operations management Unstructured text and language Customer sentiment Brand and price Sports team performance And much more

Author : Ernest Davis
ISBN : 9781466501553
Genre : Mathematics
File Size : 52.60 MB
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Based on the author’s course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB® functions and features and give sample assignments in MATLAB; the author’s website provides the MATLAB code from the book. After an introductory chapter on MATLAB, the text is divided into two sections. The section on linear algebra gives an introduction to the theory of vectors, matrices, and linear transformations over the reals. It includes an extensive discussion on Gaussian elimination, geometric applications, and change of basis. It also introduces the issues of numerical stability and round-off error, the discrete Fourier transform, and singular value decomposition. The section on probability presents an introduction to the basic theory of probability and numerical random variables; later chapters discuss Markov models, Monte Carlo methods, information theory, and basic statistical techniques. The focus throughout is on topics and examples that are particularly relevant to computer science applications; for example, there is an extensive discussion on the use of hidden Markov models for tagging text and a discussion of the Zipf (inverse power law) distribution. Examples and Programming Assignments The examples and programming assignments focus on computer science applications. The applications covered are drawn from a range of computer science areas, including computer graphics, computer vision, robotics, natural language processing, web search, machine learning, statistical analysis, game playing, graph theory, scientific computing, decision theory, coding, cryptography, network analysis, data compression, and signal processing. Homework Problems Comprehensive problem sections include traditional calculation exercises, thought problems such as proofs, and programming assignments that involve creating MATLAB functions.

Author : Doyub Kim
ISBN : 9781498719933
Genre : Computers
File Size : 31.1 MB
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From the splash of breaking waves to turbulent swirling smoke, the mathematical dynamics of fluids are varied and continue to be one of the most challenging aspects in animation. Fluid Engine Development demonstrates how to create a working fluid engine through the use of particles and grids, and even a combination of the two. Core algorithms are explained from a developer’s perspective in a practical, approachable way that will not overwhelm readers. The Code Repository offers further opportunity for growth and discussion with continuously changing content and source codes. This book helps to serve as the ultimate guide to navigating complex fluid animation and development.

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl

Author : Igor Shparlinski
ISBN : 9789401592390
Genre : Mathematics
File Size : 32.91 MB
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This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

Author : Lars Garding
ISBN : 9781461387978
Genre : Mathematics
File Size : 83.1 MB
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The aim of this book is to teach the reader the topics in algebra which are useful in the study of computer science. In a clear, concise style, the author present the basic algebraic structures, and their applications to such topics as the finite Fourier transform, coding, complexity, and automata theory. The book can also be read profitably as a course in applied algebra for mathematics students.

Author : Narsingh Deo
ISBN : 9780486820811
Genre : Mathematics
File Size : 31.24 MB
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Outstanding introductory treatment, geared toward advanced undergraduates and graduate students who require knowledge of graph theory. The first nine chapters constitute an excellent overview; the remaining chapters are more advanced and provide material for a variety of courses. 1974 edition.

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Author : C Ding
ISBN : 9789814498364
Genre : Computers
File Size : 71.61 MB
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Chinese Remainder Theorem, CRT, is one of the jewels of mathematics. It is a perfect combination of beauty and utility or, in the words of Horace, omne tulit punctum qui miscuit utile dulci. Known already for ages, CRT continues to present itself in new contexts and open vistas for new types of applications. So far, its usefulness has been obvious within the realm of “three C's”. Computing was its original field of application, and continues to be important as regards various aspects of algorithmics and modular computations. Theory of codes and cryptography are two more recent fields of application. This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications. The book is self-contained. This means that no factual knowledge is assumed on the part of the reader. We even provide brief tutorials on relevant subjects, algebra and information theory. However, some mathematical maturity is surely a prerequisite, as our presentation is at an advanced undergraduate or beginning graduate level. We have tried to make the exposition innovative, many of the individual results being new. We will return to this matter, as well as to the interdependence of the various parts of the book, at the end of the Introduction. A special course about CRT can be based on the book. The individual chapters are largely independent and, consequently, the book can be used as supplementary material for courses in algorithmics, coding theory, cryptography or theory of computing. Of course, the book is also a reference for matters dealing with CRT. Contents:Introduction and PhilosophyChinese Remainder AlgorithmIn Modular ComputationsIn AlgorithmicsIn Bridging ComputationsIn Coding TheoryIn CryptographyTutorial in Information TheoryTutorial in AlgebraList of Mathematical SymbolsBibliography Readership: Postgraduate students, researchers and scientists of theoretical foundations of computer science, numerical and computational methods. keywords: “It is a good book about the basic principles of trellis decoding for block codes, existing open problems, some recent solutions, and different applications of this technique.” Computing Reviews

Author : Andrew Butterfield
ISBN : 9780199688975
Genre :
File Size : 59.71 MB
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Previously named A Dictionary of Computing, this bestselling dictionary has been renamed A Dictionary of Computer Science, and fully revised by a team of computer specialists, making it the most up-to-date and authoritative guide to computing available. Containing over 6,500 entries and with expanded coverage of multimedia, computer applications, networking, and personal computer science, it is a comprehensive reference work encompassing all aspects of the subject and is as valuable for home and office users as it is indispensable for students of computer science. Terms are defined in a jargon-free and concise manner with helpful examples where relevant. The dictionary contains approximately 150 new entries including cloud computing, cross-site scripting, iPad, semantic attack, smartphone, and virtual learning environment. Recommended web links for many entries, accessible via the Dictionary of Computer Science companion website, provide valuable further information and the appendices include useful resources such as generic domain names, file extensions, and the Greek alphabet. This dictionary is suitable for anyone who uses computers, and is ideal for students of computer science and the related fields of IT, maths, physics, media communications, electronic engineering, and natural sciences.

Author : H. E. Rose
ISBN : 3764369051
Genre : Mathematics
File Size : 43.53 MB
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This text gives an introduction to linear algebra, developing and proving its fundamental properties and theorems taking a pure mathematical approach. It includes examples, exercises and problems, some of which are theoretical and some numerical. Answers and/or sketch solutions are given.

Author : Ilias S. Kotsireas
ISBN : 9783319569321
Genre : Mathematics
File Size : 70.68 MB
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The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

Author : James B. Carrell
ISBN : 9780387794280
Genre : Mathematics
File Size : 48.78 MB
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This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Author : Richard Szeliski
ISBN : 1848829353
Genre : Computers
File Size : 27.50 MB
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Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.