- Table View
- List View
Numerals and Arithmetic in the Middle Ages (Variorum Collected Studies)
by Charles BurnettThis volume, the third by Charles Burnett in the Variorum series, brings together articles on the different numeral forms used in the Middle Ages, and their use in mathematical and other contexts. Some pieces study the introduction of Hindu-Arabic numerals into Western Europe, documenting, in more detail than anywhere else, the different forms in which they are found, before they acquired the standard shapes with which we are familiar today. Others deal with experiments with other forms of numeration within Latin script: e.g., using the first nine Roman numerals as symbols with place value, abbreviating the Roman numerals, and using the Latin letters as numerals. The author discusses how different types of numerals are used for different purposes, and the application of numerals to the abacus, and to calculation with pen and ink. The studies include the critical edition of several Latin texts.
The Numerate Leader: How to Pull Game-Changing Insights from Statistical Data
by Thomas A. KingLearn how to make informed decisions through statistical reasoning! Using a qualitative approach to introduce statistical reasoning, The Numerate Leader: How to Pull Game-Changing Insights from Statistical Data is a cutting-edge book that helps the reader extract information from unfamiliar data sets. Combining introductory statistics with a few ideas from the philosophy of science, this work helps generalists find patterns that may be expected to recur in the future. Identifying one or two such relationships can be a game-changer for the reader and their employer or client. Thomas A. King's revelatory writing is easy to understand and conversational in tone. King makes the complex, tedious topics that you studied in the classroom—but likely didn't yet understand—easily comprehensible. Historical examples and humorous anecdotes illuminate technical concepts so that readers may pull insights from data sets and then explain conclusions reached through effective storytelling. What's more, the book is fun to read. A natural teacher, King emphasizes that complex software is unnecessary for success in this field. Readers, however, will find: Real-life examples that help put statistical concepts into an understandable context A glossary of important statistical terms and their use An appendix detailing ten math facts numerate people should know Perfect for undergraduate and graduate students entering advanced data analytics courses, as well as data analysts and c-suite executives just starting out, The Numerate Leader is key in helping develop the skills to identify provisional relationships between disparate data sets and then assess the significance of conclusions reached.
A Numerate Life
by John Allen PaulosEmploying intuitive ideas from mathematics, this quirky "meta-memoir" raises questions about our lives that most of us don't think to ask, but arguably should: What part of memory is reliable fact, what part creative embellishment? Which favorite presuppositions are unfounded, which statistically biased? By conjoining two opposing mindsets--the suspension of disbelief required in storytelling and the skepticism inherent in the scientific method--bestselling mathematician John Allen Paulos has created an unusual hybrid, a composite of personal memories and mathematical approaches to re-evaluating them.Entertaining vignettes from Paulos's biography abound--ranging from a bullying math teacher and a fabulous collection of baseball cards to romantic crushes, a grandmother's petty larceny, and his quite unintended role in getting George Bush elected president in 2000. These vignettes serve as springboards to many telling perspectives: simple arithmetic puts life-long habits in a dubious new light; higher dimensional geometry helps us see that we're all rather peculiar; nonlinear dynamics explains the narcissism of small differences cascading into very different siblings; logarithms and exponentials yield insight on why we tend to become bored and jaded as we age; and there are tricks and jokes, probability and coincidences, and much more.For fans of Paulos or newcomers to his work, this witty commentary on his life--and yours--is fascinating reading.From the Trade Paperback edition.
The Numerati: How They'll Get My Number And Yours
by Stephen BakerLearn how the crisis over digital privacy and manipulation evolved in this &“utterly fascinating&” look at the growth of data mining and analysis (Seattle Post-Intelligencer). Award-winning journalist Stephen Baker traces the rise of the &“global math elite&”: computer scientists who invent ways to not only record our behavior, but also to predict and alter it. Nowadays, we don&’t need to be online to create a digital trail; we do it simply by driving through an automated tollbooth or shopping with a credit card. As massive amounts of information are collected, sifted, and analyzed, we all become targets of those who want to influence everything from what we buy to how we vote. Clear and &“highly readable,&” The Numerati is a look at the origins of our present-day world, the possibilities of the future, and those who—whether with good or bad intentions—profile us as workers, consumers, citizens, or potential terrorists (The Wall Street Journal).
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
by Peter Benner Matthias Bollhöfer Daniel Kressner Christian Mehl Tatjana StykelThis edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. "
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics
by Justin SolomonNumerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Numerical Algorithms for Personalized Search in Self-organizing Information Networks
by Sep KamvarThis book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data.Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quadratic extrapolation technique--that speed up computation, making personalized PageRank feasible. Kamvar suggests that Power Method-related techniques ultimately should be the basis for improving the PageRank algorithm, and he presents algorithms that exploit the convergence behavior of individual components of the PageRank vector. Kamvar then extends the ideas of reputation management and personalized search to distributed networks like peer-to-peer and social networks. He highlights locality and computational considerations related to the structure of the network, and considers such unique issues as malicious peers. He describes the EigenTrust algorithm and applies various PageRank concepts to P2P settings. Discussion chapters summarizing results conclude the book's two main sections.Clear and thorough, this book provides an authoritative look at central innovations in search for all of those interested in the subject.
Numerical Analysis
by Donald GreenspanFirst Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
Numerical Analysis
by Larkin Ridgway ScottComputational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin
Numerical Analysis 1993
by D.F. Griffiths G.A. WatsonThis volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.
Numerical Analysis 1999 (Chapman & Hall/CRC Research Notes in Mathematics Series)
by Df Griffiths Ga WatsonOf considerable importance to numerical analysts, this text contains the proceedings of the 18th Dundee Biennial Conference on Numerical Analysis, featuring eminent analysts and current topics. The papers cover everything from partial differential equations to linear algebra and approximation theory and contain contributions from the leading expert
Numerical Analysis and Its Applications
by Ivan Dimov István Faragó Lubin VulkovThis volume of the Lecture Notes in Computer Science series contains the p- ceedings of the 3rd Conference on Numerical Analysis and Its Applications, which was held at the University of Rousse, Bulgaria, June 29-July 3, 2004. The conference was organized by the Department of Numerical Analysis and Statistics at the University of Rousse with the support of the Department of Mathematics of North Carolina State University. This conference continued the tradition of the two previous meetings (1996, 2000 in Rousse) as a forum where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperations. Morethan100scientistsfrom28co- tries participated in the conference. A wide range of problems concerning recent achievements in numerical an- ysis and its applications in physics, chemistry, engineering, and economics were discussed. An extensive exchange of ideas between scientists who develop and studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lems took place during the conference. We thank the plenary lecturers, Profs. R. Lazarov and V. Thome, and the key lecturers and the organizers of the minisymposia, T. Boyadjiev, T. Donchev, E. Farkhi, M. Van Gijzen, S. Nicaise, and M. Todorov, for their contributions. We recognize the e?ort required to prepare these key lectures and organize the minisymposia. We appreciate your sharing your knowledge of modern hi- performancecomputingnumericalmethodswiththeconferenceparticipants. We also thank I. Brayanov for the help in putting together the book. The 4th Conference on Numerical Analysis and Its Applications will take place in 2008.
Numerical Analysis and Optimization
by Mehiddin Al-Baali Lucio Grandinetti Anton PurnamaPresenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.
Numerical Analysis and Optimization: Nao-iii, Muscat, Oman, January 2014 (Springer Proceedings in Mathematics & Statistics #134)
by Mehiddin Al-Baali Lucio Grandinetti Anton PurnamaThis volume contains 13 selected keynote papers presented at the Fourth International Conference on Numerical Analysis and Optimization. Held every three years at Sultan Qaboos University in Muscat, Oman, this conference highlights novel and advanced applications of recent research in numerical analysis and optimization. Each peer-reviewed chapter featured in this book reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Any graduate student or researched wishing to know the latest research in the field will be interested in this volume. This book is dedicated to the late Professors Mike JD Powell and Roger Fletcher, who were the pioneers and leading figures in the mathematics of nonlinear optimization.
Numerical Analysis and Scientific Computation (Textbooks in Mathematics)
by Jeffery J. LeaderThis is an introductory single-term numerical analysis text with a modern scientific computing flavor. It offers an immediate immersion in numerical methods featuring an up-to-date approach to computational matrix algebra and an emphasis on methods used in actual software packages, always highlighting how hardware concerns can impact the choice of algorithm. It fills the need for a text that is mathematical enough for a numerical analysis course yet applied enough for students of science and engineering taking it with practical need in mind.The standard methods of numerical analysis are rigorously derived with results stated carefully and many proven. But while this is the focus, topics such as parallel implementations, the Basic Linear Algebra Subroutines, halfto quadruple-precision computing, and other practical matters are frequently discussed as well.Prior computing experience is not assumed. Optional MATLAB subsections for each section provide a comprehensive self-taught tutorial and also allow students to engage in numerical experiments with the methods they have just read about. The text may also be used with other computing environments.This new edition offers a complete and thorough update. Parallel approaches, emerging hardware capabilities, computational modeling, and data science are given greater weight.
Numerical Analysis for Applied Science (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts #35)
by Myron B. Allen III Eli L. IsaacsonPragmatic and Adaptable Textbook Meets the Needs of Students and Instructors from Diverse Fields Numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists. This updated and expanded edition of Numerical Analysis for Applied Science follows the tradition of its precursor by providing a modern, flexible approach to the theory and practical applications of the field. As before, the authors emphasize the motivation, construction, and practical considerations before presenting rigorous theoretical analysis. This approach allows instructors to adapt the textbook to a spectrum of uses, ranging from one-semester, methods-oriented courses to multi-semester theoretical courses. The book includes an expanded first chapter reviewing useful tools from analysis and linear algebra. Subsequent chapters include clearly structured expositions covering the motivation, practical considerations, and theory for each class of methods. The book includes over 250 problems exploring practical and theoretical questions and 32 pseudocodes to help students implement the methods. Other notable features include: A preface providing advice for instructors on using the text for a single semester course or multiple-semester sequence of courses Discussion of topics covered infrequently by other texts at this level, such as multidimensional interpolation, quasi-Newton methods in several variables, multigrid methods, preconditioned conjugate-gradient methods, finite-difference methods for partial differential equations, and an introduction to finite-element theory New topics and expanded treatment of existing topics to address developments in the field since publication of the first edition More than twice as many computational and theoretical exercises as the first edition. Numerical Analysis for Applied Science, Second Edition provides an excellent foundation for graduate and advanced undergraduate courses in numerical methods and numerical analysis. It is also an accessible introduction to the subject for students pursuing independent study in applied mathematics, engineering, and the physical and life sciences and a valuable reference for professionals in these areas.
Numerical Analysis for Engineers: Methods and Applications, Second Edition (Textbooks In Mathematics Ser.)
by Bilal Ayyub Richard H. McCuenNumerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical methods, especially their applications, limitations,
Numerical Analysis for Engineers and Scientists
by G. MillerStriking a balance between theory and practice, this graduate-level text is perfect for students in the applied sciences. The author provides a clear introduction to the classical methods, how they work and why they sometimes fail. Crucially, he also demonstrates how these simple and classical techniques can be combined to address difficult problems. Many worked examples and sample programs are provided to help the reader make practical use of the subject material. Further mathematical background, if required, is summarized in an appendix. Topics covered include classical methods for linear systems, eigenvalues, interpolation and integration, ODEs and data fitting, and also more modern ideas like adaptivity and stochastic differential equations.
Numerical Analysis II Essentials
by The Editors of REAREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Numerical Analysis II covers simultaneous linear systems and matrix methods, differential equations, Fourier transformations, partial differential equations, and Monte Carlo methods.
Numerical Analysis of Ordinary and Delay Differential Equations (UNITEXT #145)
by Taketomo Mitsui Guang-Da HuThis book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering.One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
Numerical Analysis of Partial Differential Equations
by Lui S. HA balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs.The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including:The mathematical theory of elliptic PDEsNumerical linear algebraTime-dependent PDEsMultigrid and domain decompositionPDEs posed on infinite domainsThe book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines.Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
Numerical Analysis Using R
by Graham W. GriffithsThis book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.
Numerical Analysis Using Sage
by Razvan A. Mezei George A. AnastassiouThis is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage. The presented code, written in core components of Sage, are backward compatible, i. e. , easily applicable to other software systems such as Mathematica®. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink. com.
Numerical Analysis with Algorithms and Programming
by Santanu Saha RayNumerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.
Numerical and Analytical Methods with MATLAB (Applied and Computational Mechanics)
by William Bober Chi-Tay Tsai Oren MasoryNumerical and Analytical Methods with MATLAB presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problem