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A Student's Guide to Numerical Methods
by Ian H. HutchinsonThis concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introductory class, this compact textbook provides a thorough grounding in computational physics and engineering.
A Student's Guide to the Study, Practice, and Tools of Modern Mathematics (Discrete Mathematics and Its Applications)
by Martin Erickson Donald BindnerA Student's Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica and Maple to MATLAB and R. Along with a color insert, the text include
A Student’s Guide to Infinite Series and Sequences
by Bernhard W. Bach Jr.Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. <P><P>This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. <P>The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.<P> An informal, plain language approach enables the student to get to grips with the material quickly.<P> A focus on practical real-world examples ensures a complex topic is accessible for students.<P> The early introduction of complex numbers allows the reader to apply infinite series to applications that are typically only addressed in high level mathematics courses.<P>
A Study of Quality Management of Official Statistics in China (Research Series on the Chinese Dream and China’s Development Path)
by Wuyi ZengThis book focuses on how to improve the quality management of official statistics in China. Official statistics help to build an overview of China’s social and economic development and play an important role in policymaking for government as well as in decision-making for enterprises. Because of the great value in reference, the quality of official statistics also constitutes the concern from the public. This book summarizes three levels for understanding the concept of the quality of official statistics and analyzes possible affections from social and economic environment, political and management perspectives. Government statistical data is an important information reflecting China’s economic and social development, an important tool for Party committees at all levels, governments, enterprises and the public to understand and grasp China’s economic operation and social development, an important basis for Party committees and governments at all levels to conduct economic and social management and decision-making and an important reference for enterprises and the public to make decisions on production, operation, investment and consumption. Therefore, the government, enterprises and the public at all levels are demanding more and more government statistics. Accordingly, the quality of government statistical data is becoming more and more important, because it concerns the objectivity and accuracy of government statistical data, the scientificity of economic and social management, the decision-making of Party committees, the correctness of production, operation, investment and consumption decisions of enterprises and the public. Therefore, the quality of government statistical data is extremely important, which is not only the focus of social concern, but also the core issue of government statistics.
A Survey Of Mathematics With Applications
by Allen R. Angel Christine D. Abbott Dennis C. RundeMathematics is an exciting, living study. Its applications shape the world around you and influence your everyday life. We hope that as you read this book you will realize just how important mathematics is and gain an appreciation of both its usefulness and its beauty. We also hope to teach you some practical mathematics that you can use every day and that will prepare you for further mathematics courses. The primary purpose of this text is to provide material that you can read, under¬stand, and enjoy. To this end, we have used straightforward language and tried to re¬late the mathematical concepts to everyday experiences. We have also provided many detailed examples for you to follow.
A Survey of Computational Physics: Introductory Computational Science
by Cristian C. Bordeianu José Páez Rubin LandauComputational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau's First Course in Scientific Computing and a follow-up to Landau and Páez's Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address. Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics. Accessible to advanced undergraduates Real-world problem-solving approach Java codes and applets integrated with text Companion Web site includes videos of lectures
A Survey of Fractal Dimensions of Networks (SpringerBriefs in Computer Science)
by Eric RosenbergMany different fractal dimensions have been proposed for networks. In A Survey of Fractal Dimensions of Networks the theory and computation of the most important of these dimensions are reviewed, including the box counting dimension, the correlation dimension, the mass dimension, the transfinite fractal dimension, the information dimension, the generalized dimensions (which provide a way to describe multifractals), and the sandbox method (for approximating the generalized dimensions). The book describes the use of diameter-based and radius-based boxes, and presents several heuristic methods for box counting, including greedy coloring, random sequential node burning, and a method for computing a lower bound. We also discuss very recent results on resolving ambiguity in the calculation of the information dimension and the generalized dimensions, and on the non-monotonicity of the generalized dimensions. Anyone interested in the theory and application of networks will want to read this Brief. This includes anyone studying, e.g., social networks, telecommunications networks, transportation networks, ecological networks, food chain networks, network models of the brain, or financial networks.
A Survey of Matrix Theory and Matrix Inequalities (Dover Books on Mathematics)
by Marvin Marcus Henryk MincWritten for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, "that reflect our own prejudices," among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence matrices and generalizations of commutativity.Part Two begins with a survey of elementary properties of convex sets and polyhedra and presents a proof of the Birkhoff theorem on doubly stochastic matrices. This is followed by a discussion of the properties of convex functions and a list of classical inequalities. This material is then combined to yield many of the interesting matrix inequalities of Weyl, Fan, Kantorovich and others. The treatment is along the lines developed by these authors and their successors and many of their proofs are included. This chapter contains an account of the classical Perron Frobenius-Wielandt theory of indecomposable nonnegative matrices and ends with some important results on stochastic matrices.Part Three is concerned with a variety of results on the localization of the characteristic roots of a matrix in terms of simple functions of its entries or of entries of a related matrix. The presentation is essentially in historical order, and out of the vast number of results in this field the authors have culled those that seemed most interesting or useful. Readers will find many of the proofs of classical theorems and a substantial number of proofs of results in contemporary research literature.
A Survey of Minimal Surfaces (Dover Books on Mathematics)
by Robert OssermanNewly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein's theorem, much more, including such recent developments as new work on Plateau's problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.
A Survey of Modern Algebra
by Garrett Birkhoff Saunders Mac LaneThis classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
A Survey of Preconditioned Iterative Methods (Research Notes In Mathematics Ser.)
by Are Magnus BruasetThe problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
A Survey of the Almagest: With Annotation and New Commentary by Alexander Jones (Sources and Studies in the History of Mathematics and Physical Sciences)
by Alexander Jones Olaf PedersenThe Almagest, by the Greek astronomer and mathematician Ptolemy, is the most important surviving treatise on early mathematical astronomy, offering historians valuable insight into the astronomy and mathematics of the ancient world. Pedersen's 1974 publication, A Survey of the Almagest, is the most recent in a long tradition of companions to the Almagest. Part paraphrase and part commentary, Pedersen's work has earned the universal praise of historians and serves as the definitive introductory text for students interested in studying the Almagest. In this revised edition, Alexander Jones, a distinguished authority on the history of early astronomy, provides supplementary information and commentary to the original text to account for scholarship that has appeared since 1974. This revision also incorporates various corrections to Pedersen's original text that have been identified since its publication. This volume is intended to provide students of the history of astronomy with a self-contained introduction to the Almagest, helping them to understand and appreciate Ptolemy's great and classical work.
A Survival Guide to the Misinformation Age: Scientific Habits of Mind
by David HelfandWe live in the Information Age, with billions of bytes of data just two swipes away. Yet how much of this is mis- or even disinformation? A lot of it is, and your search engine can't tell the difference. As a result, an avalanche of misinformation threatens to overwhelm the discourse we so desperately need to address complex social problems such as climate change, the food and water crises, biodiversity collapse, and emerging threats to public health. This book provides an inoculation against the misinformation epidemic by cultivating scientific habits of mind. Anyone can do it—indeed, everyone must do it if our species is to survive on this crowded and finite planet.This survival guide supplies an essential set of apps for the prefrontal cortex while making science both accessible and entertaining. It will dissolve your fear of numbers, demystify graphs, and elucidate the key concepts of probability, all while celebrating the precise use of language and logic. David Helfand, one of our nation's leading astronomers and science educators, has taught scientific habits of mind to generations in the classroom, where he continues to wage a provocative battle against sloppy thinking and the encroachment of misinformation.
A Survivor's Guide to R: An Introduction for the Uninitiated and the Unnerved
by Kurt Taylor GaubatzFocusing on developing practical R skills rather than teaching pure statistics, Dr. Kurt Taylor Gaubatz’s A Survivor’s Guide to R provides a gentle yet thorough introduction to R. The book is structured around critical R tasks, and focuses on applied knowledge, rather than abstract concepts. Gaubatz’s easy-to-read approach helps students with little or no background in statistics or programming to develop real-world R skills through straightforward coverage of R objects and functions. Focusing on real-world data, the challenges of dataset construction, and the use of R’s powerful graphing tools, the guide is written in an accessible, sympathetic, even humorous style that ensures students acquire functional R skills they can use in their own projects and carry into their work beyond the classroom.
A Systemic Perspective on Cognition and Mathematics (Communications in Cybernetics, Systems Science and Engineering)
by Jeffrey Yi-Lin ForrestThis book is devoted to the study of human thought, its systemic structure, and the historical development of mathematics both as a product of thought and as a fascinating case analysis. After demonstrating that systems research constitutes the second dimension of modern science, the monograph discusses the yoyo model, a recent ground-breaking deve
A Systems Biology Approach to Study Metabolic Syndrome
by Matej Orešič Antonio Vidal-PuigThe aim of this book is to provide the target audience, specifically students of Medicine, Biology, Systems Biology and Bioinformatics, as well as experienced researchers in research fields relevant to metabolic syndrome (MetS) with an overview of the challenges and opportunities in systems biology and how it can be used to tackle MetS. In particular, the aims are: (1) to provide an introduction to the key biological processes involved in the pathophysiology of MetS; (2) through the use of specific examples, provide an introduction to the latest technologies that use a systems biology approach to study MetS; and (3) to give an overview of the mathematical modeling approaches for studying MetS. The clearly written chapters by leading experts in the field provides detailed descriptions crucial for the unique position of this book and its focus on the application of systems biology to tackle specific pathophysiologically relevant aspects of MetS and provides a valuable practical guide to this research community.
A Systems Description of Flow Through Porous Media (SpringerBriefs in Earth Sciences)
by Jan Dirk JansenThis text forms part of material taught during a course in advanced reservoir simulation at Delft University of Technology over the past 10 years. The contents have also been presented at various short courses for industrial and academic researchers interested in background knowledge needed to perform research in the area of closed-loop reservoir management, also known as smart fields, related to e.g. model-based production optimization, data assimilation (or history matching), model reduction, or upscaling techniques. Each of these topics has connections to system-theoretical concepts. The introductory part of the course, i.e. the systems description of flow through porous media, forms the topic of this brief monograph. The main objective is to present the classic reservoir simulation equations in a notation that facilitates the use of concepts from the systems-and-control literature. Although the theory is limited to the relatively simple situation of horizontal two-phase (oil-water) flow, it covers several typical aspects of porous-media flow. The first chapter gives a brief review of the basic equations to represent single-phase and two-phase flow. It discusses the governing partial-differential equations, their physical interpretation, spatial discretization with finite differences, and the treatment of wells. It contains well-known theory and is primarily meant to form a basis for the next chapter where the equations will be reformulated in terms of systems-and-control notation.The second chapter develops representations in state-space notation of the porous-media flow equations. The systematic use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow. The third chapter first treats the analytical solution of linear systems of ordinary differential equations for single-phase flow. Next it moves on to the numerical solution of the two-phase flow equations, covering various aspects like implicit, explicit or mixed (IMPES) time discretizations and associated stability issues, Newton-Raphson iteration, streamline simulation, automatic time-stepping, and other computational aspects. The chapter concludes with simple numerical examples to illustrate these and other aspects such as mobility effects, well-constraint switching, time-stepping statistics, and system-energy accounting. The contents of this brief should be of value to students and researchers interested in the application of systems-and-control concepts to oil and gas reservoir simulation and other applications of subsurface flow simulation such as CO2 storage, geothermal energy, or groundwater remediation.
A Tale of Two Cultures: Qualitative and Quantitative Research in the Social Sciences
by James Mahoney Gary GoertzSome in the social sciences argue that the same logic applies to both qualitative and quantitative methods. In A Tale of Two Cultures, Gary Goertz and James Mahoney demonstrate that these two paradigms constitute different cultures, each internally coherent yet marked by contrasting norms, practices, and toolkits. They identify and discuss major differences between these two traditions that touch nearly every aspect of social science research, including design, goals, causal effects and models, concepts and measurement, data analysis, and case selection. Although focused on the differences between qualitative and quantitative research, Goertz and Mahoney also seek to promote toleration, exchange, and learning by enabling scholars to think beyond their own culture and see an alternative scientific worldview. This book is written in an easily accessible style and features a host of real-world examples to illustrate methodological points.
A Tale of Two Fractals
by A. A. KirillovSince Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
A Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners
by Susan Assouline National Assoc For Gifted Children Gail R. RyserA Teacher's Guide to Using the Common Core State Standards in Mathematics provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments that are useful in making educational decisions about placement and programming. Featuring learning experiences for each grade within one math progression, the book offers insight into useful ways of both accelerating and enriching the CCSS mathematics standards. Each of the learning experiences includes a sequence of activities, implementation examples, and formative assessments. Specific instructional and management strategies for implementing the standards within the classroom, school, and school district will be helpful for both K-12 teachers and administrators.
A Teacher's Guide to Using the Common Core State Standards with Mathematically Gifted and Advanced Learners
by Gail Ryser Susan Assouline Susan JohnsenA Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments that are useful in making educational decisions about placement and programming. Featuring learning experiences for each grade within one math progression, the book offers insight into useful ways of both accelerating and enriching the CCSS mathematics standards. Each of the learning experiences includes a sequence of activities, implementation examples, and formative assessments. Specific instructional and management strategies for implementing the standards within the classroom, school, and school district will be helpful for both K-12 teachers and administrators.
A Tear at the Edge of Creation: A Radical New Vision for Life in an Imperfect Universe
by Marcelo GleiserFor millennia, shamans and philosophers, believers and nonbelievers, artists and scientists have tried to make sense of our existence by suggesting that everything is connected, that a mysterious Oneness binds us to everything else. People go to temples, churches, mosques, and synagogues to pray to their divine incarnation of Oneness. Following a surprisingly similar notion, scientists have long asserted that under Nature's apparent complexity there is a simpler underlying reality. In its modern incarnation, this Theory of Everything would unite the physical laws governing very large bodies (Einstein's theory of relativity) and those governing tiny ones (quantum mechanics) into a single framework. But despite the brave efforts of many powerful minds, the Theory of Everything remains elusive. It turns out that the universe is not elegant. It is gloriously messy. Overturning more than twenty-five centuries of scientific thought, award-winning physicist Marcelo Gleiser argues that this quest for a Theory of Everything is fundamentally misguided, and he explains the volcanic implications this ideological shift has for humankind. All the evidence points to a scenario in which everything emerges from fundamental imperfections, primordial asymmetries in matter and time, cataclysmic accidents in Earth's early life, and duplication errors in the genetic code. Imbalance spurs creation. Without asymmetries and imperfections, the universe would be filled with nothing but smooth radiation. A Tear at the Edge of Creation calls for nothing less than a new "humancentrism" to reflect our position in the universal order. All life, but intelligent life in particular, is a rare and precious accident. Our presence here has no meaning outside of itself, but it does have meaning. The unplanned complexity of humankind is all the more beautiful for its improbability. It's time for science to let go of the old aesthetic that labels perfection beautiful and holds that "beauty is truth. " It's time to look at the evidence without centuries of monotheistic baggage. In this lucid, down-to-earth narrative, Gleiser walks us through the basic and cutting-edge science that fueled his own transformation from unifier to doubter--a fascinating scientific quest that led him to a new understanding of what it is to be human.
A Technical Guide to Mathematical Finance (Chapman and Hall/CRC Financial Mathematics Series)
by Derek ZweigA Technical Guide to Mathematical Finance covers those foundational mathematical topics most important to an aspiring or professional quant. The text goes beyond a simple recitation of methods and aims to impart a genuine understanding of the fundamental concepts underpinning most of the techniques and tools routinely used by those working in quantitative finance.Features Suitable for professional quants and graduate students in finance, and mathematical/quantitative finance “Concept Refreshers” used throughout to provide pithy summaries of complex topics Step-by-step detail for formal proofs and mathematical descriptions
A TextBook of Cost and Management Accounting 10 Edition - PART-I
by M. N. AroraThis book provides the students with thorough grounding in cost concepts, cost behaviour and methods, and techniques of cost and management accounting with an understanding of the uses and limitations of cost and financial data for managerial operations. The text of the subject matter has been presented in a student-friendly, simple and intelligible manner. Every discussion involving conceptual complexity is immediately illustrated by a numerical example. In addition, the book contains a liberal sprinkling of charts and diagrams so as to make the subject easily understandable and highlight its finer points. The subject matter has been organized on â first things firstâ basis for its logical presentation that sustains interest. The approach of the book is examination oriented. Thus, a good number of problems and solutions have been included in its chapters. Theoretical and numerical questions have been mostly selected from various examinations. Objective type questions have been given to serve as self test by students. This is an ideal book for self study.
A Textbook of Graph Theory (Universitext)
by K. Ranganathan R. BalakrishnanGraph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This textbook provides a solid background in the basic topics of graph theory, and is intended for an advanced undergraduate or beginning graduate course in graph theory. This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homomorphisms and colorings and the uniqueness of the Mycielskian up to isomorphism. This book also introduces several interesting topics such as Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices, and a concrete application of triangulated graphs.