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The Highway Capacity Manual: Signalized and Unsignalized Intersections (Springer Tracts on Transportation and Traffic #12)
by Elena S. Prassas Roger P. RoessSince 1950, the Highway Capacity Manual has been a standard used in the planning, design, analysis, and operation of virtually any highway traffic facility in the United States. It has also been widely used around the globe and has inspired the development of similar manuals in other countries. This book is Volume II of a series on the conceptual and research origins of the methodologies found in the Highway Capacity Manual. It focuses on the most complex points in a traffic system: signalized and unsignalized intersections, and the concepts and methodologies developed over the years to model their operations. It also includes an overview of the fundamental concepts of capacity and level of service, particularly as applied to intersections. The historical roots of the manual and its contents are important to understanding current methodologies, and improving them in the future. As such, this book is a valuable resource for current and future users of the Highway Capacity Manual, as well as researchers and developers involved in advancing the state-of-the-art in the field.
Hilary Putnam on Logic and Mathematics (Outstanding Contributions to Logic #9)
by Geoffrey Hellman Roy T. CookThis book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam’s work. It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy of mathematics. In addition, it features a short essay presenting reminiscences and anecdotes about Putnam from his friends and colleagues, and also includes an extensive bibliography of his work in mathematics and logic. The book offers readers a comprehensive review of outstanding contributions in logic and mathematics as well as an engaging dialogue between prominent scholars and researchers. It provides those interested in mathematical logic, the philosophy of logic, and the philosophy of mathematics unique insights into the work of Hilary Putnam.
Hilbert C*- Modules and Quantum Markov Semigroups
by Lunchuan ZhangThis book explains the basic theory of Hilbert C*-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The general scope of the book includes: basic theory of Hilbert C*-modules; generalized indices and module frames; operator valued Dirichlet forms; and quantum Markov semigroups.This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.
The Hilbert-Huang Transform in Engineering
by Norden Huang Nii O. Attoh-OkineData used to develop and confirm models suffer from several shortcomings: the total data is too limited, the data are non-stationary, and the data represent nonlinear processes. The Hilbert-Huang transform (HHT) is a relatively new method that has grown into a robust tool for data analysis and is ready for a wide variety of applications.Thi
Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics)
by Ralph E. ShowalterThis text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus.The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first- and second-order evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography.
Hilbert Space Methods in Signal Processing
by Rodney A. Kennedy Parastoo SadeghiThis lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.
Hill's Chemistry for Changing Times
by John Hill Terry McCreary Marilyn Duerst Rill ReuterEngage students with contemporary and relevant applications of chemistry. <p><p> Chemistry for Changing Timeshas defined the liberal arts course and remains the most visually appealing and readable introduction for the subject. Abundant applications and examples fill each chapter and enable students of varied majors to readily relate to chemistry. <p><p> For the 15th Edition, author Terry McCreary and new coauthors Marilyn Duerst and Rill Ann Reuter, introduce new examples and a consistent model for problem solving. They guide students through the problem-solving process, asking them to apply the models and combine them with previously learned concepts. <p><p>New problem types engage and challenge students to develop skills they will use in their everyday lives, including developing scientific literacy, analyzing graphs and data, recognizing fake vs. real news, and creating reports. New relevant, up-to-date applications focus on health and wellness and the environment, helping non-science and allied-health majors taking the course to see the connections between the course materials and their everyday lives.
Hill's Equation
by Wilhelm Magnus Stanley WinklerThe hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject."Hill's equation" connotes the class of homogeneous, linear, second order differential equations with real, periodic coefficients. This two part treatment encompasses the most pertinent, necessary information; only the theory's elementary facts are proved in full, with minimal use of sophisticated mathematics. Part I explains the basic theory: Floquet's theorem, characteristic values and intervals of stability, analytic properties of the discriminant, infinite determinants, asymptotic behavior of the characteristic values, theorems of Liapounoff and Borg, and related topics. Part II examines numerous details: elementary formulas, oscillatory solutions, intervals of stability and instability, discriminant, coexistence, and examples. Particular attention is given to stability problems and to the question of coexistence of periodic solutions.Although intended for professional mathematicians and engineers, the volume is written so clearly and vigorously that it can be recommended for graduate students and advanced undergraduates. List of Symbols and Notations. List of Theorems, Lemmas, and Corollaries. References. Index.
The Hindu-Arabic Numerals (Dover Books on Mathematics)
by David Eugene Smith Louis Charles KarpinskiThe numbers that we call Arabic are so familiar throughout Europe and the Americas that it can be difficult to realize that their general acceptance in commercial transactions is a matter of only the last four centuries and they still remain unknown in parts of the world.In this volume, one of the earliest texts to trace the origin and development of our number system, two distinguished mathematicians collaborated to bring together many fragmentary narrations to produce a concise history of Hindu-Arabic numerals. Clearly and succinctly, they recount the labors of scholars who have studied the subject in different parts of the world; they then assess the historical testimony and draw conclusions from its evidence. Topics include early ideas of the origin of numerals; Hindu forms with and without a place value; the symbol zero; the introduction of numbers into Europe by Boethius; the development of numerals among Arabic cultures; and the definitive introduction of numerals into Europe and their subsequent spread. Helpful supplements to the text include a guide to the pronunciation of Oriental names and an index.
Hinges: Meditations on the Portals of the Imagination
by Grace MazurGrace Dane Mazur uses the idea of the hinge to illuminate real and metaphysical thresholds in fiction, poetry, myth, and ordinary life. From ancient narratives of Gilgamesh, Odysseus, Parmenides, and Orpheus, to modern works by Katherine Mansfield and Eudora Welty, the exploration of the Other World acts as a metaphor for the entrancement of readin
Hip Prosthesis: CAD Modeling, Finite Element Analysis (FEA) and Compressive Load Testing (SpringerBriefs in Applied Sciences and Technology)
by Najwa Syakirah Hamizan Solehuddin Shuib Amir Radzi Ab GhaniThis book highlights the critical challenge of improving the design and performance of hip implants, which are essential for enhancing patient outcomes in hip replacement surgeries. The book focuses on utilizing Finite Element Analysis (FEA) to optimize implant designs, ensuring they can withstand complex mechanical loads and reduce the risk of failure. It is hoped that readers will gain a deeper understanding of the significance of implant design and the role of FEA in predicting and enhancing implant performance, ultimately leading to better, more durable solutions in orthopedic surgeries.
Historical Developments in Singular Perturbations
by Robert E. O'MalleyThis engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
The Historical Roots of Elementary Mathematics
by Lucas N. Bunt Jack D. Bedient Phillip S. Jones"Will delight a broad spectrum of readers." -- American Mathematical MonthlyDo long division as the ancient Egyptians did! Solve quadratic equations like the Babylonians! Study geometry just as students did in Euclid's day! This unique text offers students of mathematics an exciting and enjoyable approach to geometry and number systems. Written in a fresh and thoroughly diverting style, the text -- while designed chiefly for classroom use -- will appeal to anyone curious about mathematical inscriptions on Egyptian papyri, Babylonian cuneiform tablets, and other ancient records.The authors have produced an illuminated volume that traces the history of mathematics -- beginning with the Egyptians and ending with abstract foundations laid at the end of the 19th century. By focusing on the actual operations and processes outlined in the text, students become involved in the same problems and situations that once confronted the ancient pioneers of mathematics. The text encourages readers to carry out fundamental algebraic and geometric operations used by the Egyptians and Babylonians, to examine the roots of Greek mathematics and philosophy, and to tackle still-famous problems such as squaring the circle and various trisectorizations.Unique in its detailed discussion of these topics, this book is sure to be welcomed by a broad range of interested readers. The subject matter is suitable for prospective elementary and secondary school teachers, as enrichment material for high school students, and for enlightening the general reader. No specialized or advanced background beyond high school mathematics is required.
Historical Studies in Computing, Information, and Society: Insights from the Flatiron Lectures (History of Computing)
by William AsprayThis is a volume of chapters on the historical study of information, computing, and society written by seven of the most senior, distinguished members of the History of Computing field. These are edited, expanded versions of papers presented in a distinguished lecture series in 2018 at the University of Colorado Boulder – in the shadow of the Flatirons, the front range of the Rocky Mountains. Topics range widely across the history of computing. They include the digitalization of computer and communication technologies, gender history of computing, the history of data science, incentives for innovation in the computing field, labor history of computing, and the process of standardization. Authors were given wide latitude to write on a topic of their own choice, so long as the result is an exemplary article that represents the highest level of scholarship in the field, producing articles that scholars in the field will still look to read twenty years from now. The intention is to publish articles of general interest, well situated in the research literature, well grounded in source material, and well-polished pieces of writing. The volume is primarily of interest to historians of computing, but individual articles will be of interest to scholars in media studies, communication, computer science, cognitive science, general and technology history, and business.
Historiography of Mathematics in the 19th and 20th Centuries
by Volker R. Remmert Martina R. Schneider Henrik Kragh SørensenThis book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written. In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception. During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular. Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both a new professional identity and changes in its primary audience, various shifts of perspective in the way the history of mathematics was and is written can still be observed to this day. Initially concentrating on major internal, universal developments in certain sub-disciplines of mathematics, the field gradually gravitated towards a focus on contexts of knowledge production involving individuals, local practices, problems, communities, and networks. The goal of this book is to link these disciplinary and methodological changes in the history of mathematics to the broader cultural contexts of its practitioners, namely the historians of mathematics during the period in question.
Historische, logische und individuelle Genese der Trigonometrie aus didaktischer Sicht (Bielefelder Schriften zur Didaktik der Mathematik #10)
by Valentin KatterIn diesem Open-Access-Buch führt Valentin Katter eine umfassende didaktisch orientierte Sachanalyse unter historisch-, logisch-, und individualgenetischen Gesichtspunkten durch, mit der es ihm möglich ist, systematisch sechs Grundvorstellungen zum Sinusbegriff zu identifizieren. Anhand detaillierter Videoanalysen zeigt der Autor anschließend, wie diese Grundvorstellungen genutzt werden können, um Denkprozesse von Lehramtsstudierenden in kooperativen Problemlösesituationen zu rekonstruieren. Diese Rekonstruktionen gewähren einen Einblick in das komplexe individuelle Netz von Vorstellungen und ermöglichen es, das Potential und mögliche Hindernisse, die in ihm stecken, auszuloten.
History Algebraic Geometry
by Suzanne C. DieudonneThis book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.
History and Measurement of the Base and Derived Units (Springer Series in Measurement Science and Technology)
by Steven A. TreeseThis book discusses how and why historical measurement units developed, and reviews useful methods for making conversions as well as situations in which dimensional analysis can be used. It starts from the history of length measurement, which is one of the oldest measures used by humans. It highlights the importance of area measurement, briefly discussing the methods for determining areas mathematically and by measurement. The book continues on to detail the development of measures for volume, mass, weight, time, temperature, angle, electrical units, amounts of substances, and light intensity. The seven SI/metric base units are highlighted, as well as a number of other units that have historically been used as base units. Providing a comprehensive reference for interconversion among the commonly measured quantities in the different measurement systems with engineering accuracy, it also examines the relationships among base units in fields such as mechanical/thermal, electromagnetic and physical flow rates and fluxes using diagrams.
A History in Sum
by Steve Nadis Shing-Tung YauIn the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvards mathematics department was at the center of these developments. "A History in Sum "is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirces successors--William Fogg Osgood and Maxime Bocher--undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators--students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. "A History in Sum" elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
A History of Abstract Algebra: From Algebraic Equations to Modern Algebra (Springer Undergraduate Mathematics Series)
by Jeremy GrayThis textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
History of Analytic Geometry: Its Development From The Pyramids To The Heroic Age (Dover Books on Mathematics)
by Carl B. BoyerSpecifically designed as an integrated survey of the development of analytic geometry, this classic study takes a unique approach to the history of ideas. The author, a distinguished historian of mathematics, presents a detailed view of not only the concepts themselves, but also the ways in which they extended the work of each generation, from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. Appropriate as an undergraduate text, this history is accessible to any mathematically inclined reader. 1956 edition. Analytical bibliography. Index.
A History of British Actuarial Thought
by Craig TurnbullIn the first book of its kind, Turnbull traces the development and implementation of actuarial ideas, from the conception of Equitable Life in the mid-18th century to the start of the 21st century. This book analyses the historical development of British actuarial thought in each of its three main practice areas of life assurance, pensions and general insurance. It discusses how new actuarial approaches were developed within each practice area, and how these emerging ideas interacted with each other and were often driven by common external factors such as shocks in the economic environment, new intellectual ideas from academia and developments in technology.A broad range of historically important actuarial topics are discussed such as the development of the blueprint for the actuarial management of with-profit business; historical developments in mortality modelling methods; changes in actuarial thinking on investment strategy for life and pensions business; changing perspectives on the objectives and methods for funding Defined Benefit pensions; the application of risk theory in general insurance reserving; the adoption of risk-based reserving and the Guaranteed Annuity Option crisis at the end of the 20th century.This book also provides an historical overview of some of the most important external contributions to actuarial thinking: in particular, the first century or so of modern thinking on probability and statistics, starting in the 1650s with Pascal and Fermat; and the developments in the field of financial economics over the third quarter of the twentieth century. This book identifies where historical actuarial thought heuristically anticipated some of the fundamental ideas of modern finance, and the challenges that the profession wrestled with in reconciling these ideas with traditional actuarial methods. Actuaries have played a profoundly influential role in the management of the United Kingdom’s most important long-term financial institutions over the last two hundred years. This book will be the first to chart the influence of the actuarial profession to modern day. It will prove a valuable resource for actuaries, actuarial trainees and students of actuarial science. It will also be of interest to academics and professionals in related financial fields such as accountants, statisticians, economists and investment managers.
The History of Correlation
by John Nicholas ZorichAfter 30 years of research, the author of The History of Correlation organized his notes into a manuscript draft during the lockdown months of the COVID-19 pandemic. Getting it into shape for publication took another few years. It was a labor of love.Readers will enjoy learning in detail how correlation evolved from a completely non-mathematical concept to one today that is virtually always viewed mathematically. This book reports in detail on 19th- and 20th-century English-language publications; it discusses the good and bad of many dozens of 20th-century articles and statistics textbooks in regard to their presentation and explanation of correlation. The final chapter discusses 21st-century trends.Some topics included here have never been discussed in depth by any historian. For example: Was Francis Galton lying in the first sentence of his first paper about correlation? Why did he choose the word "co-relation" rather than "correlation" for his new coefficient? How accurate is the account of the history of correlation found in H. Walker's 1929 classic, Studies in the History of Statistical Method? Have 20th-century textbooks misled students as to how to use the correlation coefficient?Key features of this book: Charts, tables, and quotations (or summaries of them) are provided from about 450 publications. In-depth analyses of those charts, tables, and quotations are included. Correlation-related claims by a few noted historians are shown to be in error. Many funny findings from 30 years of research are highlighted. This book is an enjoyable read that is both serious and (occasionally) humorous. Not only is it aimed at historians of mathematics, but also professors and students of statistics and anyone who has enjoyed books such as Beckmann's A History of Pi or Stigler's The History of Statistics.
A History of Econometrics in France: From Nature to Models (Routledge Studies In The History Of Economics Ser.)
by Philippe Le GallThis text challenges the traditional view of the history of econometrics and provides a more complete story. In doing so, the book sheds light on the hitherto under-researched contribution of French thinkers to econometrics. Fascinating and authoritative, it is a comprehensive overview of what went on to be one of the defining subsets within t
A History of Folding in Mathematics: Mathematizing The Margins (Science Networks. Historical Studies #59)
by Michael FriedmanWhile it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is the cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length the cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.