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A Hands-on Introduction to Big Data Analytics
by Funmi Obembe Ofer EngelThis practical textbook offers a hands-on introduction to big data analytics, helping you to develop the skills required to hit the ground running as a data professional. It complements theoretical foundations with an emphasis on the application of big data analytics, illustrated by real-life examples and datasets. Containing comprehensive coverage of all the key topics in this area, this book uses open-source technologies and examples in Python and Apache Spark. Learning features include: - Ethics by Design encourages you to consider data ethics at every stage. - Industry Insights facilitate a deeper understanding of the link between what you are studying and how it is applied in industry. - Datasets, questions, and exercises give you the opportunity to apply your learning. Dr Funmi Obembe is the Head of Technology at the Faculty of Arts, Science and Technology, University of Northampton. Dr Ofer Engel is a Data Scientist at the University of Groningen.
A Hands-on Introduction to Big Data Analytics
by Funmi Obembe Ofer EngelThis practical textbook offers a hands-on introduction to big data analytics, helping you to develop the skills required to hit the ground running as a data professional. It complements theoretical foundations with an emphasis on the application of big data analytics, illustrated by real-life examples and datasets. Containing comprehensive coverage of all the key topics in this area, this book uses open-source technologies and examples in Python and Apache Spark. Learning features include: - Ethics by Design encourages you to consider data ethics at every stage. - Industry Insights facilitate a deeper understanding of the link between what you are studying and how it is applied in industry. - Datasets, questions, and exercises give you the opportunity to apply your learning. Dr Funmi Obembe is the Head of Technology at the Faculty of Arts, Science and Technology, University of Northampton. Dr Ofer Engel is a Data Scientist at the University of Groningen.
A History in Sum
by Shing-Tung Yau Steve NadisIn 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.
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.
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.
A History of Geometrical Methods (Dover Books on Mathematics)
by Julian Lowell CoolidgeFull and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
A History of Greek Mathematics, Volume I: From Thales to Euclid
by Thomas Heath"As it is, the book is indispensable; it has, indeed, no serious English rival." — Times Literary Supplement. "Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century." — Professor W. H. Stahl"Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry." The perspective that enabled Sir Thomas Heath to understand the Greek genius — deep intimacy with languages, literatures, philosophy, and all the sciences — brought him perhaps closer to his beloved subjects and to their own ideal of educated men, than is common or even possible today. Heath read the original texts with a critical, scrupulous eye, and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English. "Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes' proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations. Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus
by Thomas HeathThe perspective that enabled Sir Thomas Heath to understand the Greek genius — deep intimacy with languages, literatures, philosophy, and all the sciences — brought him perhaps closer to his beloved subjects, and to their own ideal of educated men than is common or even possible today. Heath read the original texts with a critical, scrupulous eye and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English."Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes's proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations.Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.
A History of Japanese Mathematics (Dover Books on Mathematics)
by David E. Smith Yoshio MikamiOne of the first books to show Westerners the nature of Japanese mathematics, this survey highlights the leading features in the development of the wasan, the Japanese system of mathematics. Topics include the use of the soroban, or abacus; the application of sangi, or counting rods, to algebra; the discoveries of the 17th-century sage Seki Kowa; the yenri, or circle principle; the work of 18th-century geometer Ajima Chokuyen; and Wada Nei's contributions to the understanding of hypotrochoids. Unabridged republication of the classic 1914 edition. 74 figures. Index.
A History of Kinematics from Zeno to Einstein: On the Role of Motion in the Development of Mathematics (History of Mechanism and Machine Science #46)
by Teun KoetsierThis book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.
A History of Mathematical Notations: Two Volumes Bound as One
by Florian CajoriThis classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author's coverage of obsolete notations -- and what we can learn from them -- is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is presented here in one volume.
A History of Mathematics (History Of Mathematics Ser. #Vol. 2)
by Carl B. Boyer Uta C. MerzbachThe updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
A History of Pi
by Petr BeckmannThe history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
A History of the Work Concept: From Physics to Economics (History of Mechanism and Machine Science #24)
by Agamenon R. E. OliveiraThis book traces the history of the concept of work from its earliest stages and shows that its further formalization leads to equilibrium principle and to the principle of virtual works, and so pointing the way ahead for future research and applications. The idea that something remains constant in a machine operation is very old and has been expressed by many mathematicians and philosophers such as, for instance, Aristotle. Thus, a concept of energy developed. Another important idea in machine operation is Archimedes' lever principle. In modern times the concept of work is analyzed in the context of applied mechanics mainly in Lazare Carnot mechanics and the mechanics of the new generation of polytechnical engineers like Navier, Coriolis and Poncelet. In this context the word "work" is finally adopted. These engineers are also responsible for the incorporation of the concept of work into the discipline of economics when they endeavoured to combine the study of the work of machines and men together.
A Holistic Approach to Ship Design: Volume 2: Application Case Studies
by Apostolos PapanikolaouThis book deals with modern Computer-Aided Design (CAD) software tools and platforms implemented in ship design, the integration of techno-economic databases, the use of optimisation and simulation software tools, which are integrated in these platforms, and the virtual modelling of ships and their operation by using a Virtual Vessel Framework (VVF). It contains a series of application case studies related to the developed holistic approach to ship design and operation. Nine case studies are described, referring to the design and operation of various ship types, namely RoPax, cruise ship, double-ended ferry, bulk carrier, containership, offshore support vessel, ocean surveillance ship and research vessel and one offshore structure. All case studies are driven by leading representatives of the European Maritime Industry. This book complements A Holistic Approach to Ship Design, volume 1, which covers methods and tools for the life cycle optimisation and assessment of ship design and operation.
A Java Library of Graph Algorithms and Optimization (Discrete Mathematics and Its Applications)
by Hang T. LauBecause of its portability and platform-independence, Java is the ideal computer programming language to use when working on graph algorithms and other mathematical programming problems. Collecting some of the most popular graph algorithms and optimization procedures, A Java Library of Graph Algorithms and Optimization provides the source code for
A Journey Along The Erie Canal: Dividing Multidigit Numbers By A One-digit Number Without Remainders
by Janey LevyThis fascinating paperback describes the construction and history of the Erie Canal. It uses the information to illustrate elementary division. Includes a scanned photocopy of a weekly toll collection statement from 1860.
A Journey Through Discrete Mathematics: A Tribute To Ji I Matou Ek
by Jaroslav Nešetřil Martin Loebl Robin ThomasThis collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiř#65533; Matousek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition - something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiř#65533; Matousek's numerous areas of mathematical interest.
A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras (Universitext)
by Caroline Gruson Vera SerganovaThis text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb (Mathematics Education Library #48)
by Anna Sfard Paul Cobb Erna Yackel Koeno GravemeijerOur objective is to publish a book that lays out the theoretical constructs and research methodologies within mathematics education that have been developed by Paul Cobb and explains the process of their development. We propose to do so by including papers in which Cobb introduced new theoretical perspectives and methodologies into the literature, each preceded by a substantive accompanying introductory paper that explains the motivation/rationale for developing the new perspectives and/or methodologies and the processes through which they were developed, and Cobb's own retrospective comments. In this way the book provides the reader with heretofore unpublished material that lays out in considerable detail the issues and problems that Cobb has confronted in his work, that, from his viewpoint, required theoretical and methodological shifts/advances and provides insight into how he has achieved the shifts/advances. The result will be a volume that, in addition to explaining Cobb's contributions to the field of mathematics education, also provides the reader with insight into what is involved in developing an aggressive and evolving research program. When Cobb confronts problems and issues in his work that cannot be addressed using his existing theories and frameworks, he looks to other fields for theoretical inspiration. A critical feature of Cobb's work is that in doing so, he consciously appropriates and adapts ideas from these other fields to the purpose of supporting processes of learning and teaching mathematics; He does not simply accept the goals or motives of those fields. As a result, Cobb reconceptualizes and reframes issues and concepts so that they result in new ways of investigating, exploring, and explaining phenomena that he encounters in the practical dimensions of his work, which include working in classrooms, with teachers, and with school systems. The effect is that the field of mathematics education is altered. Other researchers have found his "new ways of looking" useful to them. And they, in turn, adapt these ideas for their own use. The complexity of many of the ideas that Cobb has introduced into the field of mathematics education can lead to a multiplicity of interpretations by practitioners and by other researchers, based on their own experiential backgrounds. Therefore, by detailing the development of Cobb's work, including the tensions involved in coming to grips with and reconciling apparently contrasting perspectives, the book will shed additional light on the processes of reconceptualization and thus help the reader to understand the reasons, mechanisms, and outcomes of researchers' constant pursuit of new insights.
A Journey into Modern Physics: From Relativity to Quantum Technologies
by Carmine GranataThis book offers a short journey into the surprising and spectacular world of modern physics characterized by disruptive ideas and theory from both a conceptual and applicative point of view. Starting from Einstein's theory of relativity in which the concepts of space, time, and gravity are completely revised, before arriving at the bizarre and fascinating universe of quantum physics which with its applications has completely changed our way of life. Particular attention is also paid to the conceptual foundations and paradoxes of quantum mechanics thanks to which the so-called second quantum revolution has developed in more recent times, destined to introduce a new generation of quantum technologies such as computers, cryptography, and teleportation into our lives. In addition to new quantum technologies, the operating principles of the most important applications of quantum mechanics which have become widespread in everyday life are illustrated simply and concisely. The book has an essentially informative character, without making use of complicated formulas or technicalities, therefore it does not require in-depth knowledge of physics or mathematics; the knowledge acquired in high school is sufficient to understand the topics covered.
A Journey into the World of Exponential Functions
by Gautam BandyopadhyayThe number e, the function ex, the logarithmic function in (x) and different hyperbolic functions like cosh (x), sinh (x) make frequent appearances in science and engineering textbooks. Students often fail to appreciate the significance of these mathematical symbols. This book clearly illustrates why such abstract mathematical entities are needed to represent some aspects of physical reality. It provides an overview of different types of numbers and functions along with their historical background and applications. It contains four chapters covering number system, exponential function, logarithmic functions and hyperbolic functions along with the concept of complex angle. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)
A Kaleidoscopic View of Graph Colorings (SpringerBriefs in Mathematics)
by Ping ZhangThis book describes kaleidoscopic topics that have developedin the area of graph colorings. Unifying current material on graph coloring,this book describes current information on vertex and edge colorings in graphtheory, including harmonious colorings, majestic colorings, kaleidoscopiccolorings and binomial colorings. Recently there have been a number of breakthroughs in vertex coloringsthat give rise to other colorings in a graph, such as graceful labelings ofgraphs that have been reconsidered under the language of colorings. The topics presented in this book include sample detailedproofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as itcovers a broad range of topics and makes connections between recentdevelopments and well-known areas in graph theory.