This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.
This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.
May Steven Saylor's Roman empire never fall. A modern master of historical fiction, Saylor convincingly transports us into the ancient world...enthralling!" —USA Today on Roma Continuing the saga begun in his New York Times bestselling novel Roma, Steven Saylor charts the destinies of the aristocratic Pinarius family, from the reign of Augustus to height of Rome's empire. The Pinarii, generation after generation, are witness to greatest empire in the ancient world and of the emperors that ruled it—from the machinations of Tiberius and the madness of Caligula, to the decadence of Nero and the golden age of Trajan and Hadrian and more. Empire is filled with the dramatic, defining moments of the age, including the Great Fire, the persecution of the Christians, and the astounding opening games of the Colosseum. But at the novel's heart are the choices and temptations faced by each generation of the Pinarii. Steven Saylor once again brings the ancient world to vivid life in a novel that tells the story of a city and a people that has endured in the world's imagination like no other.
In the unseasonable heat of a spring morning in 80 B.C., Gordianus the Finder is summoned to the house of Cicero, a young advocate staking his reputation on a case involving the savage murder of the wealthy, sybaritic Sextus Roscius. Charged with the murder is Sextus's son, greed being the apparent motive. The punishment, rooted deep in Roman tradition, is horrific beyond imagining. The case becomes a political nightmare when Gordianus's investigation takes him through the city's raucous, pungent streets and deep into rural Umbria. Now, one man's fate may threaten the very leaders of Rome itself.
Following his international bestsellers Roma and Empire, Steven Saylor's Dominus continues his saga of the greatest, most storied empire in history from the eternal city at the very center of it all. A.D. 165: The empire of Rome has reached its pinnacle. Universal peace—the Pax Roma—reigns from Britannia to Egypt, from Gaul to Greece. Marcus Aurelius, as much a philosopher as he is an emperor, oversees a golden age in the city of Rome. The ancient Pinarius family and their workshop of artisans embellish the richest and greatest city on earth with gilded statues and towering marble monuments. Art and reason flourish. But history does not stand still. The years to come bring wars, plagues, fires, and famines. The best emperors in history are succeeded by some of the worst. Barbarians descend in endless waves, eventually appearing before the gates of Rome itself. The military seizes power and sells the throne to the highest bidder. Chaos engulfs the empire. Through it all, the Pinarius family endures, thanks in no small part to the protective powers of the fascinum, a talisman older than Rome itself, a mystical heirloom handed down through countless generations. But an even greater upheaval is yet to come. On the fringes of society, troublesome cultists disseminate dangerous and seditious ideas. They insist that everyone in the world should worship only one god, their god. They call themselves Christians. Some emperors deal with the Christians with toleration, others with bloody persecution. Then one emperor does the unthinkable. He becomes a Christian himself. His name is Constantine, and the revolution he sets in motion will change the world forever. Spanning 160 years and seven generations, teeming with some of ancient Rome’s most vivid figures, Saylor's epic brings to vivid life some of the most tumultuous and consequential chapters of human history, events which reverberate still.
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.” - From the foreword by Richard Stanley
A History of Roman Art provides a wide-ranging survey of the subject from the founding of Rome to the rule of Rome's first Christian emperor, Constantine. Incorporating the most up-to-date information available on the topic, this new textbook explores the creation, use, and meaning of art in the Roman world. Extensively illustrated with 375 color photographs and line drawings Broadly defines Roman art to include the various cultures that contributed to the Roman system Focuses throughout on the overarching themes of Rome's cultural inclusiveness and art's important role in promoting Roman values Discusses a wide range of Roman painting, mosaic, sculpture, and decorative arts, as well as architecture and associated sculptures within the cultural contexts they were created and developed Offers helpful and instructive pedagogical features for students, such as timelines; key terms defined in margins; a glossary; sidebars with key lessons and explanatory material on artistic technique, stories, and ancient authors; textboxes on art and literature, art from the provinces, and important scholarly perspectives; and primary sources in translation A book companion website is available at www.wiley.com/go/romanart with the following resources: PowerPoint slides, glossary, and timeline Steven Tuck is the 2014 recipient of the American Archaeological Association's Excellence in Undergraduate Teaching Award.
Gordianus the Finder is in a tough spot when Pompey takes his son-in-law hostage, and to save both their lives, Gordianus must prove that his son did not kill Pompey's beloved cousin.
Torchlight flickers on the elegant marble walls. The sound of a mob echoes in the street. The year is 52 B.C. and the naked body of Publius Clodius is about to be carried through the teaming streets of Rome. Clodius, a rich man turned rabble-rouser, was slain on the most splendid road in the world, the Appian Way. Now Clodius's rival, Milo, is being targeted for revenge and the city teeters on the verge of chaos. An explosive trial will feature the best oration of Cicero and Marc Antony, while Gordianus the Finder has been charged by Pompey the Great himself to look further into the murder. With the Senate House already in ashes, and his own life very much in danger, Gordianus must return to a desrted stretch of the Appian Way - to find the truth that can save a city drunk on power, rent by fear, and filled with the madness and glory of Rome.
It is 48 B.C. For years now, the rival Roman generals Caesar and Pompey have engaged in a contest for world domination. Both now turn to Egypt, where Pompey plans a last desperate stand on the banks of the Nile, while Caesar's legendary encounter with queen Cleopatra will spark a romance that reverberates down the centuries. But Egypt is a treacherous land, torn apart by the murderous rivalry between the goddess-queen and her brother King Ptolemy. Into this hot-house atmosphere of intrigue and deception comes Gordianus the Finder, innocently seeking a cure for his wife Bethesda in the sacred waters of the Nile. But when his plans go awry, he finds himself engaged in an even more desperate pursuit - to prove the innocence of the son he once disowned, who stands accused of murder. The judgment of Caesar will determine the fate of Gordianus's son; the choice Caesar makes between Cleopatra and her brother Ptolemy will determine the future of Rome's empire. At the center of these two dilemmas, Gordianus becomes the unwitting fulcrum that will shift the balance of history. Witness to the death throes of the old world, he is to play a critical role in the birth of the world to come. Drawing scrupulously on historical sources, this is the most ambitious novel yet in Steven Saylor's Roma Sub Rosa series. Saylor presents a bold new vision of Caesar and paints a compelling and original portrait of Cleopatra, amid bloodshed, battles and storms, in a setting of Egyptian magic and mystery.
This updated edition introduces the important aspects of the language and explains the .NET framework. The alphabetical reference covers the functions, statements, directives, objects, and object members that make up the VB .NET language.
This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.
The &"classical,&" Steven Shankman argues, should not be confused with a particular historical period of Western antiquity, although it may owe its original articulation to the literary and philosophical explorations of ancient Greek authors. Shankman's book searches for and attempts to formulate the shape of the continuing presence&—as embodied in particular literary works mainly from Western antiquity and the neoclassical and modern periods&—of what the author calls a &"classical&" understanding of literature. For Shankman, literature, defined from a classical perspective, is a coherent, compelling, and rationally defensible representation that resists being reduced either to the mere recording of material reality or to the bare exemplification of an abstract philosophical precept. He derives his definition largely from his reading of Greek literature from Homer through Plato, from the history of literary criticism, and from the Greco-Roman tradition in English, American, and French literature. Shankman reveals unsuspected yet convincing connections among authors of such widely disparate times and places. His idea of the &"classic&" that authorizes these connections is presented as normative, thus making possible the evaluation of literary works and, in turn, forthright discussion of what constitutes the &"literary&" as distinct from other kinds of discourse. Shankman's study runs counter to a strong tendency of contemporary criticism that argues precisely against any distinct category of the &"literary.&" He offers a series of interpretations that cumulatively advance theoretical discussion by challenging scholars to rethink the critical paradigms of postmodernism. At the center of the book is a discussion of the quintessentially classic Val&éry poem Le Cimeti&ère marin and the classic qualities it shares with Pindar's third Pythian ode, from which Val&éry derives the epigraph for his poem.
The Roman sophist Claudius Aelianus, born in Praeneste in the late second century CE, spent his career cultivating a Greek literary persona. Aelian was a highly regarded writer during his own lifetime, and his literary compilations would be influential for a thousand years and more in the Roman world. This book argues that the De natura animalium, a miscellaneous treasury of animal lore and Aelian's greatest work, is a sophisticated literary critique of Severan Rome. Aelian's fascination with animals reflects the cultural issues of his day: philosophy, religion, the exoticism of Egypt and India, sex, gender, and imperial politics. This study also considers how Aelian's interests in the De natura animalium are echoed in his other works, the Rustic Letters and the Varia Historia. Himself a prominent figure of mainstream Roman Hellenism, Aelian refined his literary aesthetic to produce a reading of nature that is both moral and provocative.
Newly updated for Excel 2002, Writing Excel Macros with VBA, 2nd Edition provides Excel power-users, as well as programmers who are unfamiliar with the Excel object model, with a solid introduction to writing Visual Basic for Applications (VBA) macros and programs for Excel. In particular, the book focuses on: The Visual Basic Editor and the Excel VBA programming environment. Excel features a complete, state-of-the-art integrated development environment for writing, running, testing, and debugging VBA macros. The VBA programming language, the same programming language used by the other applications in Microsoft Office XP and 2000, as well as by the retail editions of Visual Basic 6.0. The Excel object model, including new objects and new members of existing objects in Excel 2002. Excel exposes nearly all of its functionality through its object model, which is the means by which Excel can be controlled programmatically using VBA. While the Excel object model, with 192 objects, is the second largest among the Office applications, you need to be familiar with only a handful of objects to write effective macros. Writing Excel Macros focuses on these essential objects, but includes a discussion of many more objects as well.Writing Excel Macros with VBA, 2nd Edition is written in a terse, no-nonsense manner that is characteristic of Steven Roman's straightforward, practical approach. Instead of a slow-paced tutorial with a lot of handholding, Roman offers the essential information about Excel VBA that you must master to write macros effectively. This tutorial is reinforced by interesting and useful examples that solve common problems you're sure to have encountered.Writing Excel Macros with VBA, 2nd Edition is the book you need to delve into the basics of Excel VBA programming, enabling you to increase your power and productivity.
Nine crime stories featuring Gordianus the Finder, a detective in ancient Rome who marries his slave. Part mystery, part a social history of the period from the end of Sulla's dictatorship to the Spartacan slave revolt.
On the eve of the Ides of March, Gordianus the Finder is directed by newly appointed dictator Julius Caesar to investigate possible conspiracies as the Roman Senate prepares to fight the Parthian Empire.
Steven Saylor's Roma Sub Rosa series of novels, set in the late Roman Republic and featuring Gordianus the Finder, has garnered unusual acclaim from readers and reviewers alike, establishing him as one of the pre-eminent historical crime writers. In A Gladiator Dies Only Once, the second collection of his award-winning stories featuring Gordianus, Saylor more than meets his own high standards. Set during period between the events of his novels Roman Blood and Catalina's Riddle, these previously untold adventures range from twisted search for truth behind a threatening blind item in the Acta Diurna ("The Consul's Wife") and a kidnapping and murder during the revolt of Sertorius ("The White Fawn") to the story behind Cicero's discovery of Archimedes's tomb ("Archimedes Tomb") and a perplexing domestic situation in Gordianus's own home ("If a Cyclops Could Vanish in a Glimpse of an Eye.") These tales from the early career of Gordianus - when his adopted son Eco was still a mute boy and his wife Bethesda was but his slave - will delight Saylor's many fans while illuminating the details of the ancient world like no other writer can.
Visual Basic .NET is a radically new version of Microsoft Visual Basic, the world's most widely used rapid application development (RAD) package. Whether you are just beginning application development with Visual Basic .NET or are already deep in code, you will appreciate just how easy and valuable the VB.NET Language Pocket Reference is.VB.NET Language Pocket Reference contains a concise description of all language elements by category. These include language elements implemented by the Visual Basic compiler, as well as all procedures and functions implemented in the Microsoft.VisualBasic namespace. Use it anytime you want to look up those pesky details of Visual Basic syntax or usage. With concise detail and no fluff, you'll want to take this book everywhere.
As the title suggests, this book has two separate - though intertwined - goals: a description of the general concepts of object-orientation, and how to do object-oriented programming in Visual Basic. Readers are assumed to have no more than a familiarity with Visual Basic and some rudimentary knowledge of programming. Working on this premise, Steve Roman introduces the abstract concepts of object orientation, such as class, abstraction, and encapsulation, and then shows how each is implemented in a meaningful and useful application. He uses a hands-on style throughout: plenty of code is given and discussed, including error-handling. As a result, Visual Basic programmers and students will find this an invaluable introduction to the topic.
In light of modern scepticism towards the practice, it is easy to overlook just how important a role astrology played in the career of Rome's first Emperor, Augustus. Augustus' enthusiasm for employing astrological predictions and symbols to cement his own position of power was matched by an equally forceful desire to restrict their use by his political rivals. Astrology in Rome was, then, to use Tacitus' neat formulation, both "forbidden and maintained" (Tacitus, Histories, 1.22). This volume is the first to take seriously this imperial complex as a key to understanding the diverse ways in which contemporary commentators handle the volatile topic of astrology in their writings. It shows how Roman writers engage in elaborate discourses of discretion as they simultaneously celebrate the power of astrology and shy away from the sort of astrological revelations that might offend imperial sensibilities. With a particular focus on the key astrological poem of Manilius, this study provides a new conceptual framework in which to appreciate the complex treatments of astrology during the period of Octavian/Augustus.
Roman Edessa offers a comprehensive and erudite analysis of the ancient city of Edessa (modern day Urfa, Turkey), which constituted a remarkable amalgam of the East and the West. Among the areas explored are: * the cultural life and antecedents of Edessa * Edessene religion * the extent of the Hellenization at Edessa before the advent of Christianity * the myth of an exchange of letters between a King Abgar and Jesus.
A Town and Country magazine design pick, a monograph of the work of a California lifestyle and interior design firm, from the company’s founders. Commune was established in Los Angeles in 2004 by four like-minded souls—Roman Alonso, Steven Johanknecht, Pamela Shamshiri, and Ramin Shamshiri—with a common mission: to enhance life through design and to blur the lines between disciplines, eras, and styles. California is for those who refuse to conform and who live for freedom of expression, indoor/outdoor living, and that golden sunshine glinting off the waves of the Pacific. Commune perfectly captures this spirit and embodies a new California style that freely mixes old and new in its layered, highly personal interiors that embrace color, pattern, and texture. This book is the first monograph of Commune’s work, featuring its designs for private residences, hotels, commercial spaces, and restaurants, as well as the works they specially commission from virtually everyone in the artisan craftsman movement in California today. “Heavyweight Champs—Our picks from this year’s tempting crop of design books. Commune highlights work by the Los Angeles design group, known for its bohemian-chic approach to houses, hotels (such as LA’s Ace), and home products.” ―Town & Country Magazine
This edition’s selected passages from Tacitus’ historical and minor works give a sample of a Latin author acknowledged as one of the most difficult—and also the most rewarding. Rutledge presents a Tacitus he unapologetically terms “the greatest of the Roman historians” in reading selections that highlight major subjects and themes: the corruption of power, confrontation with barbarians, and narratives of historically significant episodes, many marked by the era’s signature violence, promiscuity, and murderous death. Tacitus’ stylistic brilliance likewise finds its due here: his powerful language, vivid character portrayal, use of speeches, and the authority he claims for himself as historian. The commentary addresses problems Tacitean syntax and grammar may pose for readers new to the author, and helps to situate Tacitus among other Roman historians.
A compelling storyteller, with a striking talent for historical reconstruction' Mary Beard A.D. 165: The empire of Rome has reached its pinnacle. Pax Roma reigns from Britannia to Egypt, from Gaul to Greece. Emperor Marcus Aurelius oversees a golden age and the ancient Pinarius family of artisans embellish the greatest city on Earth with gilded statues and towering marble monuments. But history does not stand still. The years to come bring wars, plagues, fires, and famines. The best emperors in history are succeeded by some of the worst. Barbarians descend, eventually appearing before the gates of Rome itself. Chaos engulfs the empire. Through it all, the Pinarius family endures, thanks in no small part to the fascinum, a protective talisman older than Rome itself, handed down through countless generations. But on the fringes of society, a band of troublesome cultists disseminate dangerous and seditious ideas. They call themselves Christians. Some emperors deal with the Christians with toleration, others with bloody persecution. Then one emperor does the unthinkable. He becomes a Christian himself and the revolution he sets in motion will change the world forever. Spanning 160 years and seven generations, teeming with some of ancient Rome's most vivid figures, Saylor's epic brings to vivid life some of the most tumultuous chapters of human history, events which reverberate still. Praise for Steven Saylor: 'Saylor expertly weaves the true history of Rome with the lives and loves of its fictional citizens.' Daily Express 'Saylor's scholarship is breathtaking and his writing enthrals' Ruth Rendell 'With the scalpel-like deftness of a Hollywood director, Saylor puts his finger on the very essence of Roman history.' Times Literary Supplement 'Readers will find his work wonderfully (and gracefully) researched... this is entertainment of the first order.' Washington Post 'Saylor's scholarship is breathtaking and his writing enthrals' Ruth Rendell 'The most reliably entertaining and well-researched novels about the ancient world [are] Steven Saylor's tales of the Roman proto-detective Gordianus the Finder. The Throne of Caesar brings the series to a satisfying conclusion [and offers] a new, compelling perspective on familiar historic events' Sunday Times
The Latin inscriptions in the Kelsey Museum are among the best primary sources we have for documenting the lives of the lower classes in the Roman world. They provide unique evidence of the details of Roman daily life, including beliefs, occupations, families, and attitudes toward death. The 400 entries in this volume include all of the Latin inscriptions on stone or metal in the Kelsey Museum of Archaeology at the University of Michigan; they represent the largest, and arguably the most important, collection of Latin inscriptions in the Western Hemisphere. The collection is notable not just for its size but for the fact that almost all the inscriptions were acquired by purchase for their scholarly and educational value to the members of the university community. Because of this, the collection is also an important testimony to a seminal phase in the development of the study of Classics at the University of Michigan. For the first time ever, this project makes the Latin inscriptions of the Kelsey available in one volume and has provided an opportunity to reexamine some texts that have not been edited in over a century. The commentaries for this edition have benefited from a wealth of recent scholarship resulting in some amended readings and reidentification of texts. Steven L. Tuck is Assistant Professor of Classics at Miami University of Ohio. The Kelsey Museum Studies series, edited by University of Michigan professors Elaine Gazda, Margaret Cool Root, and John Pedley, is designed to publish unusual material in the Museum's collections, together with reports of current and past archaeological expeditions sponsored by the University of Michigan.
Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.
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