All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.
...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL
Littlewood's Miscellany, which includes most of the earlier work as well as much of the material Professor Littlewood collected after the publication of A Mathematician's Miscellany, allows us to see academic life in Cambridge, especially in Trinity College, through the eyes of one of its greatest figures. The joy that Professor Littlewood found in life and mathematics is reflected in the many amusing anecdotes about his contemporaries, written in his pungent, aphoristic style. The general reader should, in most instances, have no trouble following the mathematical passages. For this publication, the new material has been prepared by Béla Bollobás; his foreword is based on a talk he gave to the British Society for the History of Mathematics on the occasion of Littlewood's centenary.
Prepared by an international team of eminent atmospheric scientists, Mechanisms of Atmospheric Oxidation of the Oxygenates is an authoritative source of information on the role of oxygenates in the chemistry of the atmosphere. The oxygenates, including the many different alcohols, ethers, aldehydes, ketones, acids, esters, and nitrogen-atom containing oxygenates, are of special interest today due to their increased use as alternative fuels and fuel additives. This book describes the physical properties of oxygenates, as well as the chemical and photochemical parameters that determine their reaction pathways in the atmosphere. Quantitative descriptions of the pathways of the oxygenates from release or formation in the atmosphere to final products are provided, as is a comprehensive review and evaluation of the extensive kinetic literature on the atmospheric chemistry of the different oxygenates and their many halogen-atom substituted analogues. This book will be of interest to modelers of atmospheric chemistry, environmental scientists and engineers, and air quality planning agencies as a useful input for development of realistic modules designed to simulate the atmospheric chemistry of the oxygenates, their major oxidation products, and their influence on ozone and other trace gases within the troposhere.
Ozone, an important trace component, is critical to life on Earth and to atmospheric chemistry. The presence of ozone profoundly impacts the physical structure of the atmosphere and meteorology. Ozone is also an important photolytic source for HO radicals, the driving force for most of the chemistry that occurs in the lower atmosphere, is essential to shielding biota, and is the only molecule in the atmosphere that provides protection from UV radiation in the 250-300 nm region. However, recent concerns regarding environmental issues have inspired a need for a greater understanding of ozone, and the effects that it has on the Earth's atmosphere. The Mechanisms of Reactions Influencing Atmospheric Ozone provides an overview of the chemical processes associated with the formation and loss of ozone in the atmosphere, meeting the need for a greater body of knowledge regarding atmospheric chemistry. Renowned atmospheric researcher Jack Calvert and his coauthors discuss the various chemical and physical properties of the earth's atmosphere, the ways in which ozone is formed and destroyed, and the mechanisms of various ozone chemical reactions in the different spheres of the atmosphere. The volume is rich with valuable knowledge and useful descriptions, and will appeal to environmental scientists and engineers alike. A thorough analysis of the processes related to tropospheric ozone, The Mechanisms of Reactions Influencing Atmospheric Ozone is an essential resource for those hoping to combat the continuing and future environmental problems, particularly issues that require a deeper understanding of atmospheric chemistry.
This volume covers the years 1483-1558, a period of immense social, political, and intellectual changes, which profoundly affected the law and its workings. It first considers constitutional developments, and addresses the question of whether there was a rule of law under king Henry VIII. In a period of supposed despotism, and enhanced parliamentary power, protection of liberty was increasing and habeas corpus was emerging. The volume considers the extent to which the law was affected by the intellectual changes of the Renaissance, and how far the English experience differed from that of the Continent. It includes a study of the myriad jurisdictions in Tudor England and their workings; and examines important procedural changes in the central courts, which represent a revolution in the way that cases were presented and decided. The legal profession, its education, its functions, and its literature are examined, and the impact of printing upon legal learning and the role of case-law in comparison with law-school doctrine are addressed. The volume then considers the law itself. Criminal law was becoming more focused during this period as a result of doctrinal exposition in the inns of court and occasional reports of trials. After major conflicts with the Church, major adjustments were made to the benefit of clergy, and the privilege of sanctuary was all but abolished. The volume examines the law of persons in detail, addressing the impact of the abolition of monastic status, the virtual disappearance of villeinage, developments in the law of corporations, and some remarkable statements about the equality of women. The history of private law during this period is dominated by real property and particularly the Statutes of Uses and Wills (designed to protect the king's feudal income against the consequences of trusts) which are given a new interpretation. Leaseholders and copyholders came to be treated as full landowners with rights assimilated to those of freeholders. The land law of the time was highly sophisticated, and becoming more so, but it was only during this period that the beginnings of a law of chattels became discernible. There were also significant changes in the law of contract and tort, not least in the development of a satisfactory remedy for recovering debts.
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
In Science in Action, John Lenihan shares his irrepressible enthusiasm for science. With characteristic wit and humor, he explains how science affects our daily lives in diverse areas such as medicine, poetry, politics, the environment, and the paranormal-cheerfully debunking some popular pseudo-scientific myths along the way. John Fleming's delightful cartoons add wry comment to the text, making this a book enjoyable to read time and again.
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
A great theater critic brings twentieth-century playwright Arthur Miller’s dramatic story to life with bold and revealing new insights “New Yorker critic Lahr shines in this searching account of the life of playwright Arthur Miller. . . . It’s a great introduction to a giant of American letters.”—Publishers Weekly Distinguished theater critic John Lahr brings unique perspective to the life of Arthur Miller (1915–2005), the playwright who almost single-handedly propelled twentieth-century American theater into a new level of cultural sophistication. Organized around the fault lines of Miller’s life—his family, the Great Depression, the rise of fascism, Elia Kazan and the House Committee on Un-American Activities, Marilyn Monroe, Vietnam, and the rise and fall of Miller’s role as a public intellectual—this book demonstrates the synergy between Arthur Miller’s psychology and his plays. Concentrating largely on Miller’s most prolific decades of the 1940s, 1950s, and 1960s, Lahr probes Miller’s early playwriting failures; his work writing radio plays during World War II after being rejected for military service; his only novel, Focus; and his succession of award-winning and canonical plays that include All My Sons, Death of a Salesman, and The Crucible, providing an original interpretation of Miller’s work and his personality.
The fourth edition of this, the 'first' textbook of palliative care, continues to provide a concise, but authoritative, guide to the provision of palliative care. The text has been thoroughly revised and reorganized throughout to reflect the recent pace of change in this rapidly moving field.Coverage is comprehensive, ranging from symptom control t
The Memoirs of John Douglas Forbes encompass watching the streetlamp lighters of San Francisco in 1912, to visiting the Royal Crescent in Bath in 2001, among many other memories. Art curator, educator, First Professor of the Darden School of the University of Virginia; hiker, kite flyer and traveler, who made a second family with the new wife he found through placing a Personal Ad in a magazine after becoming a widower --- John Douglas Forbes followed an unusual path. M.E. Forbes, in An Afterword to the Memoirs, speaks of the 38-year “May-December” journey she shared with Dr. Forbes.
While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental mathematics on the one hand and computerized formal proofs on the other hand. The main theses of Rigor and Structure are that the features of mathematical practice that a large group of philosophers of mathematics, the structuralists, have attributed to the peculiar nature of mathematical objects are better explained in a different way, as artefacts of the manner in which the ancient ideal of rigor is realized in modern mathematics. Notably, the mathematician must be very careful in deriving new results from the previous literature, but may remain largely indifferent to just how the results in the previous literature were obtained from first principles. Indeed, the working mathematician may remain largely indifferent to just what the first principles are supposed to be, and whether they are set-theoretic or category-theoretic or something else. Along the way to these conclusions, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed.
Reprint of the original, first published in 1872. The publishing house Anatiposi publishes historical books as reprints. Due to their age, these books may have missing pages or inferior quality. Our aim is to preserve these books and make them available to the public so that they do not get lost.
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