The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation — Classical Theory; Fourier Approximation — Modern Theory; and Exponential Approximation.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    These provide the basis for a detailed critical study of the principal individual thinkers of the time. Besides serving as an essential text for undergraduate and graduate courses in Greek philosophy and in the history of science, this book will appeal to a wide range of readers with interests in philosophy, theology, the history of ideas and of the ancient world, and indeed to anyone who wants an authoritative account of the Presocratics.

    Remarkable for his range of thought and his mastery of treatment, Archimedes addressed such topics as the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the measurement of a circle; the properties of conoids, spheroids, and spirals; and the quadrature of the parabola. This edition offers an informative introduction with many valuable insights into the ancient mathematician's life and thought as well as the views of his contemporaries. Modern mathematicians, physicists, science historians, and logicians will find this volume a source of timeless fascination.

    Purchasers are entitled to a free trial membership in the General Books Club where they can select from more than a million books without charge. Subjects: Astronomy; History / General; Juvenile Nonfiction / Science

    No qualifications. Go out and buy it everybody."Kenneth Rexroth, The Nation"The translations deliberately avoid the highly wrought and affectedly poetic; their idiom is contemporary....They have life and speed and suppleness of phrase."Times Education Supplement"These translations belong to our time. A keen poetic sensibility repeatedly quickens them; and without this inner fire the most academically flawless rendering is dead."Warren D. Anderson, American Oxonian"The critical commentaries and the versions themselves...are fresh, unpretentious, above all, functional."Commonweal"Grene is one of the great translators."Conor Cruise O'Brien, London Sunday Times"Richmond Lattimore is that rara avis in our age, the classical scholar who is at the same time an accomplished poet."Dudley Fitts, New York Times Book Review

    

    Later he did considerable public service there, and otherwise devoted himself to poetry and to society. Famous at first, he offended the emperor Augustus by his Ars Amatoria, and was banished because of this work and some other reason unknown to us, and dwelt in the cold and primitive town of Tomis on the Black Sea. He continued writing poetry, a kindly man, leading a temperate life. He died in exile. Ovid's main surviving works are the Metamorphoses, a source of inspiration to artists and poets including Chaucer and Shakespeare; the Fasti, a poetic treatment of the Roman year of which Ovid finished only half; the Amores, love poems; the Ars Amatoria, not moral but clever and in parts beautiful; Heroides, fictitious love letters by legendary women to absent husbands; and the dismal works written in exile: the Tristia, appeals to persons including his wife and also the emperor; and similar Epistulae ex Ponto. Poetry came naturally to Ovid, who at his best is lively, graphic and lucid. The Loeb Classical Library edition of Ovid is in six volumes.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Mingling acute observation with often wild speculation, it offers a fascinating view of the world as it was understood in the first century AD, whether describing the danger of diving for sponges, the first water-clock, or the use of asses’ milk to remove wrinkles. Pliny himself died while investigating the volcanic eruption that destroyed Pompeii in AD 79, and the natural curiosity that brought about his death is also very much evident in the Natural History — a book that proved highly influential right up until the Renaissance and that his nephew, Pliny the younger, described ‘as full of variety as nature itself’. John F. Healy has made a fascinating and varied selection from the Natural History for this clear, modern translation. In his introduction, he discusses the book and its sources topic by topic. This edition also includes a full index and notes.

    J. Ayer in a fabled debate about the existence of God and the possibility of metaphysics, knew that seminary students were fed a woefully inadequate diet of theses and proofs, and that their familiarity with most of history's great thinkers was reduced to simplistic caricatures. Copleston set out to redress the wrong by writing a complete history of Western philosophy, one crackling with incident and intellectual excitement -- and one that gives full place to each thinker, presenting his thought in a beautifully rounded manner and showing his links to those who went before and to those who came after him. The result of Copleston's prodigious labors is a history of philosophy that is unlikely ever to be surpassed. Thought magazine summed up the general agreement among scholars and students alike when it reviewed Copleston's A History of Philosophy as "broad-minded and objective, comprehensive and scholarly, unified and well proportioned... We cannot recommend [it] too highly."