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Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics."  Bulletin of the American Mathematical Society.

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"The text is very clearly written [with] many illustrative examples and exercises [and] should be considered by those instructors who would like to introduce a more modern (and a more logical) approach in a basic course in statistics." Journal of the American Statistical AssociationThis volume is a well-known, well-respected introduction to a lively area of statistics. Professors Chernoff and Moses bring years of professional expertise as classroom teachers to this straightforward approach to statistical problems. And happily, for beginning students, they have by-passed involved computational reasonings which would only confuse the mathematical novice.Developed from nine years of teaching statistics at Stanford, the book furnishes a simple and clear-cut method of exhibiting the fundamental aspects of a statistical problem. Beginners will find this book a motivating introduction to important mathematical notions such as set, function and convexity. Examples and exercises throughout introduce new topics and ideas.The first seven chapters are recommended for beginning courses in the basic ideas of statistics and require only a knowledge of high school math. These sections include material on data processing, probability and random variables, utility and descriptive statistics, uncertainty due to ignorance of the state of nature, computing Bayes strategies and an introduction to classical statistics. The last three chapters review mathematical models and summarize terminology and methods of testing hypotheses. Tables and appendixes provide information on notation, shortcut computational formulas, axioms of probability, properties of expectations, likelihood ratio test, game theory, and utility functions.Authoritative, yet elementary in its approach to statistics and statistical theory, this work is also concise, well-indexed and abundantly equipped with exercise material. Ideal for a beginning course, this modestly priced edition will be especially valuable to those interested in the principles of statistics and scientific method.

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The Origins of Cauchy's Rigorous Calculus

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This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 edition.

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Nonlinear equations have existed for hundreds of years; their systematic study, however, is a relatively recent phenomenon. This volume, together with its companion, Nonlinear Mathematics (Dover 64233-X), provides exceptionally comprehensive coverage of this recently formed area of study. It encompasses both older and more recent developments in the field of equations, with particular emphasis on nonlinear equations because, as Professor Saaty, maintains, "that is what is needed today."Together the two volumes cover all the major types of classical equations (except partial differential equations, which require a separate volume). This volume includes material on seven types: operator equations, functional equations, difference equations, delay-differential equations, integral equations, integro-differential equations and stochastic differential equations. Special emphasis is placed on linear and nonlinear equations in function spaces and on general methods of solving different types of such equations.Above all, this book is practical. It reviews the variety of existing types of equations and provides methods for their solution. It is meant to help the reader acquire new methods for formulating problems. Its clear organization and copious references make it suitable for graduate students as well as scientists, technologists and mathematicians."...a welcome contribution to the existing literature..."  Math. Reviews.

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Elementary Quantum Chemistry, Second Edition

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As the author notes in the Preface to this valuable text, experimental chemists have moved past studying the average behavior of atoms or molecules "to probe the step-by-step behavior of individual atoms and molecules as they collide, form 'transition states,' and ultimately form products." In such experiments, quantum mechanical computations do two useful tasks: They fill in the observational gaps and help to interpret what has been observed.This introductory course  developed by the former chairman of the chemistry department at the University of New Hampshire  covers, among other topics, the origins of the quantum theory, the Schrodinger wave equation, the quantum mechanics of simple systems, the rigid rotator, the hydrogen atom, electron spin and many-electron systems, the quantum states of atoms, the Hartree-Fock self-consistent field method, the electronic structure of molecules, and semi-empirical molecular orbital methods. One of the great values of the course is its calculations and diagrams, which were created specifically for this text and which students will be able to replicate on their home computers.The text will be most useful for advanced undergraduate or beginning graduate students who have had calculus and at least a year of undergraduate physics. A knowledge of differential equations, linear algebra, and atomic physics is helpful but not essential. Seven appendices give a concise exposition of mathematical and physical material that may not be part of the students' background.

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Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to game theory. It opens with the theory of two-person zero-sum games, two-person non-zero sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory books. Succeeding sections focus on a variety of applications  including introductory explanations of gaming and meta games  that offer nonspecialists information about new areas of game theory at a comprehensible level. Numerous exercises appear with full solutions, in addition to an extensive bibliography, 80 problems with worked solutions, and over 30 illustrations useful for the theory of non-zero and n-person games. 1986 edition.

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An Introduction to the Theory of the Boltzmann Equation

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Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmanns equation, including representative applications using both Boltzmanns equation and the model Boltzmann equations developed within the text. It emphasizes physical aspects of the theory, and it represents a practical resource for researchers and other professionals. The problems following each chapter are intended as learning examples, and they frequently extend and generalize the text material. Additional editorial features include a historical introduction, references, and subject and author indexes. 1971 edition.

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This book illustrates basic practical applications of optical principle. Working models of telescopes, microscopes, photographic lenses, and optical projection systems are diagrammed and explained in full, as are the basic experiments for determining accuracy, power, angular field of view, amount of aberration, and all other necessary facts about the instrument. Throughout the book, only elementary mathematics is used, for the benefit of the student and the beginner in the field of optics.The author, an assistant professor at the Imperial College of Science and Technology in London, shows how to set up working models of each of the four types of instruments named above, so that the reader can see for himself the effects of changing the focal length, using different types of lenses, rotating the lens, and other experiments. He also includes a number of experiments to illustrate theoretical principles such as the reflection and refraction of light and focal length measurements of concave and convex lenses.A chapter on the human eye follows, and the author explains how to set up a simple working model of the eye in order to illustrate myopia, astigmatism, hypermetropia, and the visual acuity of the eye. Professor Johnson concludes with an important chapter on the working and testing of optical glass, in which he describes the roughing of lenses, the principles of the grinding and polishing processes, abrasives, edging, angle measurement, and other important steps in the production of optical glass. An appendix is included on the cleaning of glass surfaces, silvering, photographic items, developers, collodion films, and waxes and cements used for various purposes in optical work.This is a valuable work for the student and the amateur hobbyist as well as for many who use optical instruments in science and industry. It is written clearly and economically, with the needs of the practical worker in the field of optics held constantly in mind.

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This first integrated treatment of the main ideas behind Rene Thom's theory of catastrophes aims to make them accessible to scientists wishing to apply the theory in their own fields of research. The mathematical basis of the theory is therefore explained with a minimum of technicalities, although some knowledge of the calculus of variables is assumed.Thom's now-famous list of seven elementary catastrophes, broadly classifying various types of discontinuous change, is elucidated, as are the reasons for its appearance. Nearly half the book concentrates on detailed applications of the theory, emphasizing its uses in the physical sciences where applications can be made quantitative and can be experimentally verified. The more controversial and speculative applications to areas in the social sciences are also mentioned, but not discussed in detail.Over 200 illustrations help clarify the ideas and applications in this volume, which will be of interest to researchers and postgraduate students in such diverse disciplines as engineering, mathematics, physics, and biology. 1978 edition. Bibliography.

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Since its inception modern geology has been faced with an important group of problems: explaining parallel formations that are separated by great distances of sea; accounting for isolated life forms in widely separated areas (such as lemurs in Madagascar and India); explaining pre-pleistocene glaciations, and similar problems. The usual explanation has been to assume the one-time existence of land bridges (such as the hypothetical Lemuria) or parallelisms or diffusion with lost intermediary steps.In 1915, however, one of the most influential and most controversial books in the history of science provided a new solution. This was Alfred Wegener's Entstehung der Kontinente, which dispensed with land bridges and parallel evolutions and offered a more economical concept. Wegener proposed that in the remote past the earth's continents were not separate (as now), but formed one supercontinent which later split apart, the fragments gradually drifting away from one another. Wegener created his supercontinent with attractive simplicity by tucking the point of South America into the Gulf of Guinea, coalescing North America, Greenland, and Europe, rotating Australia and Antarctica up through the Indian Ocean, and closing the remaining gaps. Wegener then explained various phenomena in historical geology, geomorphy, paleontology, paleoclimatology, and similar areas of science in terms of this continental drift. To back up his revolutionary theory he drew upon a seemingly inexhaustible find of data. Later editions of his book added new data to refute his opponents or to strengthen his own views in the violent scientific quarrel that arose.Even today this important question remains undecided, and geologists are divided into strongly opposed groups about the Wegener hypothesis. At the moment it seems to be gaining steadily in acceptance. It is one of the two basic theories of earth history, and since it has often been misrepresented in summary, every earth scientist owes it to himself to examine its theories and data.

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"An unsurpassed account of the historical background  literary, cultural, and intellectual as well as political and socialagainst which Blake worked and to which he responded as engraver, painter, and poet."  English Language Notes.For many years, William Blake was seen as a brilliant eccentric on the fringes of English literature and art. In the twentieth century, however, he came to be regarded as one of the greatest English poets and painters, one whose insights have profoundly influenced such thinkers as Nietzsche, Freud, and D. H. Lawrence.In this volume, a leading Blake scholar shows how the political and social events and movements of the eighteenth and early nineteenth centuries influenced or inspired many of Blake's finest poems: "America," "Europe," "The Marriage of Heaven and Hell," "The French Revolution," "Songs of Innocence and of Experience," "The Four Zoas," and numerous others. While Blake's poems can be read on many levels, this in-depth critical study demonstrates that much of the strange symbolism of this poetry represents a literary campaign against the political tyranny of the day.For the third edition, David Erdman added much new material that came to light after the original publication of the book in 1954. Also included are over 30 illustrations, a Chronology, an Appendix of Additions and Revisions, and other materials. Written for students, scholars, and Blake specialists  anyone interested in the relationship of the poet's extraordinary symbolism and complex thought to the history of his own times  Erdman's meticulously documented study is the definitive treatment of this aspect of Blake's work and is unlikely to be superseded."For our sense of Blake in his own times we are indebted to David Erdman more than anyone else."  Times Literary Supplement.Dover (1991) republication of the third (1977) edition of Blake: Prophet Against Empire: A Poet's Interpretation of the History of His Own Times, Princeton University Press, Princeton, New Jersey, 1954.

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Religious Art in France of the Thirteenth Century

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The art in medieval cathedrals, in addition to its profound aesthetic appeal, told unlettered churchgoers a series of morality tales. From divine creation to the lives of the saints, the stone sculpture and stained glass windows provided dramatic illustrations of the key elements of Christian doctrine. Unfortunately, the true meaning of these religious artworks was gradually obscured by time. In 1913, however, this brilliant study appeared, clarifying and illuminating the original ideas and concepts behind the sacred art of the Middle Ages. The book was hailed by Bernard Berenson as "the most illuminating, the most informing and the most penetrating book on the subject."Focusing on the 13th century as the apotheosis of the medieval style, Male, a noted art historian, explains that the decorative features of French cathedrals served as testimonials of religious faith. His topics include medieval iconography, bestiaries, illustrated calendars, representations of the virtues and vices, symbolic windows, saints, the gospels, secular history, and many other aspects of medieval religious art. This groundbreaking work, enhanced with 190 illustrations that buttress the points made in the text, remains unsurpassed in its style and brilliant synthesis of many disparate elements of the topic.

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Classic biography of the great Victorian poet, designer and socialist. Published a few years after Morris death, it chronicles his childhood, days at Oxford, forays into art and literature, embrace of socialism, involvement with the Arts and Crafts movement, founding of the Kelmscott Press, much more. 22 black-and-white illus.

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Astronomy as a science began with the Ionian philosophers, with whom Greek philosophy and mathematics also began. While the Egyptians and Babylonians had accomplished much of astronomical worth, it remained for the unrivalled speculative genius of the Greeks, in particular, their mathematical genius, to lay the foundations of the true science of astronomy. In this classic study, a noted scholar discusses in lucid detail the specific advances made by the Greeks, many of whose ideas anticipated the discoveries of modern astronomy.Pythagoras, born at Samos about 572 B.C., was probably the first to hold that the earth is spherical in shape, while his later followers anticipated Copernicus with the then-startling hypothesis that the earth was not the center of the universe but a planet like the others. Heraclides of Pontus (c. 388315 B.C.), a pupil of Plato, declared that the apparent daily rotation of the heavenly bodies is due, not to a rotation of the heavenly sphere about an axis through the center of the earth, but to the rotation of the earth itself around its own axis. Secondly, Heraclides discovered that Venus and Mercury revolve around the sun like satellites. Perhaps the greatest astronomer of antiquity was Hipparchus, who flourished between 161 and 126 B.C. He compiled a catalog of fixed stars to the number 850 or more, made great improvements in the instruments used for astronomical observations, and discovered the precession of the equinoxes, among other accomplishments. The astronomy of Hipparchus takes its definitive form in the Syntaxis (commonly called the Almagest) of Ptolemy, written about A.D. 150, which held the field until the time of Copernicus.The extraordinary achievements of these and many more Greek theorists are given full coverage in this erudite account, which blends exceptional clarity with a readable style to produce a work that is not only indispensable for astronomers and historians of science but easily accessible to science-minded lay readers.

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Concerned strictly with the principles and formalism of quantum mechanics, this graduate student-oriented volume develops the subject as a fundamental discipline. Opening chapters review the origins of Schrodinger's equations and the nature of the solutions in certain simple and well-known cases, advancing to the ideas associated with vector spaces. Having provided students with the appropriate mathematical language, the author proceeds to the formulation of the main principles of quantum mechanics and their immediate consequences. The book concludes with final generalizations in which alternative "languages" or representations are discussed  each with reference to its specific advantages and applications  and the Dirac transformation theory is developed and explained.

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"Analytical Fracture Mechanics should prove to be a valuable resource to both the new student and the experienced researcher in fracture mechanics. It is recommended."  Applied Mechanics ReviewOne of the central concerns of engineering is the failure of materials. Addressing this concern, fracture mechanics  an interdisciplinary subject spanning mechanical, civil, and materials engineering, applied mathematics, and physics  predicts the conditions under which such failure will occur due to crack growth. This valuable self-contained text by an expert in the field supplements standard fracture mechanics texts by focusing on analytical methods for determining crack-tip stress and strain fields.Following a comprehensive 120-page introduction  which provides all the background necessary for understanding the remaining chapters  the book is organized around a series of elastoplastic and hydrogen-assisted crack-tip problems and their solutions. The first chapter presents the only proven solution technique for the second order nonlinear partial differential equation governing a mode I elastoplastic crack problem. Other chapters deal with plastic zone transitions, environmental cracking, and small-scale yielding versus exact linear elastic solutions.One of the excellent features of this book is the clarity with which groups of problems are presented and related to each other. Another is the careful attention it gives to the various modes of fracture (I, II, and III) and to showing the circumstances under which information from a solution for one mode may be used to infer information in another mode. For this edition, the author has added a new appendix, "Stress Across an Elastoplastic Boundary of a Mode I Crack: Parabolic to Hyperbolic Plasticity Transition."

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Twenty-five art-related essays by distinguished British art critic and painter reveal his wide-ranging interests. Writings explore relationships between ancient and modern art and between art and life, examining such diverse topics as the art of the Bushmen, African sculpture, ancient American art, Giotto and the art of Florence, the paintings of Durer, El Greco and William Blake, the drawings of Aubrey Beardsley, the works of Paul Cezanne, and contemporary domestic architecture. Also includes Fry's most important theoretical statement, his "Essay in Aesthetics." 13 black-and-white illustrations.

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Noted artist, author and educator shows how to draw every major outdoor subject  land, greenery, skies, building, people, cities, and more  in all the major drawing media: pencils, pen and ink, brush and ink, felt pens, charcoal, Rembrandt to Wyeth. Over 100 illustrations.

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Monograms are immensely useful and eye catching visual devices consisting of two or more letters interwoven in artistic harmony. They lend themselves to numerous graphic applications: stationery, fabrics, advertising, book illustration, greeting cards, posters, menus, logos  virtually any project requiring symbolic or high-recognition lettering.The present volume offers graphic designers an unusually comprehensive collection of contemporary monograms  over 1,300 attention-getting designs, arranged alphabetically for convenience. Each letter of the alphabet is combined with every other letter, creating a versatile archive of monograms in an incredible array of type styles: 3-D, shaded, calligraphic, Gothic, ribbon, block, cartoon, script, Oriental, digital letters, and hundreds of others. Moreover, many monograms appear in more than one style for added flexibility.In addition to an enormous variety of typefaces, the monograms embody numerous spacing variations: overlapping, interlocking, and various other arrangements that offer the utmost versatility to designers. You'll also find a useful selection of monograms incorporated into larger illustrations: a necktie, automobile, tote bag, coffee mug, and other familiar objects.Graphic artists, illustrators, typographers, and students will find this collection indispensable  a nearly inexhaustible array of imaginative lettering configurations, arranged for maximum convenience  ready to solve a myriad of design problems. Best of all, every monogram is royalty-free  ready to use without any prior permission or fee.

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Skeletal structure, muscles, heads, special features. Exhaustive text, anatomical figures, undraped photos. Male and female. 337 illustrations.