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This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories. Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1

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A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients - with two operations, addition and multiplication. This book guides readers from basic concepts to Noetherian rings, one of the most important classes of commutative rings and beyond.

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Kinematical problems of both classical and quantum mechanics are considered in these lecture notes ranging from differential calculus to the application of one of Chernoff's theorems. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the

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Teaches how simple mathematics can help formulate and solve real problems of research interest in a range of fields, including biology, ecology, computer science, geophysics, engineering, and the social sciences. This book also includes traditional modeling topics such as predator-prey interaction, harvesting, and wars of attrition.

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There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application

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A study of the properties of manysided figures and their ability to deform, twist, and stretch without changing their shape. It offers an in-depth introduction to the field, providing explanations of what would today be considered the basic tools of algebraic topology.

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The description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), will be forthcoming.

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Topological analysis consists of those basic theorems of analysis which are essentially topological in character, developed and proved entirely by topological and pseudotopological methods. The objective of this volume is the promotion, encouragement, and stimulation of the interaction between topology and analysis-to the benefit of both. Original

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This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is

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The description for this book, Topological Methods in the Theory of Functions of a Complex Variable. (AM-15), will be forthcoming.

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One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of t

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During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincare on the Poincare conjectures, and sketching a proof of Haken's main result.

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Takes the reader from the late nineteenth century to the aftermath of Abu Ghraib, from slavery and the electric chair to electrotorture in American inner cities, and from French and British colonial prison cells and the Spanish-American War to the fields of Vietnam, the wars of the Middle East, and the democracies of Latin America and Europe.

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Eclipses have captured attention and sparked curiosity about the cosmos since the first appearance of humankind. Having been blamed for everything from natural disasters to the fall of kings, they are now invaluable tools for understanding many celestial as well as terrestrial phenomena. This clear, easy-to-understand guide explains what causes tot

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Presents a study of the theory of totally nonnegative matrices, defined by the nonnegativity of subdeterminants. This title explores methodological background, historical highlights of key ideas, and specialized topics.