Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.

Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

In this book, Reiner Schürmann argues that what is most original about Marx is his philosophical axis. Extending his highly original engagement with the history of philosophy, Schürmann draws out this axis, which determines and localizes his theories of history, social relations, and economy. Whereas Marxist readings of Marx conceive history, classes, and social relations as primary realities, Schürmann brings out a radically immanent understanding of praxis that introduces multiplicity. This edition is complemented by a reprinting of Schürmann's Anti-Humanism essay, in which he reads Marx alongside Nietzsche and Heidegger as spelling out the dissociation of being and action. Reading Marx showcases underappreciated facets of Schürmann's work and offers an interpretation of Marx that resonates with the readings of Jacques Derrida, Michel Henry, Antonio Negri, and François Laruelle.

This book weaves together Reiner Schürmann's work on art and politics, drawing on a range of the most important thinkers and poets of the twentieth century and beyond. The Place of the Symbolic gathers Reiner Schürmann's essays on the nexus of art and politics. In keeping with his translation of the destruction of metaphysics into an anarchic philosophy of practice, Schürmann develops a radical theory of the place of symbols, irreducible either to idealist theories of symbols or structuralist accounts of the symbolic. Symbols, Schürmann argues, may provide a bridge between ontological difference and politics. They resist being grasped metaphysically, in terms of representation. Instead, their understanding requires a specific way of existence: attending to the coming-to-presence of phenomena. As such, the understanding of symbols discloses a form of praxis that abandons ultimate grounds and opens onto the manifold. Alongside Schürmann's theory of symbols, the collection includes essays on the relation between metaphysics, tragedy, and technology; on the "there is" in poetry; as well as on judgment. Throughout these characteristically lucid interventions, Schürmann's most urgent concern remains a consideration of singular and finite practices that enact a release from universal principles. Art and politics appear here as the unworking of ultimate grounds; that is, as practices attuned to a truly groundless form of life.

See and celebrate the multilayered grandeur conveyed by the first chapter of Genesis The first chapter of the Bible's first book lays the foundation for all that follows about who God is and what God is like. Our technology-age fascination with the science of origins, however, can blind us to issues of great importance that don't address our culturally conditioned questions. Instead, Genesis One itself suggests the questions and answers that are most significant to human faith and flourishing. Geologist Gregg Davidson and theologian Ken Turner shine a spotlight on Genesis One as theologically rich literature first and foremost, exploring the layers of meaning that showcase various aspects of God's character: Song Analogy Polemic Covenant Temple Calendar Land Our very knowledge of God suffers when we fail to appreciate the Bible's ability to convey multilayered truth simultaneously. The Manifold Beauty of Genesis One offers readers the chance to cultivate an openness to Scripture's richness and a deeper faith in the Creator.