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Book Synopsis Vector Bundles and Their Applications by : Glenys Luke
Download or read book Vector Bundles and Their Applications written by Glenys Luke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.
Book Synopsis Mathematical Structures by : Joachim Hilgert
Download or read book Mathematical Structures written by Joachim Hilgert and published by Springer Nature. This book was released on with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry and Mathematical Physics by : Gerd Rudolph
Download or read book Differential Geometry and Mathematical Physics written by Gerd Rudolph and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Book Synopsis Positivity in Algebraic Geometry II by : R.K. Lazarsfeld
Download or read book Positivity in Algebraic Geometry II written by R.K. Lazarsfeld and published by Springer. This book was released on 2017-07-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two volume work containing a contemporary account on "Positivity in Algebraic Geometry". Both volumes also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete". A good deal of the material has not previously appeared in book form. Volume II is more at the research level and somewhat more specialized than Volume I. Volume II contains a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. Contains many concrete examples, applications, and pointers to further developments
Book Synopsis Symmetric Functions, Schubert Polynomials and Degeneracy Loci by : Laurent Manivel
Download or read book Symmetric Functions, Schubert Polynomials and Degeneracy Loci written by Laurent Manivel and published by American Mathematical Soc.. This book was released on 2001 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text grew out of an advanced course taught by the author at the Fourier Institute (Grenoble, France). It serves as an introduction to the combinatorics of symmetric functions, more precisely to Schur and Schubert polynomials. Also studied is the geometry of Grassmannians, flag varieties, and especially, their Schubert varieties. This book examines profound connections that unite these two subjects. The book is divided into three chapters. The first is devoted to symmetricfunctions and especially to Schur polynomials. These are polynomials with positive integer coefficients in which each of the monomials correspond to a Young tableau with the property of being ``semistandard''. The second chapter is devoted to Schubert polynomials, which were discovered by A. Lascoux andM.-P. Schutzenberger who deeply probed their combinatorial properties. It is shown, for example, that these polynomials support the subtle connections between problems of enumeration of reduced decompositions of permutations and the Littlewood-Richardson rule, a particularly efficacious version of which may be derived from these connections. The final chapter is geometric. It is devoted to Schubert varieties, subvarieties of Grassmannians, and flag varieties defined by certain incidenceconditions with fixed subspaces. This volume makes accessible a number of results, creating a solid stepping stone for scaling more ambitious heights in the area. The author's intent was to remain elementary: The first two chapters require no prior knowledge, the third chapter uses some rudimentary notionsof topology and algebraic geometry. For this reason, a comprehensive appendix on the topology of algebraic varieties is provided. This book is the English translation of a text previously published in French.
Book Synopsis Differential Geometry and Lie Groups by : Jean Gallier
Download or read book Differential Geometry and Lie Groups written by Jean Gallier and published by Springer Nature. This book was released on 2020-08-18 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Book Synopsis Gavin K. Watt's Revolutionary Canadian History 6-Book Bundle by : Gavin K. Watt
Download or read book Gavin K. Watt's Revolutionary Canadian History 6-Book Bundle written by Gavin K. Watt and published by Dundurn. This book was released on 2017-06-26 with total page 1727 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special bundle collects six titles by military history specialist Gavin K. Watt. This series has a unique focus: The American War of Independence viewed from the perspective of British operations in the north. The Burning of the Valleys concerns a decisive campaign against the northern frontier of New York in the fifth year of the war. A Dirty, Trifling Piece of Business is about operations in the sixth year, including in the south. In Poisoned by Lies and Hypocrisy, Watt explores the first two campaigns of the American Revolution through their impact on Canada and describes how a motley group of militia, American loyalists, and British regulars managed to defend Quebec and repel the invaders. Rebellion in the Mohawk Valley concerns the campaign that led to the destruction of British-held Fort Ticonderoga. Fire and Desolation details how misrule and fraying alliances led to a ferocious campaign in 1777 that changed the course of the American Revolution. These titles are essential reading for military history, early Canadian history, and War of Independence history buffs. Includes: The Burning of the Valleys A Dirty, Trifling Piece of Business I Am Heartily Ashamed Poisoned by Lies and Hypocrisy Rebellion in the Mohawk Valley New in 2017! Fire and Desolation
Book Synopsis Gavin K. Watt's Revolutionary Canadian History 5-Book Bundle by : Gavin K. Watt
Download or read book Gavin K. Watt's Revolutionary Canadian History 5-Book Bundle written by Gavin K. Watt and published by Dundurn. This book was released on 2014-07-02 with total page 1431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special bundle collects five titles by military history specialist Gavin K. Watt. This series has a unique focus: The American War of Independence viewed from the perspective of British operations in the north. The Burning of the Valleys concerns a decisive campaign against the northern frontier of New York in the fifth year of the war. A Dirty, Trifling Piece of Business is about operations in the sixth year, including in the south. In Poisoned by Lies and Hypocrisy, Watt explores the first two campaigns of the American Revolution through their impact on Canada and describes how a motley group of militia, American loyalists, and British regulars managed to defend Quebec and repel the invaders. Rebellion in the Mohawk Valley concerns the campaign that led to the destruction of British-held Fort Ticonderoga. These titles are essential reading for military history, early Canadian history, and War of Independence history buffs. Includes: The Burning of the Valleys A Dirty, Trifling Piece of Business I Am Heartily Ashamed Poisoned by Lies and Hypocrisy Rebellion in the Mohawk Valley
Book Synopsis The Modern Library Collection Children's Classics 5-Book Bundle by : Kenneth Grahame
Download or read book The Modern Library Collection Children's Classics 5-Book Bundle written by Kenneth Grahame and published by Modern Library. This book was released on 2012-07-23 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt: For young dreamers, nostalgic parents, and imaginative readers of all ages, this wonderful eBook collection not only contains five of the most beloved children’s books in the world but some of the most admired and enduring literature ever put to page. Each of these can be considered a “Household Book,” as A. A. Milne so affectionately described The Wind in the Willows—books that “everybody in the household loves, and quotes continually ever afterwards; [books which are] read aloud to every new guest.” THE WIND IN THE WILLOWS Kenneth Grahame Written by Kenneth Grahame as bedtime stories for his son, The Wind in the Willows continues to delight readers today. Basing his fanciful animal characters on human archetypes, Grahame imparts a gentle, playful wisdom in his timeless tales. Few readers will be able to resist an invitation to join the Wild Wooders at Toad Hall, enjoy a quick splash in the river with Rat and Badger, or take a swerving ride with Toad in a “borrowed” motor-car. ALICE’S ADVENTURES IN WONDERLAND & THROUGH THE LOOKING-GLASS Lewis Carroll Conceived by a shy British don on a golden afternoon to entertain ten-year-old Alice Liddell and her sisters, Alice’s Adventures in Wonderland and Through the Looking-Glass have delighted generations of readers in more than eighty languages. “The clue to the enduring fascination and greatness of the Alice books,” writes A. S. Byatt in her Introduction, “lies in language. It is play, and word-play, and its endless intriguing puzzles continue to reveal themselves long after we have ceased to be children.” PETER PAN J. M. Barrie Set in London and and the magical Neverland, J. M. Barrie’s tale of a boy who refuses to grow up has delighted generations of readers. In this novel, which Barrie adapted from his 1904 play, Peter introduces Wendy, Michael, and John Darling to the fairy Tinker Bell and the lost boys. Together, they do battle with Captain Hook and his fierce band of pirates. THE THREE MUSKETEERS Alexandre Dumas First published in 1844, Alexandre Dumas’s swashbuckling epic chronicles the adventures of D’Artagnan, a gallant young nobleman who journeys to Paris in 1625 hoping to join the ranks of the musketeers guarding Louis XIII. He soon finds himself fighting alongside three heroic comrades—Athos, Porthos, and Aramis—who seek to uphold the honor of the king by foiling the wicked plots of Cardinal Richelieu and the beautiful spy “Milady.”
Download or read book Lie Groups written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This (post) graduate text gives a broad introduction to Lie groups and algebras with an emphasis on differential geometrical methods. It analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of compact Lie groups and their realization as sections of holomorphic line bundles over flag manifolds. Appendices provide background reviews.
Book Synopsis The Large Scale Structure of Space-Time by : Stephen W. Hawking
Download or read book The Large Scale Structure of Space-Time written by Stephen W. Hawking and published by Cambridge University Press. This book was released on 2023-02-16 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.
Book Synopsis Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces by : Steffen Fröhlich
Download or read book Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces written by Steffen Fröhlich and published by Springer. This book was released on 2012-06-30 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion.
Book Synopsis Atiyah-Singer Index Theorem - An Introduction by : Amiya Mukherjee
Download or read book Atiyah-Singer Index Theorem - An Introduction written by Amiya Mukherjee and published by Springer. This book was released on 2013-10-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the K -theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.
Book Synopsis Nonlinear Partial Differential Equations in Engineering and Applied Science by : Robert L. Sternberg
Download or read book Nonlinear Partial Differential Equations in Engineering and Applied Science written by Robert L. Sternberg and published by Routledge. This book was released on 2017-10-02 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume are twenty-eight papers from the Conference on Nonlinear Partial Differential Equationsin Engineering and Applied Science, sponsored by the Office of Naval Research and held at the Universityof Rhode Island in June, 1979. Included are contributions from an international group of distinguishedmathematicians, scientists, and engineers coming from a wide variety of disciplines and having a commoninterest in the application of mathematics, particularly nonlinear partial differential equations, to realworld problems.The subject matter ranges from almost purely mathematical topics in numerical analysis and bifurcationtheory to a host of practical applications that involve nonlinear partial differential equations, suchas fluid dynamics, nonlinear waves, elasticity, viscoelasticity, hyperelasticity, solitons, metallurgy, shocklessairfoil design, quantum fields, and Darcy's law on flows in porous media.Non/inear Partial Differential Equations in Engineering and Applied Science focuses on a variety oftopics of specialized, contemporary concern to mathematicians, physical and biological scientists, andengineers who work with phenomena that can be described by nonlinear partial differential equations.
Book Synopsis Riemannian Holonomy Groups and Calibrated Geometry by : Dominic D. Joyce
Download or read book Riemannian Holonomy Groups and Calibrated Geometry written by Dominic D. Joyce and published by Oxford University Press. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemannian Holonomy Groups and Calibrated Geometry covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
Download or read book Bndl Ck written by Shelly and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Maslov Index in Symplectic Banach Spaces by : Bernhelm Booß-Bavnbek
Download or read book The Maslov Index in Symplectic Banach Spaces written by Bernhelm Booß-Bavnbek and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.