Download or read book Algebra Geometry and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Download or read book Sheaves on Manifolds written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Download or read book Fifty Years of Mathematical Physics written by Molin Ge and published by World Scientific Publishing Company. This book was released on 2016-02-16 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.

Download or read book A History of Algebraic and Differential Topology 1900 1960 written by Jean Dieudonné and published by Springer Science & Business Media. This book was released on 2009-09-01 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet

Download or read book The Shape of Inner Space written by Shing-Tung Yau and published by Il Saggiatore. This book was released on 2010-09-07 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading mind behind the mathematics of string theory discusses how geometry explains the universe we see. Illustrations.

Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Download or read book Real Algebraic Geometry written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2013-04-15 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

Download or read book Clifford geometric Algebras with Applications to Physics Mathematics and Engineering written by William Eric Baylis and published by Boston : Birkhäuser. This book was released on 1996 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.

Download or read book Homotopical Algebraic Geometry II Geometric Stacks and Applications written by Bertrand Toën and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.

Download or read book A Mathematical Space Odyssey written by Claudi Alsina and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.--

Download or read book Lectures On Computation written by Richard P. Feynman and published by Addison-Wesley Longman. This book was released on 1996-09-08 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the theory of computation, information and communications, the physical aspects of computation, and the physical limits of computers, this text is based on the notes taken by one of its editors, Tony Hey, on a lecture course on computation given b

Download or read book Topics in Physical Mathematics written by Kishore Marathe and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.

Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.

Download or read book Geometric Multiplication of Vectors written by Miroslav Josipović and published by Springer Nature. This book was released on 2019-11-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.

Download or read book Clifford Geometric Algebras written by William E. Baylis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.

Download or read book Curvature in Mathematics and Physics written by Shlomo Sternberg and published by Courier Corporation. This book was released on 2013-04-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Download or read book Current Developments in Algebraic Geometry written by Lucia Caporaso and published by Cambridge University Press. This book was released on 2012-03-19 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.