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Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 0821853686
Category : Mathematics
Languages : en
Pages : 330
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Book Description
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 0821853686
Category : Mathematics
Languages : en
Pages : 330
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Book Description
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Author: A. B. Katok
Publisher: American Mathematical Soc.
ISBN: 0821846795
Category : Mathematics
Languages : en
Pages : 307
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Book Description
Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.
Author: Bertrand Eynard
Publisher: Springer Science & Business Media
ISBN: 3764387971
Category : Mathematics
Languages : en
Pages : 427
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Book Description
The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 1461209293
Category : Mathematics
Languages : en
Pages : 225
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Book Description
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Author: Jayadev S. Athreya
Publisher: American Mathematical Society
ISBN: 147047655X
Category : Mathematics
Languages : en
Pages : 195
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Book Description
This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmüller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.
Author: Shinya Inou
Publisher: World Scientific
ISBN: 9812703888
Category : Science
Languages : en
Pages : 1019
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Book Description
This book collects the publications of Shinya lnou, pioneering cell biophysicist and winner of the 2003 International Prize for Biology. The articles cover the discovery, and elucidate the behavior in living cells, of the dynamic molecular filaments which organize the cell and play a central role in cell division. Other articles report on the development of microscopes, especially those using polarized light and digital image enhancement, which make possible studies of the ever-changing molecular architecture directly in living cells. This book also contains many high quality photo-micrographs as well as an appended DVD with an extensive collection of video movies of active living cells. After training in Tokyo and at Princeton University, Dr Inou has held teaching positions at the University of Washington, Tokyo Metropolitan University, University of Rochester, Dartmouth Medical School, and University of Pennsylvania. He is a member of the U.S. National Academy of Sciences and currently holds the title of Distinguished Scientist at the Marine Biological Laboratory in Woods Hole, Massachusetts.
Author: Mike Anusas
Publisher: Routledge
ISBN: 1317296524
Category : Social Science
Languages : en
Pages : 211
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Book Description
In attending to surfaces, as they wrap, layer and grow within sentient bodies, material formations and cosmological states, this volume presents a series of ten anthropological studies stretching across five continents and in observation of earthly practices of making, knowing, living and dying. Through theoretically reflecting on time spent with Aymara and Mapuche Andean cultures; the Malagasy people of Madagascar; craftspeople and designers across Europe and Oceania; amongst the architectures of Australia and South Korea and within the folds of books, screens, landscape and the sea, the anthropologists in this volume communicate diverse ways of considering, working with and knowing surfaces. Together, these writings advance a knowledge of the world which resists any definitive settlement of existential categories and rather seeks to know the world in its emergence and transformation, as entities grow, cohere, shift, dissolve, decay and are reborn through the contact and exchange of surfaces, persisting with varying time, power and effect. The book principally invites readers from anthropology, the creative arts and environmental studies, but also across the wider humanities and social sciences as well as those in neighbouring scientific fields of archaeology, biology, geography, geoscience, material science, neurology and psychology interested in the intersections of mind, body, materials and world.
Author: Clara Grima
Publisher: Springer Science & Business Media
ISBN: 9781402002021
Category : Computers
Languages : en
Pages : 212
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Book Description
In the last thirty years Computational Geometry has emerged as a new discipline from the field of design and analysis of algorithms. That dis cipline studies geometric problems from a computational point of view, and it has attracted enormous research interest. But that interest is mostly concerned with Euclidean Geometry (mainly the plane or Eu clidean 3-dimensional space). Of course, there are some important rea sons for this occurrence since the first applieations and the bases of all developments are in the plane or in 3-dimensional space. But, we can find also some exceptions, and so Voronoi diagrams on the sphere, cylin der, the cone, and the torus have been considered previously, and there are manY works on triangulations on the sphere and other surfaces. The exceptions mentioned in the last paragraph have appeared to try to answer some quest ions which arise in the growing list of areas in which the results of Computational Geometry are applicable, since, in practiee, many situations in those areas lead to problems of Com putational Geometry on surfaces (probably the sphere and the cylinder are the most common examples). We can mention here some specific areas in which these situations happen as engineering, computer aided design, manufacturing, geographie information systems, operations re search, roboties, computer graphics, solid modeling, etc.
Author: Wolfgang Kühnel
Publisher: American Mathematical Soc.
ISBN: 0821839888
Category : Mathematics
Languages : en
Pages : 394
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Book Description
Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Author: Maria Bloch-Trojnar
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 1501505432
Category : Language Arts & Disciplines
Languages : en
Pages : 344
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Book Description
This book contributes to the recent theoretical developments in the area of mutual interactions of valency and aspect, as expressed in different types of verb-related nominal structures (nominalizations and synthetic compounds). A wide range of data from Slavic, Hellenic, Germanic, Romance and Semitic languages provides an empirical testing ground for competing theoretical explanations couched in the lexicalist and construction-based frameworks.
