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Mostly Surfaces
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Book Synopsis Mostly Surfaces by : Richard Evan Schwartz
Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Counting Surfaces by : Bertrand Eynard
Download or read book Counting Surfaces written by Bertrand Eynard and published by Springer Science & Business Media. This book was released on 2016-03-21 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry of Surfaces by : John Stillwell
Download or read book Geometry of Surfaces written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Translation Surfaces by : Jayadev S. Athreya
Download or read book Translation Surfaces written by Jayadev S. Athreya and published by American Mathematical Society. This book was released on 2024-04-19 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Practical Descriptive Geometry by : William Griswold Smith
Download or read book Practical Descriptive Geometry written by William Griswold Smith and published by . This book was released on 1912 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry of Curves and Surfaces by : Manfredo Perdigao do Carmo
Download or read book Differential Geometry of Curves and Surfaces written by Manfredo Perdigao do Carmo and published by . This book was released on 2009 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry by : Wolfgang Kühnel
Download or read book Differential Geometry written by Wolfgang Kühnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Functionalization of Semiconductor Surfaces by : Franklin Tao
Download or read book Functionalization of Semiconductor Surfaces written by Franklin Tao and published by John Wiley & Sons. This book was released on 2012-04-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents both fundamental knowledge and latest achievements of this rapidly growing field in the last decade. It presents a complete and concise picture of the the state-of-the-art in the field, encompassing the most active international research groups in the world. Led by contributions from leading global research groups, the book discusses the functionalization of semiconductor surface. Dry organic reactions in vacuum and wet organic chemistry in solution are two major categories of strategies for functionalization that will be described. The growth of multilayer-molecular architectures on the formed organic monolayers will be documented. The immobilization of biomolecules such as DNA on organic layers chemically attached to semiconductor surfaces will be introduced. The patterning of complex structures of organic layers and metallic nanoclusters toward sensing techniques will be presented as well.
Download or read book Enriques Surfaces I written by F. Cossec and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.
Book Synopsis Generation of Surfaces by : Stephen P. Radzevich
Download or read book Generation of Surfaces written by Stephen P. Radzevich and published by CRC Press. This book was released on 2014-02-03 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: A commonly used practice in industry is the machining of sculptured part surfaces on a multiaxis numerical control (NC) machine. While this practice is vital, it is also a costly aspect of the surface generation process. After investing more than 40 years of research into the theory of part surface generation, the author of Generation of Surfaces:
Book Synopsis Life at Rock Surfaces by : Burkhard Büdel
Download or read book Life at Rock Surfaces written by Burkhard Büdel and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-06-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rock surfaces provide a challenging habitat for a broad diversity of micro- or small-sized organisms. They interact with each other forming complex communities as well with their substrate causing biodeterioration of rock. Extreme fluctuation in light, temperature and hydration are the main factors that determine the rock surface habitats. The habitat includes epilithic organisms which thrive on the surface without penetrating the rock, endolithic organisms which live just beneath the surface using a thin layer of the rock surface for protection against adverse conditions of the environment (e.g. light protection, storage of water) and chasmo-endolithic organisms which use fractures of the rock surface for a more habitable environment. The book will provide an overview of the various organismal groups, from prokaryotes to vascular plants and arthropods, as well as survey organism-mediated interactions with the rock surface. The latter include biogenic weathering (biogeochemistry, state-of-the art imaging methods), photosynthesis and nitrogen fixation at and inside the rock surface.
Book Synopsis Topological Data Structures for Surfaces by : Sanjay Rana
Download or read book Topological Data Structures for Surfaces written by Sanjay Rana and published by John Wiley & Sons. This book was released on 2005-12-13 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation, analysis and visualisation of surfaces, focussing on topological data structures. Topological Data Structures for Surfaces: an introduction for Geographical Information Science describes the concepts and applications of these data structures. The book focuses on how these data structures can be used to analyse and visualise surface datasets from a range of disciplines such as human geography, computer graphics, metrology, and physical geography. Divided into two Parts, Part I defines the topological surface data structures and explains the various automated methods used for their generation. Part II demonstrates a number of applications of surface networks in diverse fields, ranging from sub-atomic particle collision visualisation to the study of population density patterns. To ensure that the material is accessible, each Part is prefaced by an overview of the techniques and application. Provides GI scientists and geographers with an accessible overview of current surface topology research. Algorithms are presented and explained with practical examples of their usage. Features an accompanying website developed by the Editor - http://geog.le.ac.uk/sanjayrana/surface-networks/ This book is invaluable for researchers and postgraduate students working in departments of GI Science, Geography and Computer Science. It also constitutes key reference material for Masters students working on surface analysis projects as part of a GI Science or Computer Science programme.
Book Synopsis Spin-Polarized Two-Electron Spectroscopy of Surfaces by : Sergey Samarin
Download or read book Spin-Polarized Two-Electron Spectroscopy of Surfaces written by Sergey Samarin and published by Springer. This book was released on 2018-09-20 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents developments of techniques for detection and analysis of two electrons resulting from the interaction of a single incident electron with a solid surface. Spin dependence in scattering of spin-polarized electrons from magnetic and non-magnetic surfaces is governed by exchange and spin-orbit effects. The effects of spin and angular electron momentum are shown through symmetry of experimental geometries: (i) normal and off normal electron incidence on a crystal surface, (ii) spin polarization directions within mirror planes of the surface, and (iii) rotation and interchange of detectors with respect to the surface normal. Symmetry considerations establish relationships between the spin asymmetry of two-electron distributions and the spin asymmetry of Spectral Density Function of the sample, hence providing information on the spin-dependent sample electronic structure. Detailed energy and angular distributions of electron pairs carry information on the electron-electron interaction and electron correlation inside the solid. The “exchange – correlation hole” associated with Coulomb and exchange electron correlation in solids can be visualized using spin-polarized two-electron spectroscopy. Also spin entanglement of electron pairs can be probed. A description of correlated electron pairs generation from surfaces using other types of incident particles, such as photons, ions, positrons is also presented.
Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts
Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Book Synopsis Introduction to Differential Geometry of Space Curves and Surfaces by : Taha Sochi
Download or read book Introduction to Differential Geometry of Space Curves and Surfaces written by Taha Sochi and published by Taha Sochi. This book was released on 2022-09-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.
Download or read book Graffiti Palace written by A. G. Lombardo and published by MCD. This book was released on 2018-03-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brilliant, exhilarating debut novel that retells The Odyssey during the 1965 Watts Riots—like nothing you’ve ever read before It’s August 1965 and Los Angeles is scorching. Americo Monk, a street-haunting aficionado of graffiti, is frantically trying to return home to the makeshift harbor community (assembled from old shipping containers) where he lives with his girlfriend, Karmann. But this is during the Watts Riots, and although his status as a chronicler of all things underground garners him free passage through the territories fiercely controlled by gangs, his trek is nevertheless diverted. Embarking on an exhilarating, dangerous, and at times paranormal journey, Monk crosses paths with a dizzying array of representatives from Los Angeles subcultures, including Chinese gangsters, graffiti bombers, witches, the Nation of Islam leader Elijah Muhammad, and others. Graffiti Palace is the story of a city transmogrified by the upsurge of its citizens, and Monk is our tour guide, cataloging and preserving the communities that, though surreptitious and unseen, nevertheless formed the backbone of 1960s Los Angeles. With an astounding generosity of imagery and imagination, Graffiti Palace heralds the birth of a major voice in fiction. A. G. Lombardo sees the writings on our walls, and with Graffiti Palace he has provided an allegorical paean to a city in revolt.
Book Synopsis Flora of New South Wales by : Gwen J. Harden
Download or read book Flora of New South Wales written by Gwen J. Harden and published by UNSW Press. This book was released on 1990 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1 of the landmark series Flora of New South Wales was first published in 1990, and describes the naturally occurring and naturalized ferns, cycads, conifers and some of the flowering plants of that state. Since 1990, parts of Volume 1 have been made substantially out of date by wide-ranging revisions to taxonomy and the discovery or identification of new plant species - such as the 'living fossil' Wollemi pine, featured on the cover of this revised edition. This revised edition of Volume 1 incorporates a 64 page insert that lists all the updates to the information contained within the book, including taxonomic changes, new species descriptions, new data about species and changes to keys. These changes are cross-referenced from the original species or key entry in the volume to the relevant section of the insert, so where necessary readers can quickly check to see what changes have occurred. Additionally, the reference list, glossary and index have all been revised.
