Author : A. B. Katok
Publisher : American Mathematical Soc.
Page : 307 pages
File Size : 21,98 MB
Release : 2008
Category : Mathematics
ISBN : 0821846795
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 : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 29,38 MB
Release : 2011
Category : Mathematics
ISBN : 0821853686
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 : L.Christine Kinsey
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 14,50 MB
Release : 1997-09-26
Category : Mathematics
ISBN : 9780387941028
" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.
Author : Sandra Duran Wilson
Publisher : Penguin
Page : 500 pages
File Size : 45,39 MB
Release : 2014-04-25
Category : Art
ISBN : 1440329540
Indulge your creative curiosity and take your art off the canvas, off the board, and into the brave new world of Alternative Art Surfaces! Mixed-media powerhouse duo Darlene Olivia McElroy and Sandra Duran Wilson, authors of the best-selling books Image Transfer Workshop, Surface Treatment Workshop and Mixed Media Revolution, blaze new creative territory with more than 100 techniques for working on more than 35 unique surfaces in this, their jam-packed fourth book!You'll find something new and exciting on every page: • More than 35 alternative surfaces, including galvanized tin, mica, rawhide, nylon, unsanded grout, slate, spray foam and more • More than 100 techniques for painting, sculpting, creating textures, encasing, carving, printing, transferring and more • More than 125 tips for troubleshooting, preparing your surfaces, finishing and mounting your art, and taking your work to the next level • More than 50 inspiring finished pieces of art showcasing the surfaces and techniques
Author : Lucian Badescu
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 19,25 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 147573512X
This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.
Author : Arnaud Beauville
Publisher : Cambridge University Press
Page : 148 pages
File Size : 41,72 MB
Release : 1996-06-28
Category : Mathematics
ISBN : 9780521498425
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor BeauviIle gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.
Author : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 31,95 MB
Release : 2003
Category : Mathematics
ISBN : 9780821834794
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
Author : Jonathan Hay
Publisher : Reaktion Books
Page : 442 pages
File Size : 41,33 MB
Release : 2010-06-25
Category : Art
ISBN : 1861898460
With Sensuous Surfaces, Jonathan Hay offers one of the most richly illustrated and in-depth introductions to the decorative arts of Ming and Qing dynasty China to date. Examining an immense number of works, he explores the materials and techniques, as well as the effects of patronage and taste, that together have formed a loose system of informal rules that define the decorative arts in early modern China. Hay demonstrates how this system—by engaging the actual and metaphorical potential of surface—guided the production and use of decorative arts from the late sixteenth century through the middle of the nineteenth, a period of explosive growth. He shows how the understanding of decorative arts made a fundamental contribution to the sensory education of China’s early modern urban population. Enriching his study with 280 color plates, he ultimately offers an elegant meditation, not only on Ming and Qing art but on the importance of the erotic in the form and function of decorations of all eras.
Author : Tobias Holck Colding
Publisher : American Mathematical Society
Page : 330 pages
File Size : 16,44 MB
Release : 2024-01-18
Category : Mathematics
ISBN : 1470476401
Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.
Author : Bertrand Eynard
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 32,58 MB
Release : 2016-03-21
Category : Mathematics
ISBN : 3764387971
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.
