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| Author | : Richard Evan Schwartz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 330 |
| Release | : 2011 |
| Genre | : 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 | : A. B. Katok |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 307 |
| Release | : 2008 |
| Genre | : 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 | : Jayadev S. Athreya |
| Publisher | : American Mathematical Society |
| Total Pages | : 195 |
| Release | : 2024-04-19 |
| Genre | : Mathematics |
| ISBN | : 1470476770 |
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 | : Stephen P. Radzevich |
| Publisher | : CRC Press |
| Total Pages | : 538 |
| Release | : 2007-12-14 |
| Genre | : Technology & Engineering |
| ISBN | : 1420063413 |
The principle of Occam's razor loosely translates tothe simplest solution is often the best. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multi-axis NC machines. He has developed a method to quickly calcu
| Author | : Karsten Lehn |
| Publisher | : Springer Nature |
| Total Pages | : 476 |
| Release | : 2023-06-05 |
| Genre | : Computers |
| ISBN | : 3031281357 |
A basic understanding of the key techniques in computer graphics can open the door to this exciting field and its many applications, including for video games and for augmented and virtual reality. This easy-to-follow textbook and reference introduces the fundamental concepts of computer graphics, integrating both technical background and theory with practical examples and applications throughout. Thoroughly revised and updated, this new edition continues to present a user-friendly approach to creating images and animations, complementing the expanded coverage of topics with usage of example programs and exercises. Topics and features: Contains pedagogical tools, including easy-to-understand example programs and end-of-chapter exercises Presents a practical guide to basic computer graphics programming using the Open Graphics Library (OpenGL) and the widely used Java programming language Includes new and expanded content on the OpenGL graphics pipelines, shader programming, drawing basic objects using the OpenGL, three-dimensional modelling, quaternions, rasterisation, antialiasing and more Supplies complete Java project examples as supplementary material This reader-friendly textbook is an essential tool for second-year undergraduate students and above, providing clear and concise explanations of the basic concepts of computer graphics. It will enable readers to immediately implement these concepts using the OpenGL and Java (with only elementary knowledge of the programming language). Prof. Dr.-Ing. Karsten Lehn works at the Faculty of Information Technology at Fachhochschule Dortmund, University of Applied Sciences and Arts. Prof. Dr. Merijam Gotzes is teaching at Hamm-Lippstadt University of Applied Sciences. Prof. Dr. Frank Klawonn is head of the Data Analysis and Pattern Recognition Laboratory at the Ostfalia University of Applied Sciences and heads the Biostatistics Research Group at the Helmholtz Centre for Infection Research.
| Author | : Bertrand Eynard |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 427 |
| Release | : 2016-03-21 |
| Genre | : 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.
| Author | : William Griswold Smith |
| Publisher | : |
| Total Pages | : 250 |
| Release | : 1912 |
| Genre | : Geometry |
| ISBN | : |
| Author | : Simeon Simoff |
| Publisher | : Springer |
| Total Pages | : 417 |
| Release | : 2008-07-23 |
| Genre | : Computers |
| ISBN | : 3540710809 |
Visual Data Mining—Opening the Black Box Knowledge discovery holds the promise of insight into large, otherwise opaque datasets. Thenatureofwhatmakesaruleinterestingtoauserhasbeendiscussed 1 widely but most agree that it is a subjective quality based on the practical u- fulness of the information. Being subjective, the user needs to provide feedback to the system and, as is the case for all systems, the sooner the feedback is given the quicker it can in?uence the behavior of the system. There have been some impressive research activities over the past few years but the question to be asked is why is visual data mining only now being - vestigated commercially? Certainly, there have been arguments for visual data 2 mining for a number of years – Ankerst and others argued in 2002 that current (autonomous and opaque) analysis techniques are ine?cient, as they fail to - rectly embed the user in dataset exploration and that a better solution involves the user and algorithm being more tightly coupled. Grinstein stated that the “current state of the art data mining tools are automated, but the perfect data mining tool is interactive and highly participatory,” while Han has suggested that the “data selection and viewing of mining results should be fully inter- tive, the mining process should be more interactive than the current state of the 2 art and embedded applications should be fairly automated . ” A good survey on 3 techniques until 2003 was published by de Oliveira and Levkowitz .
| Author | : John Stillwell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 225 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461209293 |
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 | : Clara Grima |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 212 |
| Release | : 2001-11-30 |
| Genre | : Computers |
| ISBN | : 9781402002021 |
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.
