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General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.
Discover new opportunities for building 2D and 3D games with HTML5 The newest iteration of HTML, HTML5 can be used with JavaScript, CSS3, and WebGL to create beautiful, unique, engaging games that can be played on the web or mobile devices like the iPad or Android phones. Gone are the days where games were only possible with plugin technologies such as Flash and this cutting-edge book shows you how to utilize the latest open web technologies to create a game from scratch using Canvas, HTML5 Audio, WebGL, and WebSockets. You'll discover how to build a framework on which you will create your HTML5 game. Then each successive chapter covers a new aspect of the game, including user input, sound, multiplayer functionality, 2D and 3D graphics, and more. Aims directly at a new way to develop games for the web through the use of HTML5 Demonstrates how to make iOS and Android web apps Explains how to capture player input; create 3D graphics; and incorporate textures, lighting, and sound Guides you through the process of creating a game from scratch using Canvas, HTML5 Audio, WebGL, and WebSockets By the end of this invaluable book, you will have created a fully functional game that can be played in any compatible browser or on any mobile device that supports HTML5.
From the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist
A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.