Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions (Texts in Applied and Engineering Mathematics N 12)
Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They pre a unifying framework for many seemingly disparate physical systems, such as n-particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. text.
One of the most striking characteristics of mathematics is that thoughtful and persistent mathematical analysis often provokes totally unexpected insights into what may at first have looked like an uninteresting or intractable problem. This book gives students an opportunity to discover the nature and process of mathematics by developing their ability to investigate problems without relying on the standardized methods usually taught. The techniques required are elementary, allowing the student to concentrate on the way the material is explored and developed, and on the strategies for addressing questions whose answers are not immediately obvious.
This market-leading book continues to provide users with sound, consistently structured explanations of the mathematical concepts. Designed for a one- or two-term course that prepares users to study calculus, the new Eighth Edition retains the features that have made PRECALCULUS a complete solution for users: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises.
Modern Multidimensional Scaling: Theory and Applications
The book provides a comprehensive treatment of multidimensional scaling (MDS), a family of statistical techniques for analyzing the structure of (dis)similarity data. Such data are widespread, including, for example, intercorrelations of survey items, direct ratings on the similarity on choice objects, or trade indices for a set of countries.
A unique and timely monograph, Visualization of Categorical Data contains a useful balance of theoretical and practical material on this important new area. Top researchers in the field present the books four main topics: visualization, correspondence analysis, biplots and multidimensional scaling, and contingency table models. This volume discusses how surveys, which are employed in many different research areas, generate categorical data. It will be of great interest to anyone involved in collecting or analyzing categorical data.
