Series: Chapman & Hall/CRC Computer Science & Data Analysis
Binding/Format: Hardback
ISBN: 978-1-4398358-0-7
Publish Date: 15th November 2010
Pages: 240 pages
Full of real-world case studies and practical advice, Exploratory Multivariate Analysis by Example Using R focuses on four fundamental methods of multivariate exploratory data analysis that are most suitable for applications. It covers principal component analysis (PCA) when variables are quantitative, correspondence analysis (CA) and multiple correspondence analysis (MCA) when variables are categorical, and hierarchical cluster analysis.
The authors take a geometric point of view that provides a unified vision for exploring multivariate data tables. Within this framework, they present the principles, indicators, and ways of representing and visualizing objects that are common to the exploratory methods. The authors show how to use categorical variables in a PCA context in which variables are quantitative, how to handle more than two categorical variables in a CA context in which there are originally two variables, and how to add quantitative variables in an MCA context in which variables are categorical. They also illustrate the methods and the ways they can be exploited using examples from various fields.
Throughout the text, each result correlates with an R command accessible in the FactoMineR package developed by the authors. All of the data sets and code are available at http://factominer.free.fr/book
By using the theory, examples, and software presented in this book, readers will be fully equipped to tackle real-life multivariate data.
200pp (approx.)
Pub. date: Scheduled Winter 2011
ISBN: 978-981-4299-22-0
The book provides a comprehensive overview of the theory of Galois algebras and their representations developed by the authors. It gives a unique treatment of the theory of Gelfand?Tsetlin modules for finite W-algebras, including the universal enveloping algebra of gl(n), a new treatment of an analog of the Gelfand?Kirillov Conjecture for finite W-algebras, and a description of important new theory of Galois algebras.
Graduate students in algebra.
The book will be of interests to those who specialize in Lie theory, Representation theory and Ring theory.
Skew Monoid Rings
Category of Balanced Bimodules and Hecke Algebras
Galois Rings and Galois Orders
Examples
Gelfand?Tsetlin Modules Over Galois Rings
Fibers of Characters
Gelfand?Kirillov Conjecture for Galois Rings
Finite W-Algebras of Type A as Galois Rings
Gelfand?Tsetlin Modules Over Finite W-Algebras
Gelfand?Kirillov Conjecture for Finite W-Algebras
Example of the Universal Enveloping Algebra of gl(n)
470pp (approx.)
Pub. date: Scheduled Summer 2011
ISBN: 978-981-4329-63-7
The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.
The second part of this book is on ƒÂ-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as ƒÂ-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between ƒÂ-invariants and the main extrinsic invariants. Since then many new results concerning these ƒÂ-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.
Graduate and PhD students in differential geometry and related fields;
researchers in differential geometry and related fields; theoretical physicists.
Pseudo-Riemannian Manifolds
Pseudo-Riemannian Submanifolds
Warped Products and Twisted Products
Robertson?Walker Spacetimes
Hodge Theory and Elliptic Differential Operators
Submanifolds of Finite Type
Total Mean Curvature
ƒÂ-Invariants, Inequalities
Submanifolds of Kaehler Manifolds
Submanifolds of Para-Kaehler Manifolds
Pseudo-Riemannian Submersions
Affine Hypersurface
Contact Geometry
Applications of ƒÂ-Invariants
Applications to Relativity
Mathematical Olympiad Series - Vol. 7
300pp (approx.)
Pub. date: Scheduled Fall 2011
ISBN: 978-981-4327-87-9(pbk)
The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the booklets originally produced to guide students intending to contend for placement on their country's IMO team. See also A First Step to Mathematical Olympiad Problems which was published in 2009.
The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions.
Though A Second Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.
School students keen to learn more of mathematics and specifically mathematics related to the IMO; coaches and instructors of mathematical competitions.
Combinatorics 2
Geometry 3
Solving Problems
Number Theory 2
Inequalities
Combinatorics 3
IMO Problems 2
Creating Problems