This is the first book to comprehensively cover chromatic
polynomials of graphs. It includes most of the known results and
unsolved problems in the area of chromatic polynomials. Dividing
the book into three main parts, the authors take readers from the
rudiments of chromatic polynomials to more complex topics: the
chromatic equivalence classes of graphs and the zeros and
inequalities of chromatic polynomials. The early material is well
suited to a graduate level course while the latter parts will be
an invaluable resource for postgraduate students and researchers
in combinatorics and graph theory.
Contents:
The Number of ă-Colorings and Its Enumerations
Chromatic Polynomials
Chromatic Equivalence of Graphs
Chromaticity of Multi-Partite Graphs
Chromaticity of Subdivisions of Graphs
Chromaticity of Graphs in Which any Two Color Classes Induce a
Tree
Chromaticity of Extremal 3-Colorable Graphs
Polynomials Related to Chromatic Polynomials
Real Roots of Chromatic Polynomials
Integral Roots of Chromatic Polynomials
Complex Roots of Chromatic Polynomials
Inequalities Involving Chromatic Polynomials
Readership: Postgraduate students and researchers in
combinatorics and graph theory.
400pp (approx.) Pub. date: Scheduled Summer 2005
ISBN 981-256-317-2
ISBN 981-256-383-0(pbk)
During the past three decades, the development of nonlinear
analysis, dynamical systems and their applications to science and
engineering has stimulated renewed enthusiasm for the theory of
Ordinary Differential Equations (ODE).
This useful book, which is based around the lecture notes of a
well-received graduate course, emphasizes both theory and
applications, taking numerous examples from physics and biology
to illustrate the application of ODE theory and techniques.
Written in a straightforward and easily accessible style, this
volume presents dynamical systems in the spirit of nonlinear
analysis to readers at a graduate level and serves both as a
textbook or as a valuable resource for researchers.
Contents:
Fundamental Theory
Linear Systems
Stability of Nonlinear Systems
Method of Lyapunov Functions
Two-Dimensional Systems
Second-Order Linear Equations
Index Theory and Brouwer Degree
Introduction to Regular and Singular Perturbations
Readership: Graduate students in mathematics, applied
mathematics, and engineering.
250pp (approx.) Pub. date: Scheduled Fall 2005
ISBN 981-256-319-9
This book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry.
Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a rigorous footing. It may be considered as an explication of the Kleinian view of geometry a la Erlangen Programme. The treatment in the book, however, goes beyond the Kleinian view of geometry.
Some noteworthy topics presented are
. various results about triangles (including results on areas of geodesic triangles) in Euclidean, hyperbolic and spherical planes,
. affine and projective classification of conics,
. twopoint homogeneity of the three planes, and
. the fact that the set of distance preserving maps (isometries) are essentially the same as the set of length preserving maps of these planes.
Geometric intuition is emphasized throughout the book. Figures are included wherever needed. The book has several exercises varying from computational problems to investigative or explorative open questions.
Contents:
Preface
1 Introduction
2 Affine Geometry
3 Projective Geometry
4 Classification of Conics
5 Euclidean Geometry
6 Hyperbolic Plane Geometry
7 Spherical Plane Geometry
8 Theory of Surfaces
Appendix: Group Action
Bibliography. Index.
Texts and Readings in Mathematics/ 30
2005, 242 pages, hardcover
ISBN 81-85931-50-X
The importance of cohomology theory in the study of symplectic and Hamiltonian torus actions has been recognized for a long time. The usefulness of cohomolgy theory in the field continues today, significantly in the theory of toric varieties. One of the major aims of this book is to illustrate the cohomological methods used in the study of symplectic and Hamiltonian torus actions and to present some recent results.
The other aspect of this book is to present the theory of toric manifolds, which is a study of toric varieties from a topological view point and to illustrate some applications to combinatorics
Most of the techniques used and proofs of results included, are either new and have not appeared elsewhere or are written in a style which may be more accessible to readers. The volume is suitable for graduate students in mathematics having some basic knowledge in algebraic and differential topology.
Contents
1 Localization Theorem and Symplectic Torus Actions
1.1 Introduction
1.2 The Borel Construction
1.3 The Localization Theorem
1.4 Poincare Duality
1.5 A Brief Summary of Symplectic Torus Actions
1.6 Cohomology Symplectic and Hamiltonian Torus Actions
1.7 An Example
2 Toric Varieties
2.1 Introduction
2.2 Affine toric varieties
2.3 Fans and Toric Varieties
2.4 Polytopes
2.5 Smoothness and Orbit Structure
2.6 Resolution of singularities
2.7 Complete nonsingular toric surfaces
2.8 Fundamental Group
2.9 The Euler characteristic
2.10 Line bundles
2.11 Cohomology of toric varieties
2.12 The Riemann-Roch Theorem
2.13 The moment map
3 Torus actions on manifolds
3.1 Introduction
3.2 Equivariant cohomology
3.3 Representations of a torus
3.4 Toric manifolds
3.5 Equivariant cohomology of toric manifolds
3.6 Unitary toric manifolds and multi-fans
3.7 Moment maps and equivariant index
3.8 Applications to combinatorics
Bibliography
Index
2005, 140 pages, hardcover
ISBN 81-85931-54-2
According to a remark attributed to Mark Kac, probability theory is measure theory with a soul. Furthermore, measure theory has its own ramifications in topics like function spaces, operator theory, generalized functions, ergodic theory, group representations, quantum probability etc. On the other hand recent explosive developments in the applications of probability theory have imposed the need for a good grasp of measure theory among a wide spectrum of scholars ranging from economists to engineers and physicists to psychologists. This book with its choice of proofs, remarks, examples and exercises has been prepared by taking both these aesthetic and practical aspects into account. Courses based on this book will help undergraduate and graduate students in getting a firm grasp of the fundamentals in the twin themes of probability and measure.
This is a corrected version of the book published earlier in 1977.
Contents:
1. Probability on Boolean Algbras
2. Extension of Measures
3. Borel Maps
4. Integration
5. Measures on Product Spaces
6. Hilbert Space and conditional Expectation
7. Weak Convergence of Probability Measures
8. Invariant Measures on Groups
Texts and Readings in Mathematics / 33
May 2005, 354 pages, hardcover
ISBN 81-85931-55-0