Series: Fundamental Theories of Physics , Vol. 165
1st edition, 2010, Approx. 345 p., Hardcover
ISBN: 978-90-481-3474-8
Due: October 2009
This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity.
The volume begins with an excellent retranslation of Minkowski's paper by Dennis Lehmkuhl, accompanied by the original German version of the article. The fourteen contributions are divided into three parts entitled "The Impact of Minkowski Spacetime on the Twentieth Century Physics from a Historical Perspective", "Implications of Minkowski Spacetime for Theoretical Physics", and "Conceptual and Philosophical Issues of Minkowski Spacetime."
Originally published as volume 23 in the series: Texts in the Mathematical Sciences Originally Published by Kluwer Academic Publishers 2001
Revised Edition, 2010, XIV, 438 p. 49 illus., Softcover
ISBN: 978-90-481-3563-9
Due: November 4, 2009
About this textbook
The present book is a collection of completely solved exercises on differentiable manifolds, lie groups, fibre bundles and Riemannian manifolds.
The exercises go from elementary computations to rather sophisticated tools. It is the first book of completely solved problems on differentiable manifolds and therefore will be a compliment to the books on theory.
A 42 page Formulary is included which can be useful as an aide-memoire, even for teachers and researchers on those topics.
This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering.
Differentiable manifolds.- Tensor Fields and Differential Forms.- Integration on Manifolds.- Lie Groups.- Fibre Bundles.- Riemannian Geometry.- Some Definitions and Theorems.- Some Formulas and Tables.
Series: Graduate Texts in Mathematics , Vol. 256
2010, Approx. 240 p., Hardcover
ISBN: 978-3-642-03544-9
Due: January 2010
Kemper’s "Course in Commutative Algebra" presents a thorough, modern introduction to the subject. .With carefully selected topics presented in a natural geometric context, the author's key focus is on concepts and results in the field. But, while emphasizing theory, the presentation is enriched with three chapters covering computational aspects of the subject.
This user-friendly textbook motivates the reader with numerous examples, figures, and exercises, and is well designed for a one- or two-semester course in a classroom setting.
Introduction.- Part I The Algebra Geometry Lexicon.- 1 Hilbert's Nullstellensatz.- 2 Noetherian and Artinian Rings.- 3 The Zariski Topology.- 4 A Summary of the Lexicon.- Part II Dimension.- 5 Krull Dimension and Transcendence Degree.- 6 Localization.- 7 The Principal Ideal Theorem.- 8 Integral Extensions.- Part III Computational Methods.- 9 Grobner Bases.- 10 Fibers and Images of Morphisms Revisited.- 11 Hilbert Series and Dimension.- Part IV Local Rings.- 12 Dimension Theory.- 13 Regular Local Rings.- 14 Rings of Dimension One.- References.- Notation.- Index
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.
The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations.
The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.
First Encounter with Chaos
The Language of Dynamical Systems
Examples of Chaotic Behaviors
Probabilistic Approach to Chaos
Characterization of Chaotic Dynamical Systems
From Order to Chaos in Dissipative Systems
Chaos in Hamiltonian Systems
Chaos and Information Theory
Coarse-Grained Information and Large Scale Predictability
Chaos in Numerical and Laboratory Experiments
Chaos in Low Dimensional Systems
Spatiotemporal Chaos
Turbulence as a Dynamical System Problem
Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study
Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
480pp Pub. date: Sep 2009
ISBN: 978-981-4277-65-5
This book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations ? avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vista II will provide the reader ample opportunity to find suitable formulas and the means to apply them to practical problems for actual research. It can even be used during tutorials for paper writing.
Bernoulli and Allied Polynomials
Chebyshev Polynomials and Energy Levels of Carbon Hydrates
The Gamma Function Continued ? Kummer's Fourier Series, The Stirling Formulas, Etc
The Hurwitz-Lerch Zeta-Function
The Dirichlet L-Function
Arithmetical Fourier Series
The Madelung Constants and Special Functions
Applications of Fourier Series ? Parseval Identity
The Derivative of Dirichlet L-Function and the Kronecker Limit Formula
Readership: Graduate students and researchers in pure mathematics.
200pp (approx.) Pub. date: Scheduled Winter 2009
ISBN: 978-981-4273-97-8
981-4273-97-X