Series : Graduate Texts in Contemporary Physics
2004, Approx. 500 p., Hardcover
ISBN: 0-387-21386-4
About this textbook
Based on lecture notes for a graduate course given for many years
at the City University of New York. At present, there is no
"standard" text for quantum field theory (analogous to
Goldsteinfs text on mechanics, for example); Nair intends to
fill that gap with this text. Nairfs lectures at CUNY are known
for their clarity and economy, and those qualities will be
evident in the book.
Table of contents
Results in Relativistic Quantum Mechanics.- The Construction of
Fields.- Canonical Quantization.- Commutators and Propagators.-
Interactions and the S-Matrix.- The Electromagnetic Field.-
Examples of Scattering Processes.- Functional Integral
Representations.- Renormalization.- Gauge Theories.- Symmetry.-
Spontaneous Symmetry Breaking.- Anamolies I.- Elements of
Differential Geometry.- Path Integrals.- Gauge Theory:
Configuration Space.- Anamolies II.- Finite Temperatire and
Density.- Gauge Theory: Nonperturbative Questions.- Elements of
Geometric Quantization.- Appendix: Relativistic Invariance.
Series : Bolyai Society Mathematical Studies , Vol. 13
2004, Approx. 275 p., Hardcover
ISBN: 3-540-22944-2
About this book
This book is about an investigation of recent developments in the
field of symplectic and contact structures on four and three
dimensional manifolds, respectively, from a topologistfs point
of view. The level of the book is appropriate for advanced
graduate students. There is no doubt that symplectic and contact
structures are in the center of attention nowadays for low-dimensional
geometers and topologists. In this volume there are two main
issues that are addressed: what kind of symplectic and contact
structures we can construct via surgery theory and what kind of
symplectic and contact structures are not allowed via gauge
theory and newly-invented Heegaard-Floer theory. It turns out
that interesting results about contact structures can be obtained
for example when the "classical" surgery theory is
coupled with the Heegaard-Floer theory. The close relationship
between symplectic and contact structures is another theme in the
volume which naturally arises when one wants to perform
symplectic cut and paste operation. The material in the volume is
based on two groundbreaking results of the near past Donaldson's
result on the existence of Lefschetz pencils on symplectic four
manifolds and Giroux' correspondence between contact structures
and open book decompositions on three manifolds. The volume makes
an attempt to illustrate some consequences of these results and
incorporate them with the new developments in the Heegaard-Floer
theory, especially the Ozsvath-Szabo contact invariants.
Table of contents
Preface.- Introduction.- Topological Surgeries.- Symplectic 4-Manifolds.-
Contact 3-Manifolds.- Convex Surfaces in Contact 3-Manifolds.-
Spinc Structures on 3- and 4-Manifolds.- Symplectic Surgery.-
Stein Manifolds.- Open Books and Contact Structures.- Lefschetz
Fibrations on 4-Manifolds.- Contact Dehn Surgery.- Fillings of
Contact 3-Manifolds.- Appendix: Seiberg-Witten Invariants.-
Appendix: Heegaard Floer Theory.- Appendix: Mapping Class Groups.-
Bibliography.- Index.
1st ed. 1968. 2nd printing, 2004, VIII, 414 p., Softcover
ISBN: 3-540-22525-0
About this book
This is a softcover reprint of the English translation of 1968 of
N. Bourbaki's, Theorie des Ensembles (1970).
Table of contents
I Description of Formal Mathematics: Terms and relations;
Theorems; Logical theories; Quantified theories; Equalitarian
theories.- II Theory of Sets: Collectivizing relations; Ordered
pairs; Correspondences; Union and intersection of a family of
sets; Product of a family of sets; Equivalence relations.- III
Ordered Sets, Cardinals, Integers: Well-ordered sets; Equipotent
sets; Cardinals. Natural integers. Finite sets; Properties of
integers; Infinite sets; Inverse limits and direct limits.- IV
Structures: Structures and isomorphisms; Morphisms and derived
structures; Universal mappings.
Series : Collected Works of Claude Chevalley , Vol. 3
2005, XII, 275 p., Hardcover
ISBN: 3-540-23031-9
About this book
The third volume of the Collected Works of Claude Chevalley
assembles his work on semi-simple algebraic groups contained, for
the most part, in the notes of the famous "Seminaire
Chevalley" held at the Ecole Normale Superieure in Paris
between 1956 and 1958 and written up by participants of the
seminar namely, P. Cartier, A. Grothendieck, R. Lazard and J. L.
Verdier. These texts have been entirely reset in TeX for this
edition, and edited and annotated by Pierre Cartier. Almost 50
years after the original writing, these texts still constitute a
choice reference from which to enter and learn this part of the
theory of algebraic groups.
Table of contents
Definition des Varietes Algebriques.- Schemas des Varietes
Algebriques.- Groupes Algebriques.- Groupes Algebriques Affines
Commutatifs.- Complements de Geometrie Algebrique.- Les Theoremes
de Structure Fondamentaux pour les Groupes Algebriques Affines.-
Sous-groupes de Cartan, Elements Reguliers. Groupes Algebriques
Affines de Dimension 1.- Espaces Homogenes de Groupes Algebriques.-
Le Normalisateur d'un Groupe de Borel.- Les Tores Singuliers.- Le
Groupe de Weyl: Chambres et Reflexions.- Racines.- Groupes Semi-simples:
Structure de B et de G/B.- Groupes Finis Engendres par des
Reflexions.- Les Systemes Lineaires sur G/B.- Les Poids Dominants.-
Les Sous-groupes Radiciels.- Les Isogenies.- Les Diagrammes de
Dynkin.- Les Groupes de Type An, G2, Cn.- Existence d'isogenies.-
Conclusion.- Index.
Series : Algorithms and Computation in Mathematics , Vol. 13
2005, Approx. 460 p. 500 illus., Hardcover
ISBN: 3-540-23121-8
About this textbook
Ergodic theory is hard to study because it is based on measure
theory, which is a technically difficult subject to master for
ordinary students, especially for physics majors. Many of the
examples are introduced from a different perspective than in
other books and theoretical ideas can be gradually absorbed while
doing computer experiments. Theoretically less prepared students
can appreciate the deep theorems by doing various simulations.
The computer experiments are simple but they have close ties with
theoretical implications. Even the researchers in the field can
benefit by checking their conjectures, which might have been
regarded as unrealistic to be programmed easily, against
numerical output using some of the ideas in the book. One last
remark: The last chapter explains the relation between entropy
and data compression, which belongs to information theory and not
to ergodic theory. It will help students to gain an understanding
of the digital technology that has shaped the modern information
society.
Table of contents
Prerequisites.- Invariant Measures.- The Birkhoff Ergodic Theorem.-
The Central Limit Theorem.- More on Ergodicity.- Homeomorphisms
of the Circle.- Mod 2 Uniform Distribution.- Entropy.- The
Lyapunov Exponent: One-dimensional Case.- The Lyapunov Exponent:
Multidimensional Case.- Stable and Unstable Manifolds.-
Recurrence and Entropy.- Recurrence and Dimension.- Data
Compression.- References.- Index.
2004, Approx. 800 p., Hardcover
ISBN: 3-540-20595-0
About this book
This handbook addresses a broad audience of applied
mathematicians, physicists, computer scientists, and engineers,
bringing together under a single cover the most recent advances
in the applications of geometric computing in the most important
fields related to building perception action systems: computer
vision, robotics, image processing and understanding, pattern
recognition, computer graphics, quantum computers, brain theory
and neural networks. Various kinds of problems in these fields
have been tackled using promising geometric methods, but such
efforts have been mostly confined to specific disciplines. In
this book we introduce diverse, powerful geometric methods in a
unified manner, covering geometry theory and geometric computing
methods related to the design of perception and action systems,
intelligent autonomous systems and intelligent machines. The book
is suitable for postgraduate students and researchers working on
the design of intelligent systems.
Written for:
Scientists, researchers, lecturers, graduates, libraries