Series: Lecture Notes in Mathematics, Vol. 1886
2006, Approx. 590 p. 120 illus., Softcover
ISBN: 3-540-33363-0
Due: June 19, 2006
About this book
The author develops a deformation theory for degenerations of
complex curves; specifically, he treats deformations which induce
splittings of the singular fiber of a degeneration. He constructs
a deformation of the degeneration in such a way that a subdivisor
is "barked" (peeled) off from the singular fiber. These
"barking deformations" are related to deformations of
surface singularities (in particular, cyclic quotient
singularities) as well as the mapping class groups of Riemann
surfaces (complex curves) via monodromies. Important
applications, such as the classification of atomic degenerations,
are also explained.
Written for:
Researchers and graduate students in algebraic geometry, low-dimensional
topology, singularity theory, complex analysis, and complex
geometry
Table of contents
Basic notions and Ideas: Splitting Deformations of Degenerations.-
What is a barking?- Semi-Local Barking Deformations: Ideas and
Examples.- Global Barking Deformations: Ideas and Examples.
Deformations of Tubular Neighborhoods of Branches: Deformations
of Tubular Neighborhoods of Branches.- Construction of
Deformations by Tame Subbranches.- ..... . Barking Deformations
of Degenerations: Construction of Barking Deformations (Stellar
Case).- Simple Crusts (Stellar Case).- Compound Barking (Stellar
Case).- Deformations of Tubular Neighborhoods of Trunks.-
Construction of Barking Deformations (Constellar Case).- ... .
Singularities of Subordinate Fibers near Cores: Singularities of
Fibers around Cores.- Arrangement Functions and Singularities, I.-
Arrangement Functions and Singularities, II.- Supplement.
Classifications of Atoms of Genus.
Series: Lecture Notes in Mathematics, Vol. 1887
2006, Approx. 130 p., Softcover
ISBN: 3-540-33420-3
Due: June 19, 2006
About this book
One of the basic ideas in differential geometry is that the study
of analytic properties of certain differential operators acting
on sections of vector bundles yields geometric and topological
properties of the underlying base manifold. Symplectic spinor
fields are sections in an L^2-Hilbert space bundle over a
symplectic manifold and symplectic Dirac operators, acting on
symplectic spinor fields, are associated to the symplectic
manifold in a very natural way. They may be expected to give
interesting applications in symplectic geometry and symplectic
topology. These symplectic Dirac operators are called Dirac
operators, since they are defined in an analogous way as the
classical Riemannian Dirac operator known from Riemannian spin
geometry. They are called symplectic because they are constructed
by use of the symplectic setting of the underlying symplectic
manifold. This volume is the first one that gives a systematic
and self-contained introduction to the theory of symplectic Dirac
operators and reflects the current state of the subject. At the
same time, it is intended to establish the idea that symplectic
spin geometry and symplectic Dirac operators may give valuable
tools in symplectic geometry and symplectic topology, which have
become important fields and very active areas of mathematical
research.
Table of contents
Preface.- 1. Background on Symplectic Spinors.- 2. Symplactic
Connections.- 3. Symplectic Spinor Fields.- 4. Symplectic Dirac
Operators.- 5. An Associated Second Order Operator.- 6. The
Kahler Case.- 7. Fourier Transform for Symplectic Spinors.- 8.
Lie Derivative and Quantization.- References.- Index.
Series: Universitext
2006, XII, 250 p. 10 illus., Softcover
ISBN: 0-387-33646-X
Due: July 2006
About this textbook
This book is an introduction to constructive mathematics with an
emphasis on techniques and results that have been obtained in the
last twenty years. The text covers fundamental theory of the real
line and metric spaces, focusing on locatedness in normed spaces
and with associated results about operators and their adjoints on
a Hilbert space. Some of the other areas that are discussed in
this book are the Ishihara's tricks, Separation theorems, and
Locally convex spaces. There are two appendices to the book. The
first gathers together some basic notions about sets and orders,
the second gives the axioms for intuitionistic logic. The
intended readership of the book consists of postgraduate or
senior undergraduate students, and professional research
mathematicians. No background in intuitionistic logic or
constructive analysis is needed in order to read the book, but
some familiarity with the classical theories of metric, normed
and Hilbert spaces is recommended.
Table of contents
Preface.- Introduction to Constructive Mathematics.- Techniques
of Elementary Analysis.- The Lamda Technique.- Finite-Dimensional
and Hilbert Spaces.- Linearity and Convexity.- Operators and
Locatedness.- References.- Index.
Series: Undergraduate Texts in Mathematics
2006, Approx. 360 p. 40 illus., Hardcover
ISBN: 0-387-33194-8
Due: July 2006
About this textbook
This text is intended for a one or two semester sophomore level
course in linear algebra. It is designed to provide a balance of
applications, theory and computation, and to emphasize their
interdependence. The text has a strong orientation towards
numerical computation and the linear algebra needed in applied
mathematics. At the same time, it contains a rigorous and self-contained
development of most of the traditional topics in a linear algebra
course. It provides background for numerous projects, which
frequently require computational tools, but is not tied to any
one computational platform.
Table of contents
Linear Systems of Equations.- Matrix Algebra.- Vector Spaces.-
Geometrical Aspects of Standard Spaces.- The Eigenvalue Problem.-
Geometrical Aspects of Abstract Spaces.- Table of Symbols.-
Solutions to Selected Exercises.- Bibliography.- Index
Series: Algorithms and Computation in Mathematics, Preliminary
entry 18
2006, Approx. 740 p., Hardcover
ISBN: 3-540-28371-4
Due: July 2006
About this textbook
This text offers an introduction to error-correcting linear codes
for graduate students in mathematics, computer science and
engineering. The book differs from other standard texts in its
emphasis on the classification of codes by means of isometry
classes. The relevant algebraic concepts like finite fields and
group actions are developed rigorously. Cyclic codes are
discussed in great detail, as well as their application in CD
players. In the last four chapters these isometry classes are
enumerated, and representatives are constructed algorithmically
with our without a prescribed automorphism group. Furthermore,
lattice basis reduction is presented as a tool for computing
generator matrices and the minimum distance of codes. The
attached CD provides access to generator matrices of more than 70,000
nonisometric optimal codes, covering all optimal codes for a
given set of code parameters. It also contains software for
evaluating minimum distances, weight enumerators, and for the
construction of codes.
Table of contents
Preface.- 1 Linear Codes.- 2 Bounds and Modifications.- 3 Finite
Fields.- 4 Cyclic Codes.- 5 Particular Series of Cyclic Codes.- 6
Encoding and Decoding of Cyclic Codes.- 7 Mathematics Behind
Audio Compact Discs.- 8 Enumeration of Isometry Classes.- 9
Solving Diophantine Linear Systems.- 10 Linear Codes with a
Prescribed Minimum Distance.- 11 Exhaustive Construction of
Linear Codes.- References