(Hardback )
0-19-852656-3
Publication date: March 2003
490 pages, None, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics
A comprehensive text covering the basic tools of Modern Analysis
providing an ideal source for study and convenient reference.
Each chapter includes some basic and some advanced material
Contains over 120 end of chapter exercises
Description
This graduate level text provides a comprehensive course in
Modern Analysis. The first 10 chapters discuss theoretical
methods in Measure Theory and Functional Analysis, and contain
over 120 end of chapter exercises. The final two chapters apply
theory to applications in Probability Theory and Partial
Differential Equations.
Readership: Advanced undergraduates and graduate Students,
Researchers in Mathematics.
Contents
(Hardback )
0-19-851597-9
Publication date: April 2003
380 pages, 186 line, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics
Unique text approaching the teaching of Topology via guided
exercises and extensive coverage of basic material
Contains a flexible set of topics that allows independent
assignments within a single class for students at different
levels
Contains extensive and carefully developed exercise sets (over
750) and projects, with selected solutions
Description
This introduction to topology emphasises a geometric approach
with a focus on surfaces. A primary feature is a large collection
of exercises and projects, which fosters a teaching style making
the student an active class participant. A wide range of material
at different levels supports flexible use of the book for a
variety of students. Part I is appropriate for a one semester or
two quarter course, and Part II, (which is problem based), allows
the book to be used for a year long course which supports a
variety of syllabuses.
Readership: Advanced undergraduates and beginning graduate
students in pure mathematics and topology.
Contents
Inverse and Ill-Posed Problems Series
An internal boundary value problem deals with the problem of
determining the solution of an equation, if data are given on two
manifolds. One manifold is the domain boundary and the other
manifold is situated inside the domain. This monograph in the
Inverse and Ill-Posed Problems Series studies three essentially
ill-posed internally boundary value problems for the biharmonic
equation and the Cauchy problem for the abstract biharmonic
equation, both qualitatively and quantitatively. In addition,
some variants of these problems and the Cauchy problem, as well
as the m-dimensional case are considered.
This monograph, in which the author introduces some new notions,
such as the notion of complete solvability, will be of interest
to specialists in mathematical physics.
2002; viii+158 pages
ISBN 90-6764-365-3
Contents:
2002 VIII, 209 p. 38 illus. Hardcover
1-85233-571-8
Self-contained, and collating for the first time material that
has until now only been published in journals - often in Russian
- this book will be of interest to functional analysts,
especially those with interests in topological vector spaces, and
to algebraists concerned with category theory. The closed graph
theorem is one of the corner stones of functional analysis, both
as a tool for applications and as an object for research.
However, some of the spaces which arise in applications and for
which one wants closed graph theorems are not of the type covered
by the classical closed graph theorem of Banach or its immediate
extensions. To remedy this, mathematicians such as Schwartz and
De Wilde (in the West) and Rajkov (in the East) have introduced
new ideas which have allowed them to establish closed graph
theorems suitable for some of the desired applications. In this
book, Professor Smirnov uses category theory to provide a very
general framework, including the situations discussed by De
Wilde, Rajkov and others. General properties of the spaces
involved are discussed and applications are provided in measure
theory, global analysis and differential equations.
Keywords: Functional Analysis, Hausdorff Spectra, Topology
Contents:
Series: Springer Monographs in Mathematics.
2002 VI, 267 p. Softcover
3-540-43951-X
The present book is devoted to a study of relative Prufer rings
and Manis valuations, with an eye to application in real and p-adic
geometry. If one wants to expand on the usual algebraic geometry
over a non-algebraically closed base field, e.g. a real closed
field or p-adically closed field, one typically meets lots of
valuation domains. Usually they are not discrete and hence not
noetherian. Thus, for a further develomemt of real algebraic and
real analytic geometry in particular, and certainly also rigid
analytic and p-adic geometry, new chapters of commutative algebra
are needed, often of a non-noetherian nature. The present volume
presents one such chapter.
Keywords: Bezout ring, Manis valuation, Prufer ring, holormorphy
ring, multiplicative ideal theory
Contents: Introduction.- Basics on Manis valuations and Prufer
extensions.- Multiplicative ideal theory.- PM-valuations and
valuations of weaker type.- Appendix A: Flat epimorphisms.-
Appendix B: Arithmetical rings.- Appendix C: A direct proof of
the existence of Manis valuation hulls.- References.- Index.
Series: Lecture Notes in Mathematics. Volume. 1791