2005, X, 586 p. with blank pages: 10, 172, 542, 574.,
Hardcover
ISBN: 3-540-25527-3
About this textbook
This book is the natural continuation of Computational
Commutative Algebra 1 with some twists.
The main part of this book is a breathtaking passeggiata through
the computational domains of graded rings and modules and their
Hilbert functions. Besides Grobner bases, we encounter Hilbert
bases, border bases, SAGBI bases, and even SuperG bases.
The tutorials traverse areas ranging from algebraic geometry and
combinatorics to photogrammetry, magic squares, coding theory,
statistics, and automatic theorem proving. Whereas in the first
volume gardening and chess playing were not treated, in this
volume they are.
This is a book for learning, teaching, reading, and most of all,
enjoying the topic at hand. The theories it describes can be
applied to anything from children's toys to oil production. If
you buy it, probably one spot on your desk will be lost forever!
Table of contents
Foreword.- Introduction.- The Homogeneous Case.- Hilbert
Functions.- Further Applications.- A. The ABC of CoCoA 5.- B.
Suggestions for Further Reading.- C. Hints for Selected Exercises.-
Bibliography
Series: Springer Monographs in Mathematics
2004, Approx. 245 p., Hardcover
ISBN: 0-387-40323-X
About this book
The main objective of this monograph is to lay the foundations of
tight closure theory for Noetherian rings containing a field of
characteristic 0. It has been more than ten years since the
authors first began work on tight closure. In that time they have
published many articles on the topic. This remarkably potent
method has led to a number of generalizations of old theorems,
improved proofs, and a host of beautiful new results. This
monograph will serve as a marvelous introduction to tight closure
for both researchers and graduate students in commutative algebra.
Table of contents
Preliminaries * Affine Algebras * Arbitrary Noetherian Algebras
over a Field * Further Properties of Tight Closure
Series: Mathematiques et Applications, Vol. 48
2005, XII, 335 p., Softcover
ISBN: 3-540-26211-3
About this textbook
Ce livre est une initiation aux approches modernes de l’optimisation
mathematique de formes. Il s’appuie sur les seules
connaissances de premiere annee de Master de mathematiques, mais
permet deja d’aborder les questions ouvertes dans ce domaine en
pleine effervescence. On y developpe la methodologie ainsi que
les outils d’analyse mathematique et de geometrie necessaires a
l’etude des variations de domaines. On y trouve une etude
systematique des questions geometriques associees a l’operateur
de Laplace, de la capacite classique, de la derivation par
rapport a une forme, ainsi qu’un FAQ sur les topologies
usuelles sur les domaines et sur les proprietes geometriques des
formes optimales avec ce qui se passe quand elles n’existent
pas, le tout avec une importante bibliographie.
Table of contents
Preface.- Introduction, Exemples.- Topologies sur les domaines de
RN .- Continuite par rapport au domaine.- Existence de formes
optimales.- Derivation par rapport au domaine.- Proprietes
geometriques de l'optimum.- Relaxation, homogeneisation.-
References.- Index des notes bibliographiques.- Index general.
Series: Lecture Notes in Mathematics Vol. 1869
Subseries: Ecole d'Ete Probabilit.Saint-Flour,
2005, VIII, 291 p., Softcover
ISBN: 3-540-26069-2
About this book
This volume contains two of the three lectures that were given at
the 33rd Probability Summer School in Saint-Flour (July 6-23,
2003). Amir Dembo’s course is devoted to recent studies of the
fractal nature of random sets, focusing on some fine properties
of the sample path of random walk and Brownian motion. In
particular, the cover time for Markov chains, the dimension of
discrete limsup random fractals, the multi-scale truncated second
moment and the Ciesielski-Taylor identities are explored.
Tadahisa Funaki’s course reviews recent developments of the
mathematical theory on stochastic interface models, mostly on the
so-called N f interface model. The results are formulated as
classical limit theorems in probability theory, and the text
serves with good applications of basic probability techniques.
Table of contents
A. Dembo: Favorite Point, Cover times and Fractals.- T. Funaki:
Stochastic Interface Models.
Series: Universitext
2005, Approx. 270 p., Softcover
ISBN: 3-540-23921-9
About this textbook
This book contains detailed lecture notes on four topics at the
forefront of current research in computational mathematics. Each
set of notes presents a self-contained guide to a current
research area and has an extensive bibliography. In addition,
most of the notes contain detailed proofs of the key results. The
notes start from a level suitable for first year graduate
students in applied mathematics, mathematical analysis or
numerical analysis, and proceed to current research topics. The
reader should therefore be able to gain quickly an insight into
the important results and techniques in each area without
recourse to the large research literature. Current (unsolved)
problems are also described and directions for future research
are given. This book is also suitable for professional
mathematicians who require a succint and accurate account of
recent research in areas parallel to their own, and graduates in
mathematical sciences.
Written for:
Researchers and graduate students
Keywords:
meshless methods
particle methods
smoothed particle hydrodynamics
wavelet-based multiresolution methods
Series: Universitext
2005, Approx. 400 p., Softcover
ISBN: 3-540-25753-5
About this textbook
The book is aimed at teachers and students as well as practising
experts in the financial area, in particular at actuaries in the
field of property-casualty insurance, life insurance, reinsurance
and insurance supervision. Persons working in the wider world of
finance will also find many relevant ideas and examples even
though credibility methods have not yet been widely applied here.
The book covers the subject of Credibility Theory extensively and
includes most aspects of this topic from the simplest case to the
most general dynamic model. Credibility is a lifeless topic if it
is not linked closely to practical applications. The book
therefore treats explicitly the tasks which the actuary
encounters in his daily work such as estimation of loss ratios,
claim frequencies and claim sizes.
This book deserves a place on the bookshelf of every actuary and
mathematician who works, teaches or does research in the area of
insurance and finance.
Table of contents
Introduction.- The Bayes Premium.- Credibility Estimators.- The
Buhlmann-Straub Model.- Treatment of Large Claims in Credibility.-
Hierarchical Credibility.- Multidimensional Credibility.-
Credibility in the Regression Model.- Evolutionary Credibility
Models and Recursive Calculation Methods (Kalman-Filter).-
Multidimensional Evolutionary Credibility Models and Recursive
Calculation Methods (Kalman-Filter).- Bibliography.- Index.
Series: Problem Books in Mathematics
2006, XII, 375 p., Hardcover
ISBN: 0-387-98850-5
About this book
This volume offers a compendium of exercises of varying degree of
difficulty in the theory of modules and rings. All exercises are
solved in full detail. Each section begins with an introduction
giving the general background and the theoretical basis for the
problems that follow.
Table of contents
Free Modules.-Projective and Injective Modules.-Flat Modules and
Homological Dimensions.-More Theory of Modules.-Rings of
Quotients.-More Rings of Quotients.-Frobenius and Quasi-Frobenius
Rings.-Matrix Rings, Categories of Modules, and Morita Theory.
Series: Universitext
2005, Approx. 300 p., Softcover
ISBN: 3-540-22347-9
The Gaussian Space of BM.- Quadratic Functionals of Brownian
Motion.- Ray Knight Theorems for Brownian Local Times.- On
Squared Bessel Processes.- On the Ciesielski-Taylor Identities.-
On the Winding Number of Planar BM.- Exponential Functionals of
Brownian Motion.- Some Asymptotic Laws for Multidimensional
Brownian Motion.- Some Extensions of Paul Levy's Arc Sine Law.-
Further Results about Perturbed Reflecting Brownian Motion. On
Principal Values of Brownian and Bessel Local Times.-
Probabilistic Representations of the Riemann Zeta Function.