The topic of credibility theory has been for many years -- and still is -- one of our major interests. This interest has led us not only to many publications, but also has been the motivation for teaching many courses on this topic over more than 20 years. These courses have undergone considerable changes over time. What we present here, "A Course in Credibility Theory and its Applications," is the ?nal product of this evolution. Credibility theory can be seen as the basic paradigm underlying the pricing of insurance products. It resides on the two fundamental concepts "individual risk" and...
The topic of credibility theory has been for many years -- and still is -- one of our major interests. This interest has led us not only to many publi...
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the - proach to analysis presented here from what has by its protagonists been called "Modern Analysis." "Modern Analysis" as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis...
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pos...
The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with deep geometric problems and conjectures. The relevant questions studied in this book for general groups are motivated by specific examples. A variety of techniques is employed from commutative algebra, homological algebra and functional analysis.
The book can serve as an introduction to this lively research area. The pace is suitable for independent study and the level of the presentation not very demanding. The exercises at the end of each...
The theory of idempotent matrices with entries in complex group algebras has recently experienced a revival, in view of its close relationship with...
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction - for an audience knowing basic functional analysis and measure theory, but not necessarily probability theory - to analysis in a separable Hilbert space of infinite dimension. Moreover, some details as well as some new material has been added on dynamical systems with dissipative non-linearities and asymptotic behavior for gradient systems.
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction -...
This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, "what everytheoreticalcomputerscientistshouldknowaboutlinearprogramming." The book is relatively concise, in order to allow the reader to focus on the basic ideas. For a number of topics commonly appearing in thicker books on the subject, we were seriously tempted to add them to the main text, but we decided to present them only very brie?y in a separate glossary. At the same time, we aim at covering the main results with complete proofs and in...
This is an introductory textbook of linear programming, written mainly for students of computer science and mathematics. Our guiding phrase is, "what ...
Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x, y), (0.1) y? = Q(x, y), r 2 where P and Q are C functions de?ned on an open subset U of R, with ? r=1,2, ..., ?, ?.AsusualC standsforanalyticity.Weputspecialemphasis onto polynomial di?erential systems, i.e., on systems (0.1) where P and Q are polynomials. Instead of talking about the di?erential system (0.1), we frequently talk about its associated vector ?eld ? ? X = P(x, y) +Q(x, y) (0.2) ?x ?y 2 on U? R . This will enable a coordinate-free approach, which is typical in...
Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x, y), (0.1) y? = Q(x, y), r 2 where P ...
Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions.
This new edition contains computational exercises in the form of case studies which help...
Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in ...
A second edition of a book is a success and an obligation at the same time. We are satis ed that a number of university courses have been orga> nized on the basis of the rst volume of Comprehensive Mathematics for Computer Scientists. The instructors recognized that the self>contained presentation of a broad specturm of mathematical core topics is a rm point of departure for a sustainable formal education in computer sci> ence. We feel obliged to meet the valuable feedback of the responsible in> structors of such courses, in particular of Joel Young (Computer Science Department, Brown...
A second edition of a book is a success and an obligation at the same time. We are satis ed that a number of university courses have been orga> nized ...
Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a...
Choice Outstanding Title (January 2006)
Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates eve...
I wish that algebra would be the Cinderella ofour story. In the math- ematics program in schools, geometry has often been the favorite daugh- ter. The amount of geometric knowledge studied in schools is approx- imately equal to the level achieved in ancient Greece and summarized by Euclid in his Elements (third century B. C. ). For a long time, geom- etry was taught according to Euclid; simplified variants have recently appeared. In spite of all the changes introduced in geometry cours- es, geometry retains the influence of Euclid and the inclination of the grandiose scientific revolution...
I wish that algebra would be the Cinderella ofour story. In the math- ematics program in schools, geometry has often been the favorite daugh- ter. The...
