2 Paperback books (ISBN-13: 9780521137386)
Size: 244 x 170 mm
Weight: 4.2 kg
Throughout his life Lewis Fry Richardson made many inspired contributions to various disciplines. Often his ideas were ahead of contemporary thinking, and preceded the technical means necessary for their practical implementation. He is best known for his wealth of important work on meteorology and his groundbreaking application of mathematics to the causes of war. But his field of interest was in no way limited to these and various aspects of psychology and mathematical approximation also benefited from his novel modes of thought. Richardson had a rare determination to trust his own ideas, even when they were not well received. These two volumes show that much of his thinking has long been underrated and that much of his work was ahead of its time.
The Collected Papers of Lewis Fry Richardson Volume One: Meteorology and Numerical Analysis; The Collected Papers of Lewis Fry Richardson Volume Two: Quantitative Psychology and Studies of Conflict.
Series: Encyclopedia of Mathematics and its Applications
Hardback (ISBN-13: 9780521195034)
This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the Hamilton-Jacobi-Bellman (HJB) equation with boundary conditions. Major mathematical prerequisites are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.
* Ideal for students and researchers who do not major in control theory
Part I. Stochastic Calculus and Optimal Control Theory: 1. Foundations of stochastic calculus; 2. Stochastic differential equations: weak formulation; 3. Dynamic programming; 4. Viscosity solutions of Hamilton-Jacobi-Bellman equations; 5. Classical solutions of Hamilton-Jacobi-Bellman equations; Part II. Applications to Mathematical Models in Economics: 6. Production planning and inventory; 7. Optimal consumption/investment models; 8. Optimal exploitation of renewable resources; 9. Optimal consumption models in economic growth; 10. Optimal pollution control with long-run average criteria; 11. Optimal stopping problems; 12. Investment and exit decisions; Part III. Appendices: A. Dini's theorem; B. The Stone-Weierstrass theorem; C. The Riesz representation theorem; D. Rademacher's theorem; E. Vitali's covering theorem; F. The area formula; G. The Brouwer fixed point theorem; H. The Ascoli-Arzela theorem.
Series: London Mathematical Society Lecture Note Series (No. 369)
Paperback (ISBN-13: 9780521734431)
Information propagation through peer-to-peer systems, online social systems,
wireless mobile ad hoc networks and other modern structures can be modelled
as an epidemic on a network of contacts. Understanding how epidemic processes
interact with network topology allows us to predict ultimate course, understand
phase transitions and develop strategies to control and optimise dissemination.
This book is a concise introduction for applied mathematicians and computer
scientists to basic models, analytical tools and mathematical and algorithmic
results. Mathematical tools introduced include coupling methods, Poisson
approximation (the Stein*Chen method), concentration inequalities (Chernoff
bounds and Azuma*Hoeffding inequality) and branching processes. The authors
examine the small-world phenomenon, preferential attachment, as well as
classical epidemics. Each chapter ends with pointers to the wider literature.
An ideal accompaniment for graduate courses, this book is also for researchers
(statistical physicists, biologists, social scientists) who need an efficient
guide to modern approaches to epidemic modelling on networks.
* Provides a clear and rigorous treatment using both probabilistic and
algorithmic approaches * Coverage includes well-known techniques and results
as well as more recent advances * Includes end-of-chapter guides to the
wider literature, ideal for researchers new to the field
Introduction; Part I. Shapeless Networks: 1. Galton-Watson branching processes;
2. Reed-Frost epidemics and Erd*s-Renyi random graphs; 3. Connectivity
and Poisson approximation; 4. Diameter of Erd*s-Renyi graphs; 5. From microscopic
to macroscopic dynamics; Part II. Structured Networks: 6. The small-world
phenomenon; 7. Power laws via preferential attachment; 8. Epidemics on
general graphs; 9. Viral marketing and optimised epidemics; References;
Index.
Series: Cambridge Studies in Advanced Mathematics (No. 121)
Hardback (ISBN-13: 9780521118170)
The representation theory of the symmetric groups is a classical topic
that, since the pioneering work of Frobenius, Schur and Young, has grown
into a huge body of theory, with many important connections to other areas
of mathematics and physics. This self-contained book provides a detailed
introduction to the subject, covering classical topics such as the Littlewood*Richardson
rule and the Schur*Weyl duality. Importantly the authors also present many
recent advances in the area, including Lasallefs character formulas, the
theory of partition algebras, and an exhaustive exposition of the approach
developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises
makes this an ideal textbook for graduate students. It will also serve
as a useful reference for more experienced researchers across a range of
areas, including algebra, computer science, statistical mechanics and theoretical
physics.
* Covers the most recent results and theories in a topic that has fruitful
relations with many areas of mathematics and physics * The first book to
contain a complete treatment of the Okounkov*Vershik theory * Serves as
a useful reference for researchers across a range of subjects, including
algebra, computer science and statistical mechanics
Preface; 1. Representation theory of finite groups; 2. The theory of Gelfand*Tsetlin bases; 3. The Okounkov*Vershik approach; 4. Symmetric functions; 5. Content evaluation and character theory; 6. The Littlewood*Richardson rule; 7. Finite dimensional *-algebras; 8. Schur*Weyl dualities and the partition algebra; Bibliography; Index.
History of Mathematics
Highways and Byways
Series: Spectrum
Hardback (ISBN-13: 9780883855621)
This is a novel, short, and eminently readable history of mathematics.
Many histories provide a chronological history of the entire subject, which
can sometimes make it difficult to follow the development of a particular
branch over time. Dahan-Delmmedico and Pfeiffer succeed splendidly in tracing
each branch from its beginnings forward. They also give an outstanding
account of how the Arabs not only preserved Greek mathematics, but extended
it in the 800 year period from 400*1200. The large number of informative
illustrations support the text and contribute to what is a great read.
* The birth and development of mathematical activity are placed in their
historical, cultural and economic context * Organized to present the development
of the different branches of mathematics * Contains many illustrations
that support the text
Translator's preface; 1. Landscapes; 2. A moment of rationality: Greece; 3. The constitution of classical algebra; 4. Figures, spaces, and geometries; 5. Limits: from the unconceived to the concept; 6. The concept of function and the development of analysis; 7. At the crossroads of algebra, analysis, and geometry: complex numbers; 8. New objects, new laws: the emergence of algebraic structures.