Edited by Ian Sutherland

The Collected Papers of Lewis Fry Richardson Set

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.

Contents

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.

Hiroaki Morimoto / Ehime University, Japan

Stochastic Control and Mathematical Modeling
Applications in Economics

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

Contents

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.

Moez Draief / Imperial College of Science, Technology and Medicine, London
Laurent Massoulie

Epidemics and Rumours in Complex Networks

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

Contents

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.


Tullio Ceccherini-Silberstein / Universita degli Studi del Sannio
Fabio Scarabotti / Universita degli Studi di Roma 'La Sapienza', Italy
Filippo Tolli / Universita degli Studi Roma Tre, Italy

Representation Theory of the Symmetric Groups
The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras

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 Lasallefs 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

Contents

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.

Amy Dahan-Dalmedico / Centre National de la Recherche Scientifique (CNRS), Paris
Jeanne Peiffer / Centre National de la Recherche Scientifique (CNRS), Paris

Translated by Sanford Segal

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

Contents

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.