J. Michael DunnIndiana University,
and Gary Hardegree, A University of Massachusetts

Algebraic Methods in Philosophical Logic

Comprehensive text on algebraic logic Includes algebraic logic with attention to philosophy
Authors well known in field of algebraic logic Main theme involves representation theorems translating to completeness theorems Also identifies classes of algebras appropriate for the study of logics including gaggles, distributoids, partial gaggles and tonoids

320 pages, 234mm x 156mm
Series: Oxford Logic Guides

Hardback, 0-19-853192-3
Publication date: 21 June 2001

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

Readership: Graduate and Advanced Undergraduates of Logics in Mathematics, Philosophy, Computer Science and Linguistics.
Contents/contributors
1 Introduction
2 Universal Algebra
3 Order, Lattices and Boolean Algebras
4 Syntax
5 Semantics
6 Logic
7 Matrices and Atlases
8 Representation Theorems
9 Classical Propositional Logic
10 Modal Logic and Closure Algebras
11 Intuitionistic Logic
12 Gaggles: General Galois Logics
13 Representation and Duality
14 References
15 Index

Steven Terrence Buckland, University of St. Andrews, Scotland, David R. Anderson, Colorado Cooperative Fish and Wildlife Research Unit, Colorado, USA, Kenneth Paul Burnham, Colorado Cooperative Fish and Wildlife Research Unit, Colorado, USA, Jeffrey Lee Laake, National Maritime Mammal Laboratory, Seattle, USA, and others

Introduction to Distance Sampling
Estimating Abundance of Biological Populations

432 pages, 5 halftone, 75 line, 234mm x 156mm

Hardback, 0-19-850649-X
Paperback, 0-19-850927-8
Publication date: July 2001

Description

Offers a comprehensive introduction to distance sampling, a statistical method used by many biologists and conservationists to estimate animal abundance.

Readership: Graduate biologists with a quantitative background, who carry out population assessments of wildlife: mammalogists, ornithologists, and fisheries biologists. Advanced undergraduate statisticians with an interest in this topic.

Contents/contributors
1 Introductory concepts
2 Assumptions and modelling philosophy
3 Statistical theory
4 Line transects
5 Point transects
6 Related methods
7 Study design and field methods
8 Illustrative examples

Jurgen Moser

Stable and Random Motions in Dynamical Systems:
With Special Emphasis on Celestial Mechanics

With a new foreword by Philip J. Holmes

Paper | June 2001 |
200 pp. | 6 x 9

For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Ju"rgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entre'es to the fascinating worlds of order and chaos in dynamics.

Series:
Princeton Landmarks in Mathematics and Physics
Hardcover published in 1973

ISBN: 0-691-08910-8 Paper:

Huggett, S., University of Plymouth, UK
Jordan, D., University of Hull, UK

A Topological Aperitif

2001. IX, 166 pp. 128 figs. Softcover
1-85233-377-4

This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology.
After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.
There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.
"A Topological Aperitif provides a marvellous introduction to the subject, with many different tastes of ideas.Stephen Huggett and David Jordan have excellent credentials for explaining the beauty of this curiously austere but potentially enormously general form of geometry".
Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK

Contents: Foreword (written by Roger Penrose).- Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.- Appendix A: Continuity.- Appendix B: Knots.- Appendix C: History.- Appendix D: Solutions.- Notes.- Bibliography.- Index.

Brigo, D., Banca IMI, Milano, Italy
Mercurio, F., Banca IMI, Milano, Italy

Interest Rate Models - Theory and Practice

2001. Approx. 500 pp. Hardcover
3-540-41772-9

In implementing mathematical models for pricing interest rate derivatives one has to address a number of practical issues such as the choice of a satisfactory model, the calibration to market data, the implementation of efficient routines, and so on. This book aims both at explaining rigorously how models work in theory and at suggesting how to implement them for concrete pricing. This is an area that is rarely covered by books on mathematical finance. The book is meant both to help quantitative analysts and advanced traders price and hedge with a sound theoretical apparatus, and to encourage academics to develop a feeling for the practical problems in the interest rate market that can be solved with the use of relatively advanced tools of mathematics and stochastic calculus in particular. Advanced undergraduate students, graduate students and researchers should benefit from seeing how mathematics can be used in concrete financial problems.

Keywords: Interest rate models, Libor market models, mathematical finance, financial derivatives, pricing and hedging MSC ( 2000 ): 60H10 ; 60H35 ; 62P05 ; 65C05 ; 65C20 ; 90A09 JEL classification : G12 ; G13 ; E43

Contents: Part I: Models: Theory and Implementation. Definitions and Notation.- No-Arbitrage Pricing and Numeraire Change.- One-Factor Short-Rate Models.- Two-Factor Short-Rate Models.- The Heath-Jarrow-Morton (1992) Framework.- The Libor and Swap Market Models (LFM and LSM).- Cases of Calibration of the Libor Market Model.- Monte Carlo Tests for LFM Analytical Approximations.- Other Interest-Rate Models.
Part II:Pricing Derivatives in Practice . Pricing Derivatives on a Single Interest Rate Curve.- Pricing Derivatives on Two Interest-Rate Curves.- Pricing Equity Derivatives Under Stochastic Rates.
Part III: Appendices.

Series: Springer Finance.